Codebook cardinality spectrum of distributed arithmetic codes for stationary memoryless binary sources

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Abstract

It was demonstrated that, as a nonlinear implementation of Slepian-Wolf Coding, Distributed Arithmetic Coding (DAC) outperforms traditional Low-Density Parity-Check (LPDC) codes for short code length and biased sources. This fact triggers research efforts into theoretical analysis of DAC. In our previous work, we proposed two analytical tools, Codebook Cardinality Spectrum (CCS) and Hamming Distance Spectrum, to analyze DAC for independent and identically-distributed (i.i.d.) binary sources with uniform distribution. This article extends our work on CCS from uniform i.i.d. binary sources to biased i.i.d. binary sources. We begin with the final CCS and then deduce each level of CCS backwards by recursion. The main finding of this article is that the final CCS of biased i.i.d. binary sources is not uniformly distributed over [0, 1). This article derives the final CCS of biased i.i.d. binary sources and proposes a numerical algorithm for calculating CCS effectively in practice. All theoretical analyses are well verified by experimental results.

Original languageEnglish
Pages (from-to)6580-6596
Number of pages17
JournalIEEE Transactions on Information Theory
Volume66
Issue number10
Early online date7 Aug 2020
DOIs
Publication statusPublished - Oct 2020

Keywords

  • distributed source coding
  • Slepian-Wolf coding
  • distributed arithmetic coding
  • codebook cardinality spectrum
  • biased sources

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