Computer Science – Information Theory
Scientific paper
2011-01-31
Computer Science
Information Theory
The material in this paper was presented in part at the 6th International Symposium on Turbo Codes & Iterative Information Pro
Scientific paper
In this paper, we consider weighted nonbinary repeat multiple-accumulate (WNRMA) code ensembles obtained from the serial concatenation of a nonbinary rate-1/n repeat code and the cascade of L>= 1 accumulators, where each encoder is followed by a nonbinary random weighter. The WNRMA codes are assumed to be iteratively decoded using the turbo principle with maximum a posteriori constituent decoders. We derive the exact weight enumerator of nonbinary accumulators and subsequently give the weight enumerators for WNRMA code ensembles. We formally prove that the symbol-wise minimum distance of WNRMA code ensembles asymptotically grows linearly with the block length when L >= 3 and n >= 2, and L=2 and n >= 3, for all powers of primes q >= 3 considered, where q is the field size. Thus, WNRMA code ensembles are asymptotically good for these parameters. We also give iterative decoding thresholds, computed by an extrinsic information transfer chart analysis, on the q-ary symmetric channel to show the convergence properties. Finally, we consider the binary image of WNRMA code ensembles and compare the asymptotic minimum distance growth rates with those of binary repeat multiple-accumulate code ensembles.
Amat Alexandre Graell i.
Rosnes Eirik
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