On the Stopping Distance and Stopping Redundancy of Product Codes

Morteza HIVADI  Morteza ESMAEILI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E91-A    No.8    pp.2167-2173
Publication Date: 2008/08/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e91-a.8.2167
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Coding Theory
stopping set,  stopping distance,  stopping redundancy,  product code,  

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Stopping distance and stopping redundancy of product binary linear block codes is studied. The relationship between stopping sets in a few parity-check matrices of a given product code C and those in the parity-check matrices for the component codes is determined. It is shown that the stopping distance of a particular parity-check matrix of C, denoted Hp, is equal to the product of the stopping distances of the associated constituent parity-check matrices. Upper bounds on the stopping redundancy of C is derived. For each minimum distance d=2r, r≥ 1, a sequence of [n,k,d] optimal stopping redundancy binary codes is given such k/n tends to 1 as n tends to infinity.