865 research outputs found
Low-Density Parity-Check Codes for Nonergodic Block-Fading Channels
We solve the problem of designing powerful low-density parity-check (LDPC)
codes with iterative decoding for the block-fading channel. We first study the
case of maximum-likelihood decoding, and show that the design criterion is
rather straightforward. Unfortunately, optimal constructions for
maximum-likelihood decoding do not perform well under iterative decoding. To
overcome this limitation, we then introduce a new family of full-diversity LDPC
codes that exhibit near-outage-limit performance under iterative decoding for
all block-lengths. This family competes with multiplexed parallel turbo codes
suitable for nonergodic channels and recently reported in the literature.Comment: Submitted to the IEEE Transactions on Information Theor
Good Concatenated Code Ensembles for the Binary Erasure Channel
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.Comment: To appear in IEEE Journal on Selected Areas in Communications,
special issue on Capacity Approaching Code
Binary Message Passing Decoding of Product Codes Based on Generalized Minimum Distance Decoding
We propose a binary message passing decoding algorithm for product codes
based on generalized minimum distance decoding (GMDD) of the component codes,
where the last stage of the GMDD makes a decision based on the Hamming distance
metric. The proposed algorithm closes half of the gap between conventional
iterative bounded distance decoding (iBDD) and turbo product decoding based on
the Chase--Pyndiah algorithm, at the expense of some increase in complexity.
Furthermore, the proposed algorithm entails only a limited increase in data
flow compared to iBDD.Comment: Invited paper to the 53rd Annual Conference on Information Sciences
and Systems (CISS), Baltimore, MD, March 2019. arXiv admin note: text overlap
with arXiv:1806.1090
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