Coding Bounds for Multiple Phased-Burst Correction and Single Burst Correction Codes

TL;DR

This paper introduces two new upper bounds on the achievable code rate for linear block codes capable of correcting multiple phased bursts, extending existing bounds and providing insights into burst correction capabilities.

Contribution

It presents novel upper bounds for MPBC codes, including one that generalizes the Abramson bound for single burst correction, enhancing understanding of code rate limits.

Findings

First bound constrained by maximum cyclic burst length

Second bound without minimum error free gap constraint

Comparison shows differences in code rate limits

Abstract

In this paper, two upper bounds on the achievable code rate of linear block codes for multiple phased-burst correction (MPBC) are presented. One bound is constrained to a maximum correctable cyclic burst length within every subblock, or equivalently a constraint on the minimum error free length or gap within every phased-burst. This bound, when reduced to the special case of a bound for single burst correction (SBC), is shown to be the Abramson bound when the cyclic burst length is less than half the block length. The second MPBC bound is developed without the minimum error free gap constraint and is used as a comparison to the first bound.