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$m$ -ary Balanced Codes With Parallel Decoding.
- Source :
-
IEEE Transactions on Information Theory . Jun2015, Vol. 61 Issue 6, p3251-3264. 14p. - Publication Year :
- 2015
-
Abstract
- An m -ary block code, m=2,3,4,\ldots , of length n \!\in \! \mathbfI\!\mathbfI\mskip -7mu\mathbfN 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 \left \lfloor (m-1)n/2 \right \rfloor . 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 Knuthâs complementation method with parallel decoding. Let indicate the number of m -ary words of length n and weight . For any m \!\in \! {\mathbf{I}}\!{\mathbf{I}}\mskip -7mu{\mathbf{N}} , m\geq 2 , a simple implementation of the method is given which uses r \!\in \! \mathbfI\!\mathbfI\mskip -7mu\mathbfN check digits to balance k\leq \\binomr \left \lfloor (m-1)r/2 \right \rfloor \vphantom {RRm-\{m\bmod {2}+[(m-1)k]\bmod 2\}\}/(m-1) information digits with an encoding time complexity of O(mk\log mk) digit operations. A refined implementation of the parallel decoding method is also given with r check digits and k\leq (m^{r}-1)/(m-1) information digits, where the encoding time complexity is O(k\sqrt {\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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 61
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 102771777
- Full Text :
- https://doi.org/10.1109/TIT.2015.2429139