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Некоторые свойства многочленов и их использование в задачах связи (курсовая)

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НЕКОТОРЫЕ СВОЙСТВА МНОГОЧЛЕНОВ И ИХ ИСПОЛЬЗОВАНИЕ В ЗАДАЧАХ СВЯЗИ

Лисицына Е.С.,

Фауре Э.В.,

Швыдкий В.В., к.т.н., доцент,

Щерба А.И. , к.ф-м.н., доцент

Черкасский государственный технологический университет

Вестник ЧГТУ,№4,2006, стр134-140

Постановка проблемы

Создание эффективных систем передачи данных, используемых для передачи
основных информационных потоков, обеспечивающих жизнедеятельность
современного общества (речь, изображение, данные ЭВМ), базируется на
использовании современной математической базы и, в частности, на теории
конечных полей.

Теория конечных полей нашла широкое применение при решении задач
помехоустойчивого кодирования, шифрования, передачи данных сигналами с
большой базой (шумоподобных сигналов – ШПС) [1,2,3,4] и т.п.

В этих системах информация передается блоками (кадрами, пакетами), в
связи с чем каждый блок может быть представлен многочленом (вектором)
фиксированной размерности вида:

picscalex100010009000003130300000200a70000000000050000000201010000000500
00000102ffffff00050000002e0119000000050000000b0200000000050000000c026004
40091300000026060f001c00ffffffff00004e0010000000c0ffffffafffffff00090000
0f0400000b00000026060f000c004d617468547970650000f00005000000090200000002
050000001402ec03a4051c000000fb0222ff000000000000900100000000000200105469
6d6573204e657720526f6d616e00d89ff377e19ff3772020f577a30a66de040000002d01
000009000000320a00000000010000003079bc0105000000140280023c011c000000fb02
80fe0000000000009001000000000002001054696d6573204e657720526f6d616e00d89f
f377e19ff3772020f577a30a66de040000002d01010004000000f00100000a000000320a
0000000002000000282950010003050000001402fa0022051c000000fb0222ff00000000
00009001010000000002001054696d6573204e657720526f6d616e00d89ff377e19ff377
2020f577a30a66de040000002d01000004000000f001010009000000320a000000000100
00006e29bc01050000001402d40197081c000000fb0222ff000000000000900101000000
0002001054696d6573204e657720526f6d616e00d89ff377e19ff3772020f577a30a66de
040000002d01010004000000f001000009000000320a00000000010000006a29bc010500
00001402e30243071c000000fb0222ff0000000000009001010000000002001054696d65
73204e657720526f6d616e00d89ff377e19ff3772020f577a30a66de040000002d010000
04000000f001010009000000320a00000000010000006a29bc01050000001402ec03cd04
1c000000fb0222ff0000000000009001010000000002001054696d6573204e657720526f
6d616e00d89ff377e19ff3772020f577a30a66de040000002d01010004000000f0010000
09000000320a00000000010000006a29bc01050000001402800258001c000000fb0280fe
0000000000009001010000cc0002001054696d6573204e657720526f6d616e00d89ff377
e19ff3772020f577a30a66de040000002d01000004000000f00101000d000000320a0000
000004000000c07861788001830456010003050000001402ec0320051c000000fb0222ff
0000000000009001000000010002001053796d626f6c00005f0a0aa364df1200d89ff377
e19ff3772020f577a30a66de040000002d01010004000000f001000009000000320a0000
0000010000003d29bc01050000001402800264031c000000fb0280fe0000000000009001
000000010002001053796d626f6c0000380b0af564df1200d89ff377e19ff3772020f577
a30a66de040000002d01000004000000f001010009000000320a00000000010000003d29
0003050000001402d8028d041c000000fb02c0fd00000000000090010000000100020010
53796d626f6c00005f0a0aa468df1200d89ff377e19ff3772020f577a30a66de04000000
2d01010004000000f001000009000000320a0000000001000000e5298004a70000002606
0f0044014d6174685479706555553801050100050244534d543500001357696e416c6c42
61736963436f6465506167657300110554696d6573204e657720526f6d616e0011035379
6d626f6c001105436f7572696572204e65770011044d5420457874726100120008212f45
8f442f4150f4100f475f4150f21f1e4100f4150f4100f445f425f48f425f4100f4100f43
5f4100f48f45f42a5f48f48f4100f4100f40f48f417f48f4100f412a5f445f45f45f45f4
5f410f0c01000100010202020200020001010100030001000400000a0100020083100402
00822800020083780002008229000204863d003d03001070000100020083610003001b00
000b01000200836a00000101000a020083780003001c00000b010101000200836a000000
0001000200836a000204863d003d020088300000010462010200836e00000d0204861122
e50000000b00000026060f000c00ffffffff01000000000000001c000000fb0210000700
00000000bc02000000cc0102022253797374656d00dea30a66de00000a0021008a010000
000000000000b4e91200040000002d01000004000000f0010100030000000000. (1)

Отметим, что старший коэффициент аn многочлена А(х) может равняться
нулю. Записью Аn(х)=А(х) подчеркивается тот факт, что рассматриваются
многочлены из линейного пространства размерности не выше “n+1”.

Инверсный многочлен обозначим как:
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 (2)
или, что тоже самое,
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,

где Еn(х) – единичный многочлен размерности n, такой, что все элементы
вектора равны единице.

Обозначим взаимный (двойственный) многочлен, у которого обратный порядок
считывания символов, как:
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. (3)

Под симметричным многочленом понимаем такой, что
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.

Очевидна связь взаимных многочленов между собой, однако вопросы
взаимосвязи продуктов их переработки в кодирующих, шифрующих и других
связных устройствах до настоящего времени мало изучены.

1. Анализ источников и публикаций по взаимным и инверсным многочленам и
их применению в задачах связи

В [2] указано, что корни взаимного многочлена обратным корням исходного
прямого многочлена, а многочлен взаимный к неприводимому – неприводим. В
работе [5] показано, что условием самосинхронизации префиксных кодов
является непрефиксность взаимного кода. Этими известными фактами
исчерпывается применяемость свойств взаимных многочленов в решении задач
связи. Очевидно, что дополнительные исследования свойств и связей прямых
инверсных и взаимных многочленов расширит круг решаемых задач.

В данной работе устанавливаются новые свойства взаимных и инверсных
многочленов, определяется возможность применения вновь установленных
свойств для решения задач связи.

2. Выделение нерешенных ранее частей общей проблемы

К числу нерешенных задач современной техники передачи данных, связанных
со свойствами многочленов, можно отнести следующие.

1. Как связаны обнаруживающие свойства циклического кода со структурой
кодового полинома и его весом?

2. Как связаны между собой обнаруживающие свойства прямого и взаимного
кодового полинома. Этот вопрос может быть сформулирован проще – какой
код лучше: по прямому или по взаимному многочлену, и чем они отличаются?

3. Общепринятой схемой построения генераторов М-последовательностей и
кодеров циклических кодов являются схемы, основанные на использовании
регистров сдвига с обратными связями. Существуют ли иные схемы
построения генераторов М-последовательностей и кодеров циклических
кодов? Чем они отличаются от регистровых?

4. Сколько разных М-последовательностей в пространстве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 и как они связаны между
собой?

5. Сколько разных проверочных полиномов степени “n” может быть
использовано?

3. Постановка задачи

Целью настоящей работы является выявление новых свойств взаимных и
инверсных многочленов и их применение для решения задач связи, таких как
помехоустойчивое кодирование с кодами Боуза-Чоудхури-Хоквингема (БЧХ
кодами), использование шумоподобных сигналов, а также задач
синхронизации с шумоподобными синхросигналами.

5. Решение задачи

Новые свойства многочленов

Рассмотрим дополнительно свойства взаимных многочленов, для чего
сформулируем несколько теорем.

Теорема 1. Взаимный многочлен произведения вектора на скаляр равен
произведению взаимного многочлена сомножителя на этот скаляр, т.е.
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Доказательство:

Если
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,

то
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,

что и требовалось доказать.

Теорема 2. Сдвиг вектора не изменяет взаимный многочлен, т.е.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, а изменяет только размерность
пространства до значения n+k.

Доказательство:

Пусть
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Или
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Тогда
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,

что и требовалось доказать.

Следствие.

Если мощность пространства увеличивается в 2m раз, а вектор сдвигается
на k разрядов, то взаимный к нему многочлен определяется как A^(x)xm-k.

Теорема 3. Взаимный многочлен суммы многочленов одной и той же степени
равен сумме взаимных многочленов, т.е.
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.

Доказательство

Пусть
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илиpicscalex100010009000003f90100000200ac0000000000050000000201010000000
50000000102ffffff00050000002e0119000000050000000b0200000000050000000c024
002c00d1300000026060f001c00ffffffff00004e0010000000c0ffffffa6ffffff800d0
000e60100000b00000026060f000c004d617468547970650000600005000000090200000
0020500000014028001da011c000000fb0280fe000000000000900100000000000200105
4696d6573204e657720526f6d616e001643c7771f43c77720c0c97700003000040000002
d01000010000000320a00000000060000002829282928295001b00350018603500100030
50000001402e30130011c000000fb0222ff0000000000009001010000000002001054696
d6573204e657720526f6d616e001643c7771f43c77720c0c97700003000040000002d010
10004000000f00100000c000000320a00000000030000006e6e6e7d0005d604bc0105000
000140280012e001c000000fb0280fe0000000000009001010000000002001054696d657
3204e657720526f6d616e001643c7771f43c77720c0c97700003000040000002d0100000
4000000f001010010000000320a00000000060000004378417842784802ee021202b2022
402000305000000140280010e041c000000fb0280fe00000000000090010000000100020
01053796d626f6c00774000000074060aa81643c7771f43c77720c0c9770000300004000
0002d01010004000000f00100000a000000320a00000000020000003d2be8040003ac000
00026060f004e014d6174685479706555554201050100050244534d543500011357696e4
16c6c4261736963436f6465506167657300110554696d6573204e657720526f6d616e001
10353796d626f6c001105436f7572696572204e65770011044d542045787472610012000
8212f458f442f4150f4100f475f4150f21f1e4100f4150f4100f445f425f48f425f4100f
4100f435f4100f48f45f42a5f48f48f4100f4100f40f48f417f48f4100f412a5f445f45f
45f45f45f410f0c01000100010202020200020001010100030001000400000a010002008
3430003001b00000b01000200836e00000101000a0200822800020083780002008229000
204863d003d020083410003001b00000b01000200836e00000101000a020082280002008
3780002008229000204862b002b020083420003001b00000b01000200836e00000101000
a02008228000200837800020082290000000b00000026060f000c00ffffffff010000000
00000001c000000fb021000070000000000bc02000000cc0102022253797374656d00000
0000a0021008a01000000000000000008e912002942c777040000002d01000004000000f
0010100030000000000

Обозначим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 взаимный многочлен к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,тогда
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что и требовалось доказать.

Теорема 4. Взаимный многочлен произведения многочленов одной и той же
степени равен произведению взаимных многочленов, т.е.
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.

Доказательство

Пусть
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 или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.

Тогда
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что и требовалось доказать.

Следствие.

Если
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,
или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,

то
picscalex1000100090000031a0200000200c40000000000050000000201010000000500
00000102ffffff00050000002e0119000000050000000b0200000000050000000c024002
80121300000026060f001c00ffffffff00004e0010000000c0ffffffb5ffffff40120000
f50100000b00000026060f000c004d617468547970650000500005000000090200000002
050000001402a001fb011c000000fb0280fe000000000000900100000000000200105469
6d6573204e657720526f6d616e001643c7771f43c77720c0c97700003000040000002d01
000013000000320a000000000800000028292829282928295001d7035001170350019b03
50010003050000001402a00158001c000000fb0280fe0000000000009001010000000002
001054696d6573204e657720526f6d616e001643c7771f43c77720c0c977000030000400
00002d01010004000000f001000013000000320a00000000080000004178517847785278
3f02ac027b02e60181029a0251020003050000001402f40045011c000000fb0222ff0000
000000009001000000010002001053796d626f6c007740000000f7040a2b1643c7771f43
c77720c0c97700003000040000002d01000004000000f00101000d000000320a00000000
04000000d9d9d9d927056704eb04bc01050000001402a00123041c000000fb0280fe0000
000000009001000000010002001053796d626f6c00774000000002050aa71643c7771f43
c77720c0c97700003000040000002d01010004000000f00100000c000000320a00000000
030000003dd72b2bfd0479040003c400000026060f007e014d6174685479706555557201
050100050244534d543500011357696e416c6c4261736963436f64655061676573001105
54696d6573204e657720526f6d616e00110353796d626f6c001105436f7572696572204e
65770011044d5420457874726100120008212f458f442f4150f4100f475f4150f21f1e41
50f4150f4100f445f425f48f425f4100f4100f435f4100f48f45f42a5f48f48f4100f410
0f40f48f417f48f4100f412a5f445f45f45f45f45f410f0c010001000102020202000200
01010100030001000400000a0100020083410003001c00000b010101000204862722d900
000a0200822800020083780002008229000204863d003d020083510003001c00000b0101
01000204862722d900000a020082280002008378000200822900020486c522d702008347
0003001c00000b010101000204862722d900000a02008228000200837800020082290002
04862b002b020083520003001c00000b010101000204862722d900000a02008228000200
837800020082290000000b00000026060f000c00ffffffff01000000000000001c000000
fb021000070000000000bc02000000cc0102022253797374656d000000000a0021008a01
000000000000000008e912002942c777040000002d01000004000000f001010003000000
0000 или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.

Таким образом, вычет взаимного многочлена по взаимному модулю есть
многочлен взаимный к вычету прямого многочлена по прямому модулю. Это
значит, что кодирование по прямому или взаимному модулю совершенно
равноценны и однозначно связаны (взаимно друг в друга пересчитываются).

Теорема 5. Взаимный взаимного многочлена есть прямой многочлен, т.е.
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Доказательство

Если
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, то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что и требовалось доказать.

Следствие 1. Сумма (произведение) прямого и взаимного к нему многочленов
есть симметричный многочлен, т.е. если

1.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, то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;

2.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, то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.

Доказательство:

1.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,

что и требовалось доказать.

2.
picscalex910100090000031f03000002002601000000000500000002010100000005000
0000102ffffff00050000002e0119000000050000000b0200000000050000000c020004c
01a1300000026060f001c00ffffffff00004e0010000000c0ffffffacffffff801a0000a
c0300000b00000026060f000c004d617468547970650000d000050000000902000000020
50000001402a90107021c000000fb0280fe0000000000009001000000000002001054696
d6573204e657720526f6d616e00d89ff377e19ff3772020f577c8086636040000002d010
0001c000000320a000000000e00000028292828292829292829282829295001fe018c015
001ff0250017e008404500138014b0250017e000003050000001402580327031c000000f
b0280fe0000000000009001000000000002001054696d6573204e657720526f6d616e00d
89ff377e19ff3772020f577c8086636040000002d01010004000000f0010000100000003
20a0000000006000000282928292829500140025001120350010003050000001402a9012
e001c000000fb0280fe0000000000009001010000cc0002001054696d6573204e6577205
26f6d616e00d89ff377e19ff3772020f577c8086636040000002d01000004000000f0010
10016000000320a000000000a000000d1784178c078c078c07875025a03800110023f021
3043f0294023f020003050000001402580384011c000000fb0280fe00000000000090010
10000cc0002001054696d6573204e657720526f6d616e00d89ff377e19ff3772020f577c
8086636040000002d01010004000000f001000010000000320a0000000006000000c078c
078d1f53f0210028001ac02b6010003050000001402fd0051011c000000fb0222ff00000
00000009001000000010002001053796d626f6c00003f090aae64df1200d89ff377e19ff
3772020f577c8086636040000002d01000004000000f001010010000000320a000000000
6000000d9d9d9d9d9d9290911034103d3041103bc01050000001402ac027102090000003
20a0000000001000000d979bc01050000001402a9012f041c000000fb0280fe000000000
0009001000000010002001053796d626f6c00007d090acc64df1200d89ff377e19ff3772
020f577c8086636040000002d01010004000000f00100000f000000320a0000000005000
0003dd73dd73d00b004b605eb043a06000305000000140258033a000c000000320a00000
000030000003dd73dd7eb04ba0300032601000026060f0041024d6174685479706555553
502050100050244534d543500011357696e416c6c4261736963436f64655061676573001
10554696d6573204e657720526f6d616e00110353796d626f6c001105436f75726965722
04e65770011044d5420457874726100120008212f458f442f4150f4100f475f4150f21f1
e4100f4150f4100f445f425f48f425f4100f4100f435f4100f48f45f42a5f48f48f4100f
4100f40f48f417f48f4100f412a5f445f45f45f45f45f410f0c010001000102020202000
20001010100030001000400000a040001010100020083210403001c00000b01010100020
4862722d900000a0200822800020083780002008229000204863d003d020082280002008
34100020082280002008378000200822900020486c522d7020083100403001c00000b010
101000204862722d900000a020082280002008378000200822900020082290003001c000
00b010101000204862722d900000a0204863d003d020083100403001c00000b010101000
204862722d900000a020082280002008378000200822900020486c522d70200822800020
083100403001c00000b010101000204862722d900000a020082280002008378000200822
900020082290003001c00000b010101000204862722d900000a0204863d003d000100020
4863d003d020083100403001c00000b010101000204862722d900000a020082280002008
378000200822900020486c522d7020083100402008228000200837800020082290002048
63d003d0200832104020082280002008345040200822900000000000b00000026060f000
c00ffffffff01000000000000001c000000fb021000070000000000bc02000000cc01020
22253797374656d0036c808663600000a0021008a010000000000000000b4e9120004000
0002d01000004000000f0010100030000000000,

что и требовалось доказать.

Следствие 2. Сумма, произведение и частное симметричных многочленов есть
симметричный многочлен, т.е. если
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и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, то

1.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;

2.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;

3.
picscalex100010009000003dd0200000400ab0000000000050000000201010000000500
00000102ffffff00050000002e0119000000050000000b0200000000050000000c022004
000d1300000026060f001c00ffffffff00004e0010000000c0ffffffb8ffffffc00c0000
d80300000b00000026060f000c004d617468547970650000e00008000000fa0200001300
000000000002040000002d0100000500000014020002a20405000000130200029c070500
00000902000000020500000014026e01bc051c000000fb0280fe00000000000090010000
00000002001054696d6573204e657720526f6d616e001643c7771f43c77720c0c9770000
3000040000002d0101000a000000320a0000000002000000282950010003050000001402
600248011c000000fb0280fe0000000000009001000000000002001054696d6573204e65
7720526f6d616e001643c7771f43c77720c0c97700003000040000002d01020004000000
f00101000d000000320a0000000004000000282928295001630850010003050000001402
8c03bc051c000000fb0280fe0000000000009001000000000002001054696d6573204e65
7720526f6d616e001643c7771f43c77720c0c97700003000040000002d01010004000000
f00102000a000000320a00000000020000002829500100030500000014026e01d8041c00
0000fb0280fe0000000000009001010000000002001054696d6573204e657720526f6d61
6e001643c7771f43c77720c0c97700003000040000002d01020004000000f00101000a00
0000320a000000000200000041788001000305000000140260022e001c000000fb0280fe
0000000000009001010000000002001054696d6573204e657720526f6d616e001643c777
1f43c77720c0c97700003000040000002d01010004000000f00102000d000000320a0000
00000400000043784378b6013e07750200030500000014028c03c6041c000000fb0280fe
0000000000009001010000000002001054696d6573204e657720526f6d616e001643c777
1f43c77720c0c97700003000040000002d01020004000000f00101000a000000320a0000
000002000000427892010003050000001402b401450a1c000000fb0222ff000000000000
9001000000010002001053796d626f6c007740000000ac050adf1643c7771f43c77720c0
c97700003000040000002d01010004000000f001020009000000320a0000000001000000
d978bc01050000001402600270031c000000fb0280fe0000000000009001000000010002
001053796d626f6c007740000000af050aac1643c7771f43c77720c0c977000030000400
00002d01020004000000f00101000a000000320a00000000020000003d3d92040003ab00
000026060f004b014d6174685479706555553f01050100050244534d543500001357696e
416c6c4261736963436f6465506167657300110554696d6573204e657720526f6d616e00
110353796d626f6c001105436f7572696572204e65770011044d54204578747261001200
08212f458f442f4150f4100f475f4150f21f1e4100f4150f4100f445f425f48f425f4100
f4100f435f4100f48f45f42a5f48f48f4100f4100f40f48f417f48f4100f412a5f445f45
f45f45f45f410f0c01000100010202020200020001010100030001000400000a01000200
8343000200822800020083780002008229000204863d003d03000b000001000200834100
020082280002008378000200822900000100020083420002008228000200837800020082
290000000204863d003d020083430003001c00000b010101000204862722d900000a0200
822800020083780002008229000000000b00000026060f000c00ffffffff010000000000
000008000000fa0200000000000000000000040000002d0101001c000000fb0210000700
00000000bc02000000cc0102022253797374656d000000000a0021008a0100000000ffff
ffff08e912002942c777040000002d01030004000000f0010200030000000000.

Доказательство:
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,

что и требовалось доказать;
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,

что и требовалось доказать.

3.
Пустьpicscalex1000100090000038d02000004009400000000000500000002010100000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, т.е.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.

Тогда
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Отсюда
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,

что и требовалось доказать.

5.2. Применение новых свойств многочленов к задачам связи

Применение новых свойств многочленов к задачам помехоустойчивого
кодирования

Типовые (стандартные) процедуры помехоустойчивого кодирования базируются
на вычислении вычета (остатка или контрольной суммы) в регистре сдвига с
обратными связями [7]:
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, (4)

где G(x) – неприводимый многочлен, образующий код, а А(х) – вектор
информационной части блока.

Полученный остаток дополняет блок и передается по каналу связи на
приемную станцию. По принятому блоку
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, (5)

где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– вектор ошибки, вычисляется
синдром ошибки:
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.
(6)

Вычисление контрольной суммы в кодере и синдрома ошибки в декодере
выполняется одинаковыми регистрами сдвига кодера и декодера. Стандартный
кодер систем передачи данных для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 оговорен рекомендацией V-41 МККТТ [7].

Логичным является следующий вопрос:

– имеют ли одинаковую обнаруживающую способность полиномы одной и той же
степени (включая взаимные)?

Прежде всего отметим, что контрольная сумма есть вычет информационного
многочлена по модулю образующего полинома, т.е.:

picscalex68010009000003eb05000004008201000000000500000002010100000005000
0000102ffffff00050000002e0119000000050000000b0200000000050000000c0200054
0291300000026060f001c00ffffffff00004e0010000000c0ffffffbaffffff00290000b
a0400000b00000026060f000c004d617468547970650000200108000000fa02000013000
00000000002040000002d0100000500000014024600f8040500000013027a04f80405000
00014024600bf090500000013027a04bf090500000014024d01790d05000000130273037
90d0500000014024d01b1250500000013027303b12505000000090200000002050000001
4023a0139061c000000fb0222ff0000000000009001000000000002001054696d6573204
e657720526f6d616e00d89ff377e19ff3772020f577e7086688040000002d01010009000
000320a00000000010000003179bc01050000001402140251121c000000fb0222ff00000
00000009001000000000002001054696d6573204e657720526f6d616e00d89ff377e19ff
3772020f577e7086688040000002d01020004000000f00101000d000000320a000000000
400000031323130c9062507bb04bc0105000000140223030c011c000000fb0222ff00000
00000009001000000000002001054696d6573204e657720526f6d616e00d89ff377e19ff
3772020f577e7086688040000002d01010004000000f00102000f000000320a000000000
5000000313132313000470ea00652089504bc0105000000140284038b261c000000fb022
2ff0000000000009001000000000002001054696d6573204e657720526f6d616e00d89ff
377e19ff3772020f577e7086688040000002d01020004000000f00101000a000000320a0
0000000020000002829da00bc010500000014022c043b061c000000fb0222ff000000000
0009001000000000002001054696d6573204e657720526f6d616e00d89ff377e19ff3772
020f577e7086688040000002d01010004000000f001020009000000320a0000000001000
0003029bc010500000014028b04990a1c000000fb0222ff0000000000009001000000000
002001054696d6573204e657720526f6d616e00d89ff377e19ff3772020f577e70866880
40000002d01020004000000f00101000a000000320a00000000020000002829da00bc010
50000001402c00295011c000000fb0280fe0000000000009001000000000002001054696
d6573204e657720526f6d616e00d89ff377e19ff3772020f577e7086688040000002d010
10004000000f00102000a000000320a00000000020000002829500100030500000014023
a014d051c000000fb0222ff0000000000009001010000000002001054696d6573204e657
720526f6d616e00d89ff377e19ff3772020f577e7086688040000002d01020004000000f
001010009000000320a00000000010000006e29bc0105000000140214022e091c000000f
b0222ff0000000000009001010000000002001054696d6573204e657720526f6d616e00d
89ff377e19ff3772020f577e7086688040000002d01010004000000f00102000c0000003
20a00000000030000006a6e6e2c3708b106bc010500000014022303da071c000000fb022
2ff0000000000009001010000000002001054696d6573204e657720526f6d616e00d89ff
377e19ff3772020f577e7086688040000002d01020004000000f00101000c000000320a0
0000000030000006a6e6e818d068806bc010500000014028403d4251c000000fb0222ff0
000000000009001010000000002001054696d6573204e657720526f6d616e00d89ff377e
19ff3772020f577e7086688040000002d01010004000000f00102000a000000320a00000
0000200000047781c01bc010500000014022c0464051c000000fb0222ff0000000000009
001010000000002001054696d6573204e657720526f6d616e00d89ff377e19ff3772020f
577e7086688040000002d01020004000000f001010009000000320a00000000010000006
a78bc010500000014028b04e2091c000000fb0222ff00000000000090010100000000020
01054696d6573204e657720526f6d616e00d89ff377e19ff3772020f577e708668804000
0002d01010004000000f00102000a000000320a000000000200000047781c01bc0105000
0001402c00246001c000000fb0280fe0000000000009001010000000002001054696d657
3204e657720526f6d616e00d89ff377e19ff3772020f577e7086688040000002d0102000
4000000f001010019000000320a000000000c000000527861786178617861786178eb01c
104560160050003880329034506fc018402220200030500000014023a01ca051c000000f
b0222ff0000000000009001000000010002001053796d626f6c00005f080a8464df1200d
89ff377e19ff3772020f577e7086688040000002d01010004000000f0010200090000003
20a00000000010000002d78bc010500000014021402e2110a000000320a0000000002000
0002d2db106bc010500000014022303e40e0a000000320a00000000020000002d2d8806b
c010500000014022c04b70509000000320a00000000010000003d2dbc01050000001402c
002bd031c000000fb0280fe0000000000009001000000010002001053796d626f6c0000a
8080a3064df1200d89ff377e19ff3772020f577e7086688040000002d01020004000000f
00101001c000000320a000000000e0000003d3dd72bd72bd7d7d72bd72bd73d8108c8031
003a103390308017e007e00900074020c029a0292040003050000001402180324051c000
000fb02c0fd0000000000009001000000010002001053796d626f6c00005f080a8568df1
200d89ff377e19ff3772020f577e7086688040000002d01010004000000f001020009000
000320a0000000001000000e52d80048201000026060f00fa024d617468547970655555e
e02050100050244534d543500001357696e416c6c4261736963436f64655061676573001
10554696d6573204e657720526f6d616e00110353796d626f6c001105436f75726965722
04e65770011044d5420457874726100120008212f458f442f4150f4100f475f4150f21f1
e4150f4150f4100f445f425f48f425f4100f4100f435f4100f48f45f42a5f48f48f4100f
4100f40f48f417f48f4100f412a5f445f45f45f45f45f410f0c010001000102020202000
20001010100030001000400000a0100020083520003001b00000b0100020088310000010
1000a0200822800020083780002008229000204863d003d0300040300010003001070000
100020083610003001b00000b01000200836a00000101000a020083780003001c00000b0
10101000200836a0000000001000200836a000204863d003d02008830000001000200836
e0002048612222d0200883100000d0204861122e500000a02009607ec02009608ec00030
01b00000b01000200834700020082280002008378000200822900000101000a0204863d0
03d03000403000100020083610003001b00000b01000200836e0002048612222d0200883
100000101000a020486c522d7020083780003001c00000b010101000200836e000204861
2222d020088310000000a0204862b002b020083610003001b00000b01000200836e00020
48612222d0200883200000101000a020486c522d7020083780003001c00000b010101000
200836e0002048612222d020088320000000a0204862b002b020486c522d7020486c522d
7020486c522d70204862b002b020083610003001b00000b01000200883100000101000a0
20486c522d7020083780003001c00000b01010100020088310000000a0204862b002b020
083610003001b00000b01000200883000000101000a020486c522d7020083780003001c0
0000b0101010002008830000000000a02009607ec02009608ec0003001b00000b0100020
0834700020082280002008378000200822900000101000a0204863d003d00000b0000002
6060f000c00ffffffff010000000000000008000000fa020000000000000000000004000
0002d0102001c000000fb021000070000000000bc02000000cc0102022253797374656d0
000e708668800000a0021008a0100000000ffffffffb4e91200040000002d01030004000
000f0010100030000000000

picscalex72010009000003d30600000400a101000000000500000002010100000005000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(7)

где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 – элемент кольца вычетов по модулю
G(x).

Вычислим вычет инверсного к информационному многочлена:
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 (8)

Отметим, что для циклического кода Боуза-Чоудхури-Хоквингема (БЧХ кода)
длину информационной части блока берут из условия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, где k – степень
кодового полинома, а L – длина блока. Это значит, что длина
информационной части блока не должна превышать длины периода кольца
вычетов.

Всегда можно выбрать L=T, а любой двучлен вида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 представить в виде
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.

Учтем, что:

– неприводимый многочлен делит без остатка
двучленpicscalex100010009000003b901000002007e000000000005000000020101000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, что обозначает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;

– многочлены
picscalex100010009000003500100000200770000000000050000000201010000000500
00000102ffffff00050000002e0119000000050000000b0200000000050000000c020002
60031300000026060f001c00ffffffff00004e0010000000c0ffffffc6ffffff20030000
c60100000b00000026060f000c004d617468547970650000500005000000090200000002
050000001402600154011c000000fb0280fe000000000000900100000000000200105469
6d6573204e657720526f6d616e001643c7771f43c77720c0c97700003000040000002d01
00000a000000320a000000000200000028295001000305000000140260012e001c000000
fb0280fe0000000000009001010000000002001054696d6573204e657720526f6d616e00
1643c7771f43c77720c0c97700003000040000002d01010004000000f00100000a000000
320a00000000020000004778c20100037700000026060f00e4004d617468547970655555
d800050100050244534d543500011357696e416c6c4261736963436f6465506167657300
110554696d6573204e657720526f6d616e00110353796d626f6c001105436f7572696572
204e65770011044d5420457874726100120008212f458f442f4150f4100f475f4150f21f
1e4150f4150f4100f445f425f48f425f4100f4100f435f4100f48f45f42a5f48f48f4100
f4100f40f48f417f48f4100f412a5f445f45f45f45f45f410f0c01000100010202020200
020001010100030001000400000a01000200834700020082280002008378000200822900
00000b00000026060f000c00ffffffff01000000000000001c000000fb02100007000000
0000bc02000000cc0102022253797374656d000000000a0021008a010000000000000000
08e912002942c777040000002d01000004000000f0010100030000000000 и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 имеют одинаковую степень,
поэтомуpicscalex100010009000003a20200000400a1000000000005000000020101000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.

Отсюда прямой и взаимный многочлен без остатка делит не
толькоpicscalex100010009000003b901000002007e0000000000050000000201010000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, но и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.

Поэтому, если неприводимый многочлен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несимметричен, т.е.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, то имеет место следующее разложение:
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. (9)

Учитывая, что
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– симметричные многочлены, то F(x) – также симметричный многочлен,
степень которого равна d = (T-1)-2k.

Здесь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 – взаимные несимметричные многочлены (их
произведение есть симметричный многочлен). Симметричные многочлены, если
они имеются в разложении, записываются отдельно (например, Е(х), (х+1))
или входят в F(x) (см., например,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 в разложении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).

Учитывая, что
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,

получим, что

picscalex103010009000003290500000400510100000000050000000201010000000500
00000102ffffff00050000002e0119000000050000000b0200000000050000000c024006
e0161300000026060f001c00ffffffff00004e0010000000c0ffffffa7ffffffa0160000
e70500000b00000026060f000c004d617468547970650000600108000000fa0200001300
000000000002040000002d01000005000000140280005a05050000001302800044060500
0000140259002505050000001302b102250505000000140259004708050000001302b102
4708050000001402a100010c0500000013026902010c050000001402a1005b1305000000
130269025b13050000001402b20375010500000013027a057501050000001402b203a304
0500000013027a05a304050000001402b203f6070500000013027a05f607050000001402
b203180b0500000013027a05180b05000000090200000002050000001402c50566051c00
0000fb025fff0000000000009001000000000002001054696d6573204e657720526f6d61
6e00d89ff377e19ff3772020f5773c0b6651040000002d0101000d000000320a00000000
0400000028292829ae00c705ae0042010500000014027a0235141c000000fb0222ff0000
000000009001000000000002001054696d6573204e657720526f6d616e00d89ff377e19f
f3772020f5773c0b6651040000002d01020004000000f00101000a000000320a00000000
020000002829da00bc01050000001402c20221091c000000fb0222ff0000000000009001
000000000002001054696d6573204e657720526f6d616e00d89ff377e19ff3772020f577
3c0b6651040000002d01010004000000f00102000a000000320a00000000020000002829
da00bc01050000001402e501c2011c000000fb0280fe0000000000009001000000000002
001054696d6573204e657720526f6d616e00d89ff377e19ff3772020f5773c0b66510400
00002d01020004000000f001010013000000320a00000000080000002829282928292829
50014403500198055001dc0250010003050000001402f604b2021c000000fb0280fe0000
000000009001000000000002001054696d6573204e657720526f6d616e00d89ff377e19f
f3772020f5773c0b6651040000002d01010004000000f001020012000000320a00000000
070000002829282928292e29500125055001110550017e000003050000001402c505da04
1c000000fb025fff0000000000009001010000000002001054696d6573204e657720526f
6d616e00d89ff377e19ff3772020f5773c0b6651040000002d01020004000000f0010100
0d000000320a000000000400000047784778de009705de00420105000000140248021d01
1c000000fb0222ff0000000000009001010000cc0002001054696d6573204e657720526f
6d616e00d89ff377e19ff3772020f5773c0b6651040000002d01010004000000f0010200
09000000320a0000000001000000e829bc010500000014027a027e131c000000fb0222ff
0000000000009001010000000002001054696d6573204e657720526f6d616e00d89ff377
e19ff3772020f5773c0b6651040000002d01020004000000f00101000a000000320a0000
00000200000047781c01bc01050000001402c2026a081c000000fb0222ff000000000000
9001010000000002001054696d6573204e657720526f6d616e00d89ff377e19ff3772020
f5773c0b6651040000002d01010004000000f00102000a000000320a0000000002000000
47781c01bc01050000001402e50146001c000000fb0280fe000000000000900101000000
0002001054696d6573204e657720526f6d616e00d89ff377e19ff3772020f5773c0b6651
040000002d01020004000000f00101000d000000320a0000000004000000527841781802
140380014a051c000000fb0280fe0000000000009001010000cc0002001054696d657320
4e657720526f6d616e00d89ff377e19ff3772020f5773c0b6651040000002d0101000400
0000f00102000d000000320a0000000004000000c5f5c0f59e01ac028001000305000000
1402f604b0011c000000fb0280fe0000000000009001010000000002001054696d657320
4e657720526f6d616e00d89ff377e19ff3772020f5773c0b6651040000002d0102000400
0000f00101000a000000320a000000000200000045789e01f5041c000000fb0280fe0000
000000009001010000cc0002001054696d6573204e657720526f6d616e00d89ff377e19f
f3772020f5773c0b6651040000002d01010004000000f00102000d000000320a00000000
04000000c0f552788001cf0492010003050000001402e501ea031c000000fb0280fe0000
000000009001000000010002001053796d626f6c00003e0b0a2d64df1200d89ff377e19f
f3772020f5773c0b6651040000002d01020004000000f00101000d000000320a00000000
040000003d3d2b3ddc0688048c060003050000001402f6043a000c000000320a00000000
030000003d2b3d3d93068d0600035101000026060f0098024d6174685479706555558c02
050100050244534d543500011357696e416c6c4261736963436f64655061676573001105
54696d6573204e657720526f6d616e00110353796d626f6c001105436f7572696572204e
65770011044d5420457874726100120008212f458f442f4150f4100f475f4150f21f1e41
50f4150f4100f445f425f48f425f4100f4100f435f4100f48f45f42a5f48f48f4100f410
0f40f48f417f48f4100f412a5f445f45f45f45f45f410f0c010001000102020202000200
01010100030001000400000a040001010100020083520003001b00000b01000200833804
000101000a0200822800020083780002008229000204863d003d0300040300010003000d
00000100020083410000000200822800020083780002008229000002009607ec02009608
ec0003001b00000b01000200834700020082280002008378000200822900000101000a02
04863d003d0300040300010002008315040200822800020083450402008229000204862b
002b02008310040200822800020083450402008229000002009607ec02009608ec000300
1b00000b01000200834700020082280002008378000200822900000101000a0204863d00
3d0001000204863d003d0300040300010002008345000200822800020083780002008229
000002009607ec02009608ec0003001b00000b010003001b00000c010002008347000200
8228000200837800020082290000010100000b0101000a0204862b002b03000403000100
02008310040200822800020083450402008229000002009607ec02009608ec0003001b00
000b010003001b00000c0100020083470002008228000200837800020082290000010100
000b0101000a0204863d003d02008352000200822800020083780002008229000200822e
000000000b00000026060f000c00ffffffff010000000000000008000000fa0200000000
000000000000040000002d0101001c000000fb021000070000000000bc02000000cc0102
022253797374656d00003c0b665100000a0021008a0100000000ffffffffb4e912000400
00002d01030004000000f0010200030000000000 (10)

т.е. вычеты прямого и инверсного многочленов равны друг другу.

Для вычетов:

– прямого многочлена по взаимному модулю;

– взаимного многочлена по взаимному модулю;

– взаимного многочлена по прямому модулю запишем:
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26f6d616e00d89ff377e19ff3772020f577ff0a6684040000002d01020004000000f0010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(11)
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(12)

где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– элемент кольца вычетов по модулю G^(x).
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(13)

Сравнивая (7) и (13), (11) и (12) заметим, что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 и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 есть соответственно прямой и обратный элемент кольца вычетов по
модулю G(x), связанные, соответственно, как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. Аналогично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 и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 есть соответственно прямой и обратный элемент кольца вычетов по
модулю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,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. Отсюда
следует, что:

1. контрольная сумма прямой и инверсной последовательности равны,
кодирование прямой или инверсной последовательности равноценны;

2. процедура кодирования по прямому и взаимному модулю, прямого или
взаимного информационного многочлена однотипны. Поэтому, не имеет
значения порядок считывания информационных символов в процессе
кодирования, важно лишь, какие элементы кольца (прямые или обратные)
берутся для кодирования по прямому или взаимному кодовому полиному;

3. кодирующее устройство не обязательно строить в виде регистра сдвига с
обратными связями.

Кодирующее устройство может реализовать любую из процедур (7,11,12
или13).

В этом случае кодер может быть представлен структурой, показанной на
рис.1 и содержать:

– генератор элементов кольца;

– накапливающий сумматор, который складывает элементы кольца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 или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, взвешенные
с весом бита данных(0 или 1) .
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Рис.1 Структурная схема БЧХ кодера

Данный кодер отличает то полезное свойство, что он не требует битовых
операций и обеспечивает легкую смену кодового полинома. В силу этих
обстоятельств легко выполняется как аппаратная, так и программная
реализация такого кодека для БЧХ кода.

Декодер вычисляет синдром по уравнению (6), при этом, если ?(х) = 0, то
S(х) = = 0. Однако, если S(х) = 0, то это не означает, что ?(х) = 0.

Возможна ситуация, когда S(х) = 0 при ?(х) ? 0. Эта ситуация есть
необнаружение ошибки декодером или остаточная ошибка декодера. Очевидно,
ошибка декодирования возникает тогда, когда вектор ошибки кратен
порождающему полиному, т.е
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. (14)

Если кадр входных данных имеет длину L, то мощность вектора ошибки ?(х)
равна 2L, мощность множества необнаруженных ошибок D(x) равна 2(L-k),
при этом ошибки на оси 0,1,2,3… 2L (такую ось можно получить, если
записать все вектора ошибки в виде (1), положив хj = 2j) распределены
равномерно через G(х) ошибок.

Поскольку мощность множества ошибок определяется только степенью
порождающего многочлена и не зависит от его структуры и веса (веса по
Хэммингу), то все коды, порожденные полиномом одной и той же степени
(включая взаимные многочлены) имеют одинаковую обнаруживающую
способность. Меняется лишь расположение необнаруживаемых ошибок на
числовой оси. Это вовсе не означает, что вероятность остаточной ошибки
декодера будет одинакова для любого полинома одной и той же степени.
Вероятность остаточной ошибки декодера будет определяться тем, как часто
“использует” канал связи ту или иную конфигурацию ошибок, т.е. зависит
от статистики ошибок в канале. Отметим, что при равномерном
распределении ошибок в канале связи вектора ошибки равномерно
распределены по числовой оси, поэтому при любой длине блока доля
необнаруженных ошибок не меняется. Отметим также, что с учетом теоремы 1
контрольная сумма прямого и взаимного кодового многочлена взаимны,
поэтому они взаимно легко пересчитываются одна в другую и поэтому число
неприводимых многочленов степени “k”, которые можно использовать для
помехоустойчивого кодирования равно числу пар “прямой-взаимный”
многочлен.

Применение новых свойств многочленов к задачам генерации псевдослучайных
последовательностей (ПСП)

ПСП, в частности, в такой разновидности, как последовательности
максимального периода

(М-последовательности) широко используются практически во всех блочных
системах передачи данных для обеспечения цикловой синхронизации, в
системах связи с шумоподобными сигналами (ШПС) и т.д.

Единственный известный способ генерации М-последовательности заключается
в использовании для этой цели регистра сдвига с обратными связями [6].
Этот регистр (за счет наличия обратной связи) имеет бесконечную
импульсную реакцию, поэтому при любом ненулевом воздействии выдает
периодически повторяющуюся импульсную последовательность. Эта
последовательность имеет максимальный период (если многочлен
неприводим), равный
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, (15)

где k – порядок многочлена. В этом регистре выполняется вычисление
очередного символа решением уравнения вида
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.

Например, для стандартного мнногочлена
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уравнение
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обеспечивает вычисление
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, (16)

где t – номер символа в последовательности. При

t = 0 а16(-1), а12(-1),

а5(-1) – вектор начального воздействия. Очевидно, что он – ненулевой.

В силу периодичности М-последовательности при каждом применении не
обязательно выполнять процедуру генерации, достаточно запомнить один из
ее сдвигов, все остальные значения могут быть восстановлены циклическим
сдвигом последовательности.

Поэтому достаточно лишь однократно сформировать М-последовательность,
запомнить ее и многократо применять при возникновении потребности.

Поставим задачу – вычислить М-последовательность или один из ее сдвигов
по генераторному многочлену G(x), не прибегая к процедуре генерации по
уравнению (15). Кроме того, определим, сколько вообще существует разных
М-последовательностей в векторном пространстве размерности 2Т, поскольку
ответа на этот вопрос на сегодня не существует. Одну из этих
последовательностей (младшей степени) будем называть базисной и
обозначать как Ф0(х). Остальные последовательности получим циклическим
сдвигом, т.е. вычислением
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. (17)

Для решения задачи определения базисной М-последовательности
воспользуемся выражением (9), где дополнительно отметим, что
последовательность Е(х) представима в виде произведения нескольких пар
прямой-взаимный многочлен.

Например,

Для n =
3:picscalex970100090000032a0200000200ce000000000005000000020101000000050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Для n = 4: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, где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Для n = 5:
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Учитывая, что в М-последовательности всегда четно число единиц (вес
последовательности) легко показать, что М-последовательность без остатка
делится как на (х+1), так и на G(x),F(x), поэтому
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.
(18)

Остальные последовательности получают циклическим сдвигом, в
соответствии с формулой (16).

Определим
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. (19)

Учитывая, что обе части сравнения и модуль имеют общий множитель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, после
деления получим
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 и
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. (20)

Таким образом, базисная М-последовательность может быть получена из
разложения (9), все остальные значения которой получаются из (17) или
(19).

По аналогии с (17) запишем, что М-последовательность, порожденная
взаимным многочленом
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. (21)

Учтем, что
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, тогда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.

С учетом изложенного, покажем, что М-последовательности, порожденные
взаимными многочленами, взаимны.

Теорема 6. М-последовательности, порожденные взаимными многочленами,
взаимны, т.е.
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.

Доказательство:

Поскольку
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, то:
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В силу симметрии F(x) (следствие 3 теоремы 5)
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,

что и требовалось доказать.

Пример.

Пусть Т=15 разложение принимает вид:
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picscalex830100090000034c08000004003c02000000000500000002010100000005000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Отсюда следует, что разных М-последовательностей, которые могут быть
использованы для решения задач связи в пространстве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, столько, сколько пар
прямой-взаимный многочлен в разложении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. В частности, в
пространстве размерности 7 (генераторный полином 3 степени) существует
только одна М-последовательность. В пространстве размерности 15
(генераторный полином 4 степени) также существует только одна
М-последовательность. В пространстве размерности 31 (генераторный
полином 5 степени) существует три М-последовательности. Таким образом,
разложение на простые сомножители бинома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, выделение пар
прямой-взаимный многочлен определяет общее количество
М-последовательностей длины Т в пространстве и их генераторные
многочлены.

6.Полученные результаты

Выполненная работа дала возможность ответить на поставленные в разделе 3
вопросы:

– обнаруживающие свойства циклического кода не связаны со структурой
кодового полинома, поэтому при равновероятно распределенной ошибке
вероятность остаточной ошибки декодера не зависит от структуры полинома
одной и той же степени. При неравновероятной статистике вероятность
остаточной ошибки декодера определяется структурой потока ошибок и
является предметом дальнейших исследований;

– альтернативой общепринятой процедуре построения кодеров циклических
кодов, основанной на использовании регистров сдвига с обратными связями,
являются процедуры, описываемые уравнениями (7) и (11), (12) и (13),
которые в отличие от общепринятых схем не требуют битовых операций и,
следовательно, проще программируются;

– альтернативой общепринятой процедуре построения генераторов
М-последовательностей, основанной на использовании регистров сдвига с
обратными связями, являются процедуры, описываемые уравнениями (18) и
(20);

– разных М-последовательностей в пространстве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, разных кодовых
полиномов столько, сколько пар “прямой- взаимный” многочлен в разложении
двучлена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.

Выводы

Полученные результаты расширяют возможности кодирующих устройств,
обеспечивают возможность вычисления М-последовательностей в векторном
пространстве мощности 2Т.

Список литературы

1. Варакин Л.Е. Системы связи с шумоподобными сигналами. – М.: Радио и
связь, 1985. – 384с.

2. Ф.Дж. Мак-Вильямс, Н.Дж.Слоэн. Теория кодов, исправляющих ошибки. –
М.: Связь,1979. – 744с.

3. А. Молдовян, Н. Молдовян, Б. Светлов. Криптография. – СПб.: Лань,
2001. – 320с.

4. Лега Ю.Г., Лисицына Е.С., Фауре Э.В., Швидкий В.В. Основные
характеристики систем цикловой синхронизации, использующих
последовательности быстрого поиска // Вісник ЧДТУ. – 2006. – №1.

5. Новик Д.А. Эффективное кодирование. – М.: Энергия, 1965. – 235с.

6. Р. Лидл, Г. Нидеррайтер. Конечные поля (в двух томах). – М.: Мир,
1988. – 822с.

7. Рекомендация Международного консультативного комитета по телефонии и
телеграфии V-41. Женева, 1976.

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