Error-Correcting Weakly Constrained Codes: Constructions and Achievable Rates

TL;DR

This paper introduces new constructions for weakly constrained codes, achieving capacity and positive rates with linear minimum distance, and offers practical encoding and decoding methods.

Contribution

It presents a capacity-achieving code construction based on Eulerian cycles and a practical concatenated code scheme with polynomial-time algorithms.

Findings

Capacity-achieving weakly constrained code construction

Codes with linear minimum distance and positive rate

Practical encoding and decoding algorithms

Abstract

We investigate weakly constrained codes, in which specific patterns occur with prescribed frequencies rather than being strictly forbidden as in conventional constrained coding. We propose a capacity-achieving construction of a weakly constrained codebook based on Eulerian cycles. We then obtain, via expurgation, weakly constrained codes with linear minimum distance and positive rate, and analyze the rates achievable. Finally, we propose a practical concatenated code construction that supports polynomial-time encoding and decoding.