Variable Length Encoding of Binary Memoryless Sources with a Fidelity Measure

Abstract

This concise paper deals with variable length source coding for binary memoryless sources with a fidelity criterion. The encoding scheme under consideration is an ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M_{c}, N, K</tex> ) code consisting of a distortionless run-length inner code of size M <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> and an outer code that maps each source vector of length <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> to a codeword of length less than or equal to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</tex> . The encoding of the outer code is accomplished by means of a trellis search, and the distortion measure used is a Hamming distance. For composite binary memoryless sources an adaptive ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M_{c}, N</tex> ) code can be constructed by varying the constraint <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</tex> on codeword length according to the source statistics. The ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M_{c}, N, K</tex> ), and ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M_{c}, N</tex> ) codes are insensitive to the inaccuracy in estimating the source probabilities. Rate-distortion curves, obtained by computer simulation, are plotted along with the theoretical rate-distortion function <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R(D)</tex> .