On m-ary balanced codes with parallel decoding

TitleOn m-ary balanced codes with parallel decoding
Publication TypeConference Paper
Year of Publication2010
AuthorsPelusi, D., L. G. Tallini, and B. Bose
Conference Name2010 IEEE International Symposium on Information Theory - ISIT2010 IEEE International Symposium on Information Theory
Pagination1305 - 1309
Date Published06/2010
PublisherIEEE
Conference LocationAustin, TX
ISBN Number978-1-4244-7891-0
Keywordsbalanced codes, Knuth’s complementation method, m-ary alphabet, optical and magnetic recording, parallel decoding scheme, unidirectional error detection
Abstract

An m-ary block code, m = 2, 3, 4, ..., of length n ∈ IN is called balanced if, and only if, every codeword is balanced; that is, the real sum of the codeword components, or weight, is equal to ⌊(m - 1)n/2⌋. This paper presents a tight generalization of Knuth's complementation method with parallel (hence, fast) decoding scheme. Let (wn)m indicate the number of m-ary words of length n and weight w ∈ {0, 1, ..., (m-1)n}. A simple implementation of the scheme uses (m - 1)k + m mod 2 balancing functions to make a k ∈ IN digit information word to be balanced. So, r ∈ IN check digits can be used to balance k ≤ [(⌊(m-1)r r/2⌋)m -m mod 2]/(m - 1) information digits. A refined implementation of the parallel decoding scheme uses r check digits to balance k ≤ (mr -1)/(m-1) information digits.

DOI10.1109/ISIT.2010.5513733