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

Fang, Yong and Stankovic, Vladimir (2020) Codebook cardinality spectrum of distributed arithmetic codes for stationary memoryless binary sources. IEEE Transactions on Information Theory. ISSN 0018-9448

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    Abstract

    It was demonstrated that, as a nonlinear implementation of Slepian-Wolf Coding (SWC), 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 (HDS), to analyze DAC for Stationary Memoryless Binary Sources (SMBS) with uniform distribution. This paper extends our work on CCS from uniform SMBS to biased SMBS. We begin with the final CCS and then deduce each level of CCS backwards by recursion. The main finding of this paper is that the final CCS of biased SMBS is not uniformly distributed over [0; 1). This paper derives the final CCS of biased SMBS and proposes a numerical algorithm for calculating CCS effectively in practice. All theoretical analyses are well verified by experimental results.