m -ary Balanced Codes With Parallel Decoding

An m-ary block code, m = 2, 3, 4,..., of length n ϵ 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 efficient encoding schemes to m-ary balanced codes with parallel (hence, f...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 61; no. 6; pp. 3251 - 3264
Main Authors: Pelusi, Danilo, Elmougy, Samir, Tallini, Luca G., Bose, Bella
Format: Journal Article
Language:English
Published: New York IEEE 01.06.2015
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Balanced codes
Coding theory
Combinatorics
Decoding
Electronics
Encoding
Frequency modulation
Indexes
Knuth's complementation method
m-ary alphabet
optical and magnetic recording
parallel decoding scheme
Redundancy
Time complexity
unidirectional error detection
optical and magnetic recording
Balanced codes
parallel decoding scheme
unidirectional error detection
m -ary alphabet
Knuth’s complementation method
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary:An m-ary block code, m = 2, 3, 4,..., of length n ϵ 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 efficient encoding schemes to m-ary balanced codes with parallel (hence, fast) decoding. In fact, the decoding time complexity is O(1) digit operations. These schemes are a generalization to the m-ary alphabet of Knuth's complementation method with parallel decoding. Let ( n w ) m indicate the number of m-ary words w of length n and weight w ϵ(0,1, ... , (m - 1)n}. For any m ϵ IN, m ≥ 2, a simple implementation of the method is given which uses r ϵ IN check digits to balance k ≤ {(⌊(m-1) r /2⌋) m - (m mod 2 + [(m - 1)k] mod 2}}/(m - 1) information digits with an encoding time complexity of O(mk log m k) digit operations. A refined implementation of the parallel decoding method is also given with r check digits and k ≤ (m r -1)/(m -1) information digits, where the encoding time complexity is O(k√log m k). Thus, the proposed codes are less redundant than the m-ary balanced codes with parallel decoding found in the literature and yet maintain the same complexity.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2015.2429139