-Ary Distributed Arithmetic Coding for Uniform -Ary Sources

Laplacian distribution is widely used to model the differences between correlated continuous or nonbinary signals, e.g., the predictive residues of videos. Usually, distributed coding of correlated nonbinary sources, e.g., distributed video coding, is implemented by binary or nonbinary Low-Density Parity-Check (LDPC) codes. In this paper, as an alternative, we attempt using nonbinary Distributed Arithmetic Coding (DAC) to implement distributed coding of uniform nonbinary sources with Laplace-distributed correlation. To analyze $Q$ -ary DAC for uniform $Q$ -ary sources, following the methodology developed in our prior work for binary DAC, we define and deduce Coset Cardinality Spectrum (CCS) from both fixed-length and variable-length perspectives, whose physical meanings are explained in detail; while for binary DAC, our prior work totally ignored the subtle difference between these two perspectives. Compared with binary DAC, an important advantage of nonbinary DAC is that, the mapping from source symbols to coding intervals is so flexible that there are many parameters that can be tuned to achieve better performance; while for binary DAC, there are very few tunable parameters, making it very hard to achieve better performance. This paper proposes a simple method to map source symbols onto coding intervals, which results in a very lightweight codec, while possessing a good Manhattan distance distribution. Then this paper deduces the formula of path metrics for decoder design by making use of CCS. All theoretical analyses are perfectly verified by simulation results. Most important, experimental results show that $Q$ -ary DAC achieves significantly better performance than LDPC codes for distributed coding of uniform $Q$ -ary sources with Laplace-distributed correlation.

I. Introduction

An important branch of network information theory is Distributed Source Coding (DSC), which includes two (lossless and lossy) forms. In this paper, we are interested in lossless DSC, i.e., the so-called Slepian-Wolf coding (SWC) [1], whose theoretical foundation can be summarized as below. Let and be two correlated discrete random variables. If and are separately encoded and jointly decoded, then the achievable rates are lower bounded by , , and [1]. Different from traditional source coding, SWC is actually equivalent to channel coding in essence [2], [3], [4], so naturally it can be implemented with channel codes, e.g., Turbo codes [5], Low-Density Parity-Check (LDPC) codes [6], and polar codes [7]. However, since channel codes are originally designed for the purpose of error correction, they may not be well suited to data compression for several reasons. First, contemporary channel codes listed above are usually binary, while real-world sources are typically nonbinary. For example, each pixel of an image or a video frame is usually represented by 8 bits. Even though a nonbinary source can be split into several bitplanes, it is awkward to make use of inter-bitplane correlation [8], [9]. Another reason is that, the statistical feature of a real-world source is usually time-varying, while it is difficult to adapt channel codes to nonstationary source characteristics.