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

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.Comment: Submitted to IEEE Globecom 201

Codes Correcting Phased Burst Erasures

We introduce a family of binary array codes of size t2n, correcting multiple phased burst erasures of size t. The codes achieve maximal correcting capability, i.e. being considered as codes over GF(2 t ) they are MDS. The length of the codes is n = P L `=1 0 t ` 1 , where L is a constant or is slowly growing in t. The complexity of encoding and decoding is proportional to rnmL, where r is the number of correctable erasures, and m is the smallest number such that 2 t = 1 modulo m. This compares favorably with the complexity of decoding codes obtained from the shortened general Reed-Solomon codes having the same parameters. 1 Introduction Let t 2 k bits of information be encoded in a t 2 n bit array, n ? k. Due to some reasons the data stored in several columns can be lost or corrupted. We assume that we know in which columns it has happened. The data they carry is said to be erased. Such erasures are also referred to as phased burst erasures. Our purpose now is to reconstruct ..