Short Huffman Codes Producing 1s Half of the Time

TL;DR

This paper introduces half Huffman coding, a simple permutation method that makes Huffman code outputs have a 50% frequency of 1s, improving compatibility with channel assumptions without sacrificing compression efficiency.

Contribution

The paper proposes half Huffman coding, a permutation technique that adjusts Huffman codes to produce more balanced bit streams while maintaining optimal compression.

Findings

Half Huffman coding increases the frequency of 1s to about 50%.

Applying halfHc improves overall system performance over conventional Huffman coding.

The method preserves compression efficiency while balancing output bits.

Abstract

The design of the channel part of a digital communication system (e.g., error correction, modulation) is heavily based on the assumption that the data to be transmitted forms a fair bit stream. However, simple source encoders such as short Huffman codes generate bit streams that poorly match this assumption. As a result, the channel input distribution does not match the original design criteria. In this work, a simple method called half Huffman coding (halfHc) is developed. halfHc transforms a Huffman code into a source code whose output is more similar to a fair bit stream. This is achieved by permuting the codewords such that the frequency of 1s at the output is close to 0.5. The permutations are such that the optimality in terms of achieved compression ratio is preserved. halfHc is applied in a practical example, and the resulting overall system performs better than when conventional Huffman coding is used.