Hamming Distance Spectrum of DAC Codes for Equiprobable Binary Sources

Abstract

This version is available at https://strathprints.strath.ac.uk/55413/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output. Abstract-Distributed Arithmetic Coding (DAC) is an effective technique for implementing Slepian-Wolf coding (SWC). It has been shown that a DAC code partitions source space into unequalsize codebooks, so that the overall performance of DAC codes depends on the cardinality and structure of these codebooks. The problem of DAC codebook cardinality has been solved by the so-called Codebook Cardinality Spectrum (CCS). This paper extends the previous work on CCS by studying the problem of DAC codebook structure. We define Hamming Distance Spectrum (HDS) to describe DAC codebook structure and propose a mathematical method to calculate the HDS of DAC codes. The theoretical analyses are verified by experimental results.

Analysis on Tailed Distributed Arithmetic Codes for Uniform Binary Sources

“…Another motivation for this paper comes from another recent finding, namely, though the HDS calculated by equation (46) in [20] usually coincides with experimental results very well, there is a large gap in the special case of d = n, where d is the Hamming distance and n is the code length. More concretely, for d = n, the value calculated by equation (46) in [20] is roughly half of the value obtained by experiments. It is important to explain this gap analytically.…”

“…The (n, R) DA code, which stands for a tailless DA code with length n and rate R ∈ (0, 1), partitions source space B n into 2 nR codebooks, where nR ∈ Z [20]. The DA encoder replaces each binary block x n ∈ B n with a codebook index m ∈ [0 : 2 nR ), which is realized via iteratively mapping source symbols onto partially-overlapped intervals.…”

“…It is easy to see that ψ n,R (d) is the average number of d-away fellow codewords for each codeword x n ∈ B n . We refer to ψ n,R (d) as the HDS of the (n, R) DA code [20], which is a function with respect to (w.r.t.) Hamming distance d that is parameterized by code length n and code rate R.…”

“…Based on CCS, two methods were proposed to improve DAC's performance in [19]. To study the distribution of inner-codebook Hamming distance, the concept of Hamming distance spectrum (HDS) was proposed for DAC in [20], where a calculation method was also developed.…”

“…First, we derive the exact HDS formula for tailless DAC and show that equation 46in [20] is in fact an approximate version of the exact HDS formula. Further, the HDS behavior in the special case of d = n is explained.…”