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

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

Analysis on tailed distributed arithmetic codes for uniform binary sources

Distributed Arithmetic Coding (DAC) is a variant of Arithmetic Coding (AC) that can realise Slepian-Wolf Coding (SWC) in a nonlinear way. In the previous work, we defined Codebook Cardinality Spectrum (CCS) and Hamming Distance Spectrum (HDS) for DAC. In this paper, we make use of CCS and HDS to analyze tailed DAC, a form of DAC mapping the last few symbols of each source block onto non-overlapped intervals as traditional AC. We first derive the exact HDS formula for tailless DAC, a form of DAC mapping all symbols of each source block onto overlapped intervals, and show that the HDS formula previously given is actually an approximate version. Then the HDS formula is extended to tailed DAC. We also deduce the average codebook cardinality, which is closely related to decoding complexity, and rate loss of tailed DAC with the help of CCS. The effects of tail length are extensively analyzed. It is revealed that by increasing tail length to a value not close to the bitstream length, closely-spaced codewords within the same codebook can be removed at the cost of a higher decoding complexity and a larger rate loss. Finally, theoretical analyses are verified by experiments

Hamming distance spectrum of DAC codes for equiprobable binary sources

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 unequal-size 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

Distributed joint source-channel arithmetic coding

We address distributed source coding with decoder side information, when the decoder observes the source through a noisy channel. Existing approaches employ syndromeor parity-based channel codes. We propose a new approach based on distributed arithmetic coding (DAC).We introduce a DAC with forbidden symbol, which allows to tune the redundancy according to the amount of channel noise. We propose a novel sequential decoder that employs the known side information to decode the corrupted codeword. Experimental results show that the proposed scheme is better than parity-based turbo codes at relatively short block length