Moment balancing templates: constructions to add insertion/deletion correction capability to error correcting or constrained codes

Authors:
Hendrik C. Ferreira;Khaled A. S. Abdel-Ghaffar;Ling Cheng;Theo G. Swart;Khmaies Ouahada
Affiliations:
Department of Electrical and Electronic Engineering Science, University of Johannesburg, Auckland Park, South Africa;Department of Electrical and Computer Engineering, University of California, Davis, CA;Department of Electrical and Electronic Engineering Science, University of Johannesburg, Auckland Park, South Africa;Department of Electrical and Electronic Engineering Science, University of Johannesburg, Auckland Park, South Africa;Department of Electrical and Electronic Engineering Science, University of Johannesburg, Auckland Park, South Africa
Venue:
IEEE Transactions on Information Theory
Year:
2009

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Abstract

Templates are constructed to extend arbitrary additive error correcting or constrained codes, i.e., additional redundant bits are added in selected positions to balance the moment of the codeword. The original codes may have error correcting capabilities or constrained output symbols as predetermined by the usual communication system considerations, which are retained after extending the code. Using some number theoretic constructions in the literature, insertion/deletion correction can then be achieved. If the template is carefully designed, the number of additional redundant bits for the insertion/deletion correction can be kept small--in some cases of the same order as the number of parity bits in a Hamming code of comparable length.