Weak variable-length source coding

Given a general source X={X/sup n/}/sub n=1//sup /spl infin//, source coding is characterized by a pair (/spl phi//sub n/, /spl psi//sub n/) of encoder /spl phi//sub n/, and decoder /spl psi//sub n/, together with the probability of error /spl epsi//sub n//spl equiv/Pr{/spl psi//sub n/(/spl phi//sub...

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Vydané v:IEEE transactions on information theory Ročník 46; číslo 4; s. 1217 - 1226
Hlavný autor: Han, Te Sun
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York IEEE 01.07.2000
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:
Asymptotic properties
Coders
Coding
Decoders
Encoders
Errors
Information theory
Source coding
Theorems
ISSN:0018-9448, 1557-9654
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Abstract Given a general source X={X/sup n/}/sub n=1//sup /spl infin//, source coding is characterized by a pair (/spl phi//sub n/, /spl psi//sub n/) of encoder /spl phi//sub n/, and decoder /spl psi//sub n/, together with the probability of error /spl epsi//sub n//spl equiv/Pr{/spl psi//sub n/(/spl phi//sub n/(X/sup n/))/spl ne/X/sup n/}. If the length of the encoder output /spl phi//sub n/(X/sup n/) is fixed, then it is called fixed-length source coding, while if the length of the encoder output /spl phi//sub n/(X/sup n/) is variable, then it is called variable-length source coding. Usually, in the context of fixed-length source coding the probability of error /spl epsi//sub n/ is required to asymptotically vanish (i.e., lim/sub n/spl rarr//spl infin///spl epsi//sub n/=0), whereas in the context of variable-length source coding the probability of error /spl epsi//sub n/ is required to be exactly zero (i.e., /spl epsi//sub n/=0/spl forall/n=1, 2, ...). In contrast to these, we consider the problem of variable-length source coding with asymptotically vanishing probability of error (i.e., lim/sub n/spl rarr//spl infin///spl epsi//sub n/=0), and establish several fundamental theorems on this new subject.
AbstractList Given a general source X={X super(n)} sub(n=1) super( infinity ), source coding is characterized by a pair ( phi sub(n), psi sub(n)) of encoder phi sub(n), and decoder psi sub(n), together with the probability of error epsilon sub(n) identical with Pr{ psi sub(n) ( phi sub(n)(X super(n)))[ne]X super(n)}. If the length of the encoder output phi sub(n)(X super(n)) is fixed, then it is called fixed-length source coding, while if the length of the encoder output phi sub(n )(X super(n)) is variable, then it is called variable-length source coding. Usually, in the context of fixed-length source coding the probability of error epsilon sub(n) is required to asymptotically vanish (i.e., lim sub(n arrow right infinity ) epsilon sub(n)=0), whereas in the context of variable-length source coding the probability of error epsilon sub(n) is required to be exactly zero (i.e., epsilon sub(n )=0[forall]n=1, 2, ...). In contrast to these, we consider the problem of variable-length source coding with asymptotically vanishing probability of error (i.e., lim sub(n arrow right infinity ) epsilon sub(n)=0), and establish several fundamental theorems on this new subject
Given a general source X={X/sup n/}/sub n=1//sup /spl infin//, source coding is characterized by a pair (/spl phi//sub n/, /spl psi//sub n/) of encoder /spl phi//sub n/, and decoder /spl psi//sub n/, together with the probability of error /spl epsi//sub n//spl equiv/Pr{/spl psi//sub n/(/spl phi//sub n/(X/sup n/))/spl ne/X/sup n/}. If the length of the encoder output /spl phi//sub n/(X/sup n/) is fixed, then it is called fixed-length source coding, while if the length of the encoder output /spl phi//sub n/(X/sup n/) is variable, then it is called variable-length source coding. Usually, in the context of fixed-length source coding the probability of error /spl epsi//sub n/ is required to asymptotically vanish (i.e., lim/sub n/spl rarr//spl infin///spl epsi//sub n/=0), whereas in the context of variable-length source coding the probability of error /spl epsi//sub n/ is required to be exactly zero (i.e., /spl epsi//sub n/=0/spl forall/n=1, 2, ...). In contrast to these, we consider the problem of variable-length source coding with asymptotically vanishing probability of error (i.e., lim/sub n/spl rarr//spl infin///spl epsi//sub n/=0), and establish several fundamental theorems on this new subject.
Given a general source X={X(n)}(n=1)({infinity} ), source coding is characterized by a pair ({phi}(n), psi(n)) of encoder {phi}(n), and decoder psi(n ), together with the probability of error epsilon(n)=Pr{psi(n)({phi}(n)(X(n )))(not equal to)X(n)}. If the length of the encoder output {phi} (n)(X(n)) is fixed, then it is called fixed-length source coding, while if the length of the encoder output {phi}(n )(X(n)) is variable, then it is called variable-length source coding. Usually, in the context of fixed-length source coding the probability of error epsilon(n) is required to asymptotically vanish (i.e., lim(n- > {infinity})epsilon(n)=0), whereas in the context of variable-length source coding the probability of error epsilon(n) is required to be exactly zero (i.e., epsilon(n )=0∀n=1, 2, ...). In contrast to these, we consider the problem of variable-length source coding with asymptotically vanishing probability of error (i.e., lim(n- > {infinity})epsilon(n )=0), and establish several fundamental theorems on this new subject
This work focuses on a new type of variable-length source coding for the general source X with countably infinite source alphabet X. Based on this coding scheme, several new fundamental theorems on this subject are established.
Author Te Sun Han
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10.1109/18.256486
10.1002/0471200611
10.1002/j.1538-7305.1948.tb00917.x
10.1109/18.45282
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Snippet Given a general source X={X/sup n/}/sub n=1//sup /spl infin//, source coding is characterized by a pair (/spl phi//sub n/, /spl psi//sub n/) of encoder /spl...
This work focuses on a new type of variable-length source coding for the general source X with countably infinite source alphabet X. Based on this coding...
Given a general source X={X(n)}(n=1)({infinity} ), source coding is characterized by a pair ({phi}(n), psi(n)) of encoder {phi}(n), and decoder psi(n ),...
Given a general source X={X super(n)} sub(n=1) super( infinity ), source coding is characterized by a pair ( phi sub(n), psi sub(n)) of encoder phi sub(n), and...
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StartPage 1217
SubjectTerms Asymptotic properties
Coders
Coding
Decoders
Encoders
Errors
Information theory
Source coding
Theorems
Title Weak variable-length source coding
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