On Multi-Channel Huffman Codes for Asymmetric-Alphabet Channels

TL;DR

This paper explores multi-channel source coding over asymmetric channels, demonstrating that multi-channel Huffman codes can outperform single-channel codes in compression efficiency, and proposing a practical suboptimal code construction.

Contribution

It introduces the concept of multi-channel Huffman codes for asymmetric channels, extending classical single-channel results, and provides a suboptimal construction with guaranteed redundancy bounds.

Findings

Multi-channel Huffman codes are optimal tree-decodable codes.

Finding efficient multi-channel Huffman codes may be computationally hard.

A suboptimal code construction guarantees redundancy no worse than optimal single-channel codes.

Abstract

Zero-error single-channel source coding has been studied extensively over the past decades. Its natural multi-channel generalization is however not well investigated. While the special case with multiple symmetric-alphabet channels was studied a decade ago, codes in such setting have no advantage over single-channel codes in data compression, making them worthless in most applications. With essentially no development since the last decade, in this paper, we break the stalemate by showing that it is possible to beat single-channel source codes in terms of compression assuming asymmetric-alphabet channels. We present the multi-channel analog of several classical results in single-channel source coding, such as that a multi-channel Huffman code is an optimal tree-decodable code. We also show some evidences that finding an efficient construction of multi-channel Huffman codes may be hard. Nevertheless, we propose a suboptimal code construction whose redundancy is guaranteed to be no larger than that of an optimal single-channel source code.