Bounds and Codes for General Phased Burst Errors

TL;DR

This paper develops a comprehensive framework for analyzing and constructing codes capable of correcting phased burst errors, considering detailed error structures and providing bounds and asymptotically good code constructions.

Contribution

It introduces a fine-grained approach to PBE correction, models PBEs as adversarial errors, and constructs asymptotically good codes, extending classical methods.

Findings

Derived bounds on code sizes for PBE correction

Analyzed PBE-correction capabilities of generalized concatenated codes

Constructed asymptotically good PBE-correcting codes

Abstract

Phased burst errors (PBEs) are bursts of errors occurring at one or more known locations. The correction of PBEs is a classical topic in coding theory, with prominent applications such as the design of array codes for memory systems or distributed storage. We propose a general yet fine-grained approach to this problem, accounting not only for the number of bursts but also the error structure in each burst. By modeling PBEs as an error set in an adversarial channel, we investigate bounds on the maximal size of codes that can correct them. The PBE-correction capability of generalized concatenated codes is analyzed, and asymptotically good PBE-correcting codes are constructed, recovering a classical construction in a specific problem instance.