Good concatenated code ensembles for the binary erasure channel
IEEE Journal on Selected Areas in Communications - Special issue on capaciyy approaching codes
Serial concatenation of interleaved codes: performance analysis, design, and iterative decoding
IEEE Transactions on Information Theory
Finite-length analysis of low-density parity-check codes on the binary erasure channel
IEEE Transactions on Information Theory
The serial concatenation of rate-1 codes through uniform random interleavers
IEEE Transactions on Information Theory
Turbo Decoding on the Binary Erasure Channel: Finite-Length Analysis and Turbo Stopping Sets
IEEE Transactions on Information Theory
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In this work, we consider a stopping set analysis of repeat multiple-accumulate (RMA) code ensembles formed by the serial concatenation of a repetition code with multiple accumulators. The RMA codes are assumed to be iteratively decoded in a constituent code oriented fashion using maximum a posteriori erasure correction in the constituent codes. We give stopping set enumerators for RMA code ensembles and show that their stopping distance hmin, defined as the size of the smallest nonempty stopping set, asymptotically grows linearly with the block length. Thus, the RMA code ensembles are good for the binary erasure channel. Furthermore, it is shown that, contrary to the asymptotic minimum distance dmin, whose growth rate coefficient increases with the number of accumulate codes, the hmin growth rate coefficient diminishes with the number of accumulators. We also consider random puncturing and show that for sufficiently high code rates, the asymptotic hmin does not grow linearly with the block length, contrary to the asymptotic dmin, whose growth rate coefficient approaches the Gilbert-Varshamov bound as the rate increases. Finally, we give iterative decoding thresholds to show the convergence properties.