Non-restrictive MDS Array Codes for Correcting Multiple Column Erasures

Abstract

A new family of MDS array codes of size m × n, that we call Br (m, n, t), for correcting multiple column erasures is proposed. Br(m, n, t) codes achieve the maximum possible correcting capability, i.e., they are MDS codes with dmin = r + 1. The key novelty in Br(m, n, t) codes is that they can be constructed for all possible code length up to (2m–l)and for any column size; thus overcoming constrains on the code parameters of conventional array codes. Br(m, n, t) codes have a simple structure, which is based on exclusive-OR operations, avoiding computations over finite fields. Analytical results show that the complexity of the proposed decoding algorithm is proportional to rm2(n–l), where r is the number of correctable erasures, i.e., is more efficient than the Forney decoding algorithm for Reed-Solomon codes. The proposed code can be used in any system requiring large symbols, for instance multitrack magnetic recording and RAID systems.