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Center for Nonlinear Studies |
The talk considers repeat multiple accumulate (RMA) codes which are obtained by serially concatenating a repetition code with two or more accumulators. Such a code has the advantage of a very low encoding complexity and is therefore well suited for error correction in power limited environments, for example in sensor or ad-hoc networks. Decoding can be either carried out by using belief propagation (BP) on a graph or via iterative decoding. Furthermore, it has been shown that for RMA codes the resulting ensemble is asymptotically good and exhibits minimum distance growing linearly with block length if the number of accumulators is at least two. Recently, for LDPC codes, the notion of trapping sets has been introduced to estimate the performance of these codes under polynomial time decoding schemes as BP. In this talk, we address similar questions for the RMA ensemble. First, we consider simple Zyablov-Pinsker bitflipping decoding on the RMA graph and derive asymptotic expressions for the normalized minimum trapping distance. In particular, we answer the question whether the minimum trapping distance for the RMA ensemble exhibits asymptotic growth with block length. Then, we consider BP decoding and present a closed form finite length ensemble average trapping set enumerator for repeat multiple accumulate codes by creating a trellis representation of trapping sets. For this case, we also obtain asymptotic expressions and evaluate them numerically. Finally, we briefly consider the effect of absorbing sets on the decoder performance.
Host: Misha Chertkov