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On L_1 distance error control codes

TitleOn L_1 distance error control codes
Publication TypeConference Paper
Year of Publication2011
AuthorsTallini, L. G., and B. Bose
Conference Name2011 IEEE International Symposium on Information Theory - ISIT
Pagination1061 - 1065
Date Published08/2011
Conference LocationSt. Petersburg, Russia
ISBN Number978-1-4577-0596-0
Keywordsasymmetric/unidirectional/symmetric errors, error control codes, flash memories, insertion and deletion errors, m-ary alphabet, repetition errors, z-channel

This paper gives some theory and design of efficient codes capable of controlling (i. e., correcting/detecting/correcting erasure) errors measured under the L₁ distance defined over m-ary words, 2 ≤ m ≤ +∞. We give the combinatorial characterizations of such codes, some general code designs and the efficient decoding algorithms. Then, we give a class of linear and systematic m-ary codes, m = sp with s∈IN and p a prime, which are capable of controlling d ≤ p-1 errors. If n and k∈IN are respectively the length and dimension of a BCH code over GF(p) with minimum Hamming distance d + 1 then the new codes have length n and k' = k + r logm s information digits.