Information Theory, Inference & Learning Algorithms
Information Theory, Inference & Learning Algorithms
Spectra and minimum distances of repeat multiple-accumulate codes
IEEE Transactions on Information Theory
Improving the distance properties of turbo codes using a third component code: 3D turbo codes
IEEE Transactions on Communications
Serial concatenation of interleaved codes: performance analysis, design, and iterative decoding
IEEE Transactions on Information Theory
Good error-correcting codes based on very sparse matrices
IEEE Transactions on Information Theory
Efficient erasure correcting codes
IEEE Transactions on Information Theory
Coding theorems for turbo code ensembles
IEEE Transactions on Information Theory
Finite-length analysis of low-density parity-check codes on the binary erasure channel
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
The serial concatenation of rate-1 codes through uniform random interleavers
IEEE Transactions on Information Theory
Extrinsic information transfer functions: model and erasure channel properties
IEEE Transactions on Information Theory
Convergence Analysis and Optimal Scheduling for Multiple Concatenated Codes
IEEE Transactions on Information Theory
On the stopping distance and the stopping redundancy of codes
IEEE Transactions on Information Theory
An Upper Bound on the Minimum Distance of Serially Concatenated Convolutional Codes
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Turbo Decoding on the Binary Erasure Channel: Finite-Length Analysis and Turbo Stopping Sets
IEEE Transactions on Information Theory
Stopping Set Analysis of Iterative Row-Column Decoding of Product Codes
IEEE Transactions on Information Theory
Turbo decoding as an instance of Pearl's “belief propagation” algorithm
IEEE Journal on Selected Areas in Communications
Stopping set analysis of repeat multiple-accumulate codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 3
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In this work, we give good concatenated code ensembles for the binary erasure channel (BEC). In particular, we consider repeat multiple-accumulate (RMA) code ensembles formed by the serial concatenation of a repetition code with multiple accumulators, and the hybrid concatenated code (HCC) ensembles recently introduced by Koller et al. (5th Int. Symp. on Turbo Codes & Rel. Topics, Lausanne, Switzerland) consisting of an outer multiple parallel concatenated code serially concatenated with an inner accumulator. We introduce stopping sets for iterative constituent code oriented decoding using maximum a posteriori erasure correction in the constituent codes. We then analyze the asymptotic stopping set distribution for RMA and HCC 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, these code ensembles are good for the BEC. It is shown that for RMA code ensembles, 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 of RMA code ensembles 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 for the different code ensembles to compare the convergence properties.