Variable-to-Fixed Length Homophonic Coding with a Modified Shannon-Fano-Elias Code

TL;DR

This paper introduces a novel variable-to-fixed length homophonic coding method based on a modified Shannon-Fano-Elias code, improving coding rate and addressing error propagation issues in channel coding.

Contribution

It proposes the dual SFEG code for homophonic coding, enhancing robustness and efficiency over traditional FV codes, and demonstrates improved coding rate in lossless source coding.

Findings

Dual SFEG code achieves asymptotic optimality.

Modified SFE code outperforms original in coding rate.

Proposed methods mitigate error propagation in channel coding.

Abstract

Homophonic coding is a framework to reversibly convert a message into a sequence with some target distribution. This is a promising tool to generate a codeword with a biased code-symbol distribution, which is required for capacity-achieving communication by asymmetric channels. It is known that asymptotically optimal homophonic coding can be realized by a Fixed-to-Variable (FV) length code using an interval algorithm similar to a random number generator. However, FV codes are not preferable as a component of channel codes since a decoding error propagates to all subsequent codewords. As a solution for this problem an asymptotically optimal Variable-to-Fixed (VF) length homophonic code, dual Shannon-Fano-Elias-Gray (dual SFEG) code, is proposed in this paper. This code can be interpreted as a dual of a modified Shannon-Fano-Elias (SFE) code based on Gray code. It is also shown as a by-product that the modified SFE code, named SFEG code, achieves a better coding rate than the original SFE code in lossless source coding.