Non-adaptive and two-stage coding over the Z-channel

TL;DR

This paper introduces new two-stage coding strategies for the Z-channel with noiseless feedback, improving upon existing results for small lengths and single errors, and develops an optimality condition for non-adaptive codes.

Contribution

It presents novel two-stage coding strategies with feedback for the Z-channel and introduces an optimality condition for non-adaptive codes, advancing coding theory.

Findings

Improved coding results for small length and 1 error cases.

Development of a new optimality condition for non-adaptive codes.

Enhanced coding strategies outperform previous full feedback methods.

Abstract

In this paper, we developed new coding strategies for the Z-channel. In particular, we look at the case with two-stage encoding. In this case, the encoder uses noiseless feedback once and adjusts the further encoding strategy based on the previous partial output of the channel. Nevertheless, the developed codes improve the known results with full feedback for small length and 1 error. A tool for the two-stage strategy is the development of a new optimality condition for non-adaptive codes.