# Variable-to-Fixed Length Homophonic Coding Suitable for Asymmetric Channel Coding

## TL;DR

This paper introduces a new variable-to-fixed length homophonic coding scheme that adapts to asymmetric channels by allowing a one-symbol decoding delay, eliminating the need for prior probability gap knowledge.

## Contribution

It proposes a novel VF homophonic code that does not require pre-known probability gaps, enhancing practicality for long block codes in asymmetric channels.

## Key findings

- The new code achieves asymptotic optimality.
- Theoretical analysis confirms the code's performance.
- Experimental results validate the code's effectiveness.

## Abstract

In communication through asymmetric channels the capacity-achieving input distribution is not uniform in general. Homophonic coding is a framework to invertibly convert a (usually uniform) message into a sequence with some target distribution, and is a promising candidate to generate codewords with the nonuniform target distribution for asymmetric channels. In particular, a Variable-to-Fixed length (VF) homophonic code can be used as a suitable component for channel codes to avoid decoding error propagation. However, the existing VF homophonic code requires the knowledge of the maximum relative gap of probabilities between two adjacent sequences beforehand, which is an unrealistic assumption for long block codes. In this paper we propose a new VF homophonic code without such a requirement by allowing one-symbol decoding delay. We evaluate this code theoretically and experimentally to verify its asymptotic optimality.