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by Henry D. Pfister, Paul H. Siegel
in Proc. 37th Annual Allerton Conf. on Commun., Control, and Comp
http://vivaldi.ucsd.edu:8080/~pfister/papers/allerton1999.ps.gz
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Abstract:
Until the Repeat Accumulate codes of Divsalar, et al. [4], few people would have guessed that simple rate-1 codes could play a crucial role in the construction of "good" codes. In this paper, we will construct "good " linear block codes at any rate r 1 by serially concatenating an arbitrary outer code of rate r with a large number of rate-1 inner codes through uniform random interleavers. We derive the average output weight enumerator for this ensemble in the limit as the number of inner codes goes to infinity. Using a probabilistic upper bound on the minimum distance, we prove that long codes from this ensemble will achieve the Gilbert-Varshamov bound with high probability. Finally, by numerically evaluating the probabilistic upper bound, we observe that it is typically achieved with a small number of inner codes. 1
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