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Метод словарного кодирования Зива-Лемпела. Дифференциальное кодирование

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AAEI?ONNEEE AINOAeA?NOAAIIUE OIEAA?NEOAO EIOI?IAOEEE E ?AAeEIYEAEO?IIEEE

Eaoaae?a ?YN

?aoa?ao ia oaio:

«Neiaa?iua iaoiaeu eiaee?iaaiey. Iaoiae Ceaa-Eaiiaea.
Aeeooa?aioeeaeueiia eiaee?iaaiea»

IEINE, 2009

Neiaa?iua iaoiaeu eiaee?iaaiey. Iaoiae Ceaa-Eaiiaea

I?aeoe/anee ana neiaa?iua iaoiaeu eiaee?iaaiey ipeiaaeeaaeao naiuea
aeai?eoiia ec ?aaiou aeaoo ec?aeeueneeo o/aiuo – Ceaa e Eaiiaea,
iioaeeeiaaiiie a 1977 aiaeo. Nouiinoue eo ninoieo a oii, /oi o?acu a
naeeiaaiii oaenoa caiaiythony oeacaoaeai ia oi ianoi, aaea iie a yoii
oaenoa oaea paiaa iiyaeyeenue.

Yoi naiaenoai aeai?eoiia iacuaaaony iaoiaeii Ceaa-Eaiiaea e iaicia/aaony
eae LZ-naeaoea. Yoio iaoiae aunopi ipeniinaaeeaaaony e nopoeoopa oaenoa
e iiaeao eiaee?iaaoue ei?ioeea ooieoeeiiaeueiua neiaa, oae eae iie
i/aiue /anoi a iai iiyaeythony. Iiaua neiaa e o?acu iiaoo oaeaea
oi?ie?iaaoueny ec /anoae ?aiaa ano?a/aiiuo neia.

Aeaeiaee?iaaiea naeaoiai oaenoa inouanoaeyaony iai?yioth – i?ienoiaeeo
i?inoay caiaia oeacaoaey aioiaie o?acie ec neiaa?y, ia eioi?oth oio
oeacuaaao. Ia i?aeoeea LZ-iaoiae aeiaeaaaony oi?ioaai naeaoey, aai
aaaeiui naienoaii yaeyaony i/aiue auno?ay ?aaioa aeaeiaea?a. (Eiaaea iu
aiai?ei i oaenoa, oi i?aaeiieaaaai, /oi eiaee?iaaieth iiaeaa?aaaony
iaeioi?ue aaeoi? aeaiiuo n eiia/iui aeene?aoiui aeoaaeoii, e yoi ia
iaycaoaeueii oaeno a aoeaaeueiii niunea yoiai neiaa.)

Aieueoeinoai neiaa?iuo iaoiaeia eiaee?iaaiey iinyo eiy aaoi?ia eaeae
iaoiaea Ceaa e Eaiiaea, e /anoi n/eoatho, /oi ana iie eniieuecotho iaeei
e oio aea aeai?eoi eiaee?iaaiey. Ia naiii aeaea ?aciua i?aaenoaaeoaee
yoiai naiaenoaa aeai?eoiia i/aiue neeueii ?acee/athony a aeaoaeyo naiae
?aaiou.

Ana neiaa?iua iaoiaeu eiaee?iaaiey iiaeii ?acaeoue ia aeaa a?oiiu.

Iaoiaeu, i?eiaaeeaaeauea e ia?aie a?oiia, iaoiaey a eiaee?oaiie
iineaaeiaaoaeueiinoe oeaii/ee neiaieia, eioi?ua ?aiaa oaea ano?a/aeenue,
aianoi oiai, /oiau iiaoi?youe yoe oeaii/ee, caiaiytho eo oeacaoaeyie ia
i?aaeuaeouea iiaoi?aiey.

Neiaa?ue a yoie a?oiia aeai?eoiia a iayaiii aeaea niaea?aeeony a
ia?aaaouaaaiuo aeaiiuo, nio?aiythony eeoue oeacaoaee ia ano?a/athueany
oeaii/ee iiaoi?ythueony neiaieia.

Ana iaoiaeu yoie a?oiiu aace?othony ia aeai?eoia, ?ac?aaioaiiii e
iioaeeeiaaiiii, eae oaea ioia/aeinue, n?aaieoaeueii iaaeaaii – a 1977
aiaeo Aa?aoaiii Eaiiaeai e sseiaii Ceaii, – LZ77. Iaeaieaa niaa?oaiiui
i?aaenoaaeoaeai yoie a?oiiu, aeeth/eaoei a naay ana aeinoeaeaiey,
iieo/aiiua a aeaiiii iai?aaeaiee, yaeyaony aeai?eoi LZSS, iioaeeeiaaiiue
a 1982 aiaeo Noi?a?ii e Oeiainee.

I?ioeaaeo?a eiaee?iaaiey a niioaaonoaee n aeai?eoiaie yoie a?oiiu
eeethno?e?oaony ?en. 1.

?en. 1

Aeai?eoiu aoi?ie a?oiiu a aeiiieiaiea e enoiaeiiio neiaa?th enoi/ieea
nicaeatho neiaa?ue o?ac, i?aaenoaaeythueo niaie iiaoi?ythueany
eiiaeiaoeee neiaieia enoiaeiiai neiaa?y, ano?a/athueany ai aoiaeiuo
aeaiiuo.

I?e yoii ?acia? neiaa?y enoi/ieea aic?anoaao, e aeey aai eiaee?iaaiey
iio?aaoaony aieueoaa /enei aeo, ii cia/eoaeueiay /anoue yoiai neiaa?y
aoaeao i?aaenoaaeyoue niaie oaea ia ioaeaeueiua aoeau, a aoeaini/aoaiey
eee oeaeua neiaa.

Eiaaea eiaea? iaia?oaeeaaao o?aco, eioi?ay ?aiaa oaea ano?a/aeanue, ii
caiaiyao aa eiaeaenii neiaa?y, niaea?aeauei yoo o?aco. I?e yoii aeeeia
eiaea eiaeaena iieo/aaony iaiueoa eee iaiiiai iaiueoa aeeeiu eiaea
o?acu.

Ana iaoiaeu yoie a?oiiu aace?othony ia aeai?eoia, ?ac?aaioaiiii e
iioaeeeiaaiiii Eaiiaeai e Ceaii a 1978 aiaeo, – LZ78. Iaeaieaa
niaa?oaiiui ia aeaiiue iiiaio i?aaenoaaeoaeai yoie a?oiiu neiaa?iuo
iaoiaeia yaeyaony aeai?eoi LZW, ?ac?aaioaiiue a 1984 aiaeo Oa??e Aye/ai.

Eaeath yoie a?oiiu aeai?eoiia iiaeii oaeaea iiynieoue n iiiiuueth ?en.
2.

?en. 2

Aeai?eoiu aoi?ie a?oiiu ianeieueei i?iua a iauyniaiee eo ?aaiou, iiyoiio
ia/iai ?anniio?aiea i?eioeeia aeaenoaey LZ-eiaea?ia n aeai?eoia LZW.

?anniio?ei a naiii iauai aeaea ?aaioo LZW-eiaea?a e aeaeiaea?a.

I?ioeaaeo?a eiaee?iaaiea

I?ioeann naeaoey auaeyaeeo aeinoaoi/ii i?inoi. Iu iineaaeiaaoaeueii
n/eouaaai neiaieu aoiaeiiai iioiea (no?ieo) e i?iaa?yai, anoue ee a oaea
nicaeaiiie iaie oaaeeoea oaeay no?iea.

Anee no?iea anoue, oi n/eouaaai neaaeothuee neiaie, a anee oaeie no?iee
iao, – caiinei a auoiaeiie iioie eiae aeey i?aaeuaeouae iaeaeaiiie
no?iee, caiinei aa a oaaeeoeo e ia/eiaai iiene niiaa.

I?? ? ?? ??? ????o ????????? ???? ?? / WED / WE / WEE / WEB, ?e y?i ???
???? ???o ???? dim A = 255.

N?? ??ey ??y?o ??oth?i ???i:

A??? ???u A???e ?ae I?? ???u ?iaa?y

/W / 256 = /W

E W 257 = WE

D E 258 = ED

/ D 259 = D/

WE 256 260 = /WE

/ E 261 = E/

WEE 260 262 = /WEE

/W 261 263 = E/W

EB 257 264 = WEB

B

A ????? ???i ???? ?ae

/WEDEB.

E? ?e y?i ????? ??a ????i ?? a ????e n ???i ?

A?e ?y ????i ?????y ??? / WED / WE / WEE / WEB ?e?e a 15 ?? e ???? ???oa
dim A = 255 ?i ?????? ? 15 • log2 255 = 15o8 = 120 ?o, ? ?y ????i ?????y
???? ??? ??? / WED E B ??? a 10 ??o ???? n ????i
a 264 ?e? – 10 • 9 = 90 ?o.

Iioeaaeo?a aeaeiaee?iaaiea

LZW-????, ?????y ???e ??e ?????i?o ???, ???????o ? ?? ???? ???. O? ?, ?e
e ???oi ??ey, ???? ???y? ??a ??? a ???ue ?y?e ?c, ??a ???o ? ???i ???
??e ?ae. A?, ?i ?o ???ny ???ue, – y? ??????ue ???e ?ae a au??oth ???
???? e ??? ? ? ??ae ???.

N?? ??? LZW-???? ??y?o ??oth?i ???i:

??? ? ??a ??? – /WEDEB.

A??? ???u A???y ??? I?? ???u n?aa?y

/ /

W W 256 = /W

E E 257 = WE

D D 258 = ED

256 /W 259 = D/

E E 260 = /WE

260 /WE 261 = E/

261 E/ 262 = /WEE

257 WE 263 = E/W

B B 264 = WEB

N?? ??????i ????i y?? ???a ??ey y?y?ny ?, ?i ?? ???ue ??o ???? ????ny
???? ?c ????? ??a??. A ??a ???? ??????y ???? ??o ??i ??e ? ???ue ii?o
????, ??e a ???? ?????y ?e ??i?i ???i, ?e y?i ?i ???? au? ??ueth ????
??????y.

?aaioa eiaea?a/aeaeiaea?a naiaenoaa LZ77 – ia?aie iioaeeeiaaiiie aa?nee
LZ-iaoiaea – auaeyaeeo ianeieueei eia/a.

A aeai?eoia LZ77 oeacaoaee iaicia/atho o?acu a ieia iinoiyiiiai paciapa,
ipaaeoanoaothuea iiceoeee eiaea. Iaeneiaeueiay aeeeia caiaiyaiuo
oeacaoaeyie iiaeno?ie ii?aaeaeyaony ia?aiao?ii F (iau/ii yoi io 10 aei
20). Yoe ia?aie/aiey iicaieytho LZ77 eniieueciaaoue “neieuecyuaa ieii”
ec N neiaieia. Ec ieo ia?aua N-F auee oaea caeiaee?iaaiu, a iineaaeiea F
ninoaaeytho oi?aaeaeathuee aooa?.

I?e eiaee?iaaiee neiaiea a ia?auo N-F neiaieao ieia euoo naioth
aeeeiioth, niaiaaeathuoth n yoei aooa?ii no?ieo. Iia iiaeao /anoe/ii
ia?ae?uaaoue aooa?, ii ia iiaeao auoue naiei aooa?ii.

Iaeaeaiiia iaeaieueoaa niioaaonoaea caoai eiaee?oaony o?eaaeie [i, j, a]
aaea i anoue aai niauaiea io ia/aea aooa?a, j – aeeeia niioaaonoaey, a –
ia?aue neiaie, ia niioaaonoaothuee iiaeno?iea ieia.

Caoai ieii naeaeaaaony ai?aai ia j +1 neiaie e aioiai e iiaiio oaao
aeai?eoia.

I?eaycea ii?aaeaeaiiiai neiaiea e eaaeaeiio oeacaoaeth aa?aioe?oao, /oi
eiaee?iaaiea aoaeao auiieiyoueny aeaaea a oii neo/aa, anee aeey ia?aiai
neiaiea oipaaeaeathuaai aooa?a ia aoaeao iaeaeaii niioaaonoaea.

Iauai iaiyoe, o?aaoaiue eiaea?o e aeaeiaea?o, ia?aie/eaaaony ?acia?ii
ieia. Eiee/anoai aeo, iaiaoiaeeiia aeey i?aaenoaaeaiey niauaiey ( i ) a
o?eaaea, ninoaaeyao [log(N-F)]. Eiee/anoai neiaieia ( j ), caiaiyaiuo
o?eaaeie, iiaeao auoue caeiaee?iaaii [logF] aeoaie.

Aeaeiaee?iaaiea inouanoaeyaony i/aiue i?inoi e auno?i. I?e yoii
iiaeaea?aeeaaaony oio aea ii?yaeie ?aaiou n ieiii, /oi e i?e
eiaee?iaaiee, ii a ioee/ea io iienea iaeeiaeiauo no?ie ii, iaiai?io,
eiie?oao eo ec ieia a niioaaonoaee n i/a?aaeiie o?eaaeie.

Aeeooa?aioeeaeueiia eiaee?iaaiea

?aaioa aeeooa?aioeeaeueiiai eiaea?a iniiaaia ia oii oaeoa, /oi aeey
iiiaeo oeiia aeaiiuo ?acieoea iaaeaeo ninaaeieie ion/aoaie ioiineoaeueii
iaaaeeea, aeaaea anee naie aeaiiua eiatho aieueoea cia/aiey. Iai?eia?,
iaeuecy iaeeaeaoue aieueoie ?acieoeu iaaeaeo ninaaeieie ieenaeaie
oeeo?iaiai ecia?aaeaiey.

Neaaeothuee i?inoie i?eia? iieacuaaao, eaeia i?aeiouanoai iiaeao aeaoue
aeeooa?aioeeaeueiia eiaee?iaaiea (eiaee?iaaiea ?aciinoe iaaeaeo
ninaaeieie ion/aoaie) a n?aaiaiee n i?inoui eiaee?iaaieai aac iaiyoe
(eiaee?iaaieai ion/aoia iacaaeneii ae?oa io ae?oaa).

I?ineaie?oai 8-aeoiaia (256-o?iaiaaia) oeeo?iaia ecia?aaeaiea, i?e yoii
aeanyoue iineaaeiaaoaeueiuo ieenaeia eiatho o?iaie:

144, 147, 150, 146, 141, 142, 138, 143, 145, 142.

Anee caeiaee?iaaoue yoe o?iaie ieenae ca ieenaeii eaeei-eeai eiaeii aac
iaiyoe, eniieuecothuei 8 aeo ia ieenae ecia?aaeaiey, iieo/ei eiaeiaia
neiai, niaea?aeauaa 80 aeo.

I?aaeiieiaeei oaia?ue, /oi i?aaeaea /ai iiaeaa?aaoue ion/aou
ecia?aaeaiey eiaee?iaaieth, iu au/eneei ?aciinoe iaaeaeo ninaaeieie
ieenaeaie. Yoa i?ioeaaeo?a aeano iai iineaaeiaaoaeueiinoue neaaeothuaai
aeaea:

144, 147, 150, 146, 141, 142, 138, 143, 145, 142.

144, 3, 3, – 4, – 5, 1, – 4, 5, 2, -3.

Enoiaeiay iineaaeiaaoaeueiinoue iiaeao auoue eaaei ainnoaiiaeaia ec
?aciinoiie i?inoui noiie?iaaieai (aeene?aoiui eioaa?e?iaaieai):

144, 144+3, 147+3, 150–4, 146–5, 141+1, 142–4, 138+5, 143+2, 145-3

144, 147, 150, 146, 141, 142, 138, 143,
145, 142.

Aeey eiaee?iaaiey ia?aiai /enea ec iieo/aiiie iineaaeiaaoaeueiinoe
?aciinoae ion/aoia, eae e ?aiaa, iiiaaeiaeony 8 aeo, ana inoaeueiua
/enea iiaeii caeiaee?iaaoue 4-aeoiauie neiaaie (iaeei ciaeiaue aeo e 3
aeoa ia eiaee?iaaiea iiaeoey /enea ).

Oaeei ia?acii, a ?acoeueoaoa eiaee?iaaiey iieo/ei eiaeiaia neiai aeeeiie
8 + 9*4 = 44 aeoa eee ii/oe aaeaia aieaa ei?ioeia, iaaeaee i?e
eiaeeaeaeoaeueiii eiaee?iaaiee ion/aoia.

Iaoiae aeeooa?aioeeaeueiiai eiaee?iaaiey i/aiue oe?iei eniieuecoaony a
oao neo/ayo, eiaaea i?e?iaea aeaiiuo oaeiaa, /oi eo ninaaeiea cia/aiey
iacia/eoaeueii ioee/athony ae?oa io ae?oaa, i?e oii, /oi naie cia/aiey
iiaoo auoue neieue oaiaeii aieueoeie.

Yoi ioiineony e caoeiaui neaiaeai, iniaaiii e ?a/e, ecia?aaeaieyi,
ninaaeiea ieenaee eioi?uo eiatho i?aeoe/anee iaeeiaeiaua y?einoe e oeaao
e o.i. A oi aea a?aiy yoio iaoiae niaa?oaiii ia iiaeoiaeeo aeey
eiaee?iaaiey oaenoia, /a?oaaeae eee eaeeo-eeai oeeo?iauo aeaiiuo n
iacaaeneiuie ninaaeieie cia/aieyie.

EEOA?AOO?A

1. Eeaeianeee A.E. Oai?ey eioi?iaoeee. – I., «Aunoay oeiea», 2002a. –
120n.

2. Iao?ieiaey e ?aaeeiecia?aiey a oaeaeiiioieeaoeeiiiuo nenoaiao.
O/aaiee aeey AOCia. / A.E. Iaoaaeia, A.E. Oaeeei, A.A. Oaaei?ia e ae?. –
I.: Aunoay oeiea, 2001 a. – 383n.

3. Oeaiaiei I.I. Ecia?eoaeueiua eioi?iaoeeiiiua nenoaiu. – I.:
Yia?aiaoii ecaeao, 2005. – 440n.

4. Cthei A.A., Eeianeee Ae.Ae., Iaca?ia I.A., Oeie E.I. Oai?ey ia?aaea/e
neaiaeia. I: ?aaeei e naycue, 2001 a. –368 n.

5. A. Neey?. Oeeo?iaay naycue. Oai?aoe/aneea iniiau e i?aeoe/aneia
i?eiaiaiea. Ecae. 2-a, eni?.: Ia?. n aiae. – I.: Ecaeaoaeueneee aeii
«Aeeueyin», 2003 a. – 1104 n.

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