-Ary Distributed Arithmetic Coding for Uniform -Ary Sources

Abstract

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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -ary DAC for uniform <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -ary DAC achieves significantly better performance than LDPC codes for distributed coding of uniform <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -ary sources with Laplace-distributed correlation.