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Register a new userAnalysis of Saturated Belief Propagation Decoding of Low-Density Parity-Check Codes
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Shrinivas Kudekar Mr.
Publication date
2014
fields
Informatics Engineering
and research's language is
English
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We consider the effect of log-likelihood ratio saturation on belief propagation decoder low-density parity-check codes. Saturation is commonly done in practice and is known to have a significant effect on error floor performance. Our focus is on threshold analysis and stability of density evolution. We analyze the decoder for standard low-density parity-check code ensembles and show that belief propagation decoding generally degrades gracefully with saturation. Stability of density evolution is, on the other hand, rather strongly effected by saturation and the asymptotic qualitative effect of saturation is similar to reduction by one of variable node degree. We also show under what conditions the block threshold for the saturated belief propagation corresponds with the bit threshold.
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Algebraic codes such as BCH code are receiving renewed interest as their short block lengths and low/no error floors make them attractive for ultra-reliable low-latency communications (URLLC) in 5G wireless networks. This paper aims at enhancing the traditional adaptive belief propagation (ABP) decoding, which is a soft-in-soft-out (SISO) decoding for high-density parity-check (HDPC) algebraic codes, such as Reed-Solomon (RS) codes, Bose-Chaudhuri-Hocquenghem (BCH) codes, and product codes. The key idea of traditional ABP is to sparsify certain columns of the parity-check matrix corresponding to the least reliable bits with small log-likelihood-ratio (LLR) values. This sparsification strategy may not be optimal when some bits have large LLR magnitudes but wrong signs. Motivated by this observation, we propose a Perturbed ABP (P-ABP) to incorporate a small number of unstable bits with large LLRs into the sparsification operation of the parity-check matrix. In addition, we propose to apply partial layered scheduling or hybrid dynamic scheduling to further enhance the performance of P-ABP. Simulation results show that our proposed decoding algorithms lead to improved error correction performances and faster convergence rates than the prior-art ABP variants.
A product code with single parity-check component codes can be described via the tools of a multi-kernel polar code, where the rows of the generator matrix are chosen according to the constraints imposed by the product code construction. Following this observation, successive cancellation decoding of such codes is introduced. In particular, the error probability of single parity-check product codes over binary memoryless symmetric channels under successive cancellation decoding is characterized. A bridge with the analysis of product codes introduced by Elias is also established for the binary erasure channel. Successive cancellation list decoding of single parity-check product codes is then described. For the provided example, simulations over the binary input additive white Gaussian channel show that successive cancellation list decoding outperforms belief propagation decoding applied to the code graph. Finally, the performance of the concatenation of a product code with a high-rate outer code is investigated via distance spectrum analysis. Examples of concatenations performing within $0.7$ dB from the random coding union bound are provided.
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Mustafa Cemil Coc{s}kun
, Gianluigi Liva
, Alexandre Graell i Amat andn Michael Lentmaier
2017
We introduce successive cancellation (SC) decoding of product codes (PCs) with single parity-check (SPC) component codes. Recursive formulas are derived, which resemble the SC decoding algorithm of polar codes. We analyze the error probability of SPC-PCs over the binary erasure channel under SC decoding. A bridge with the analysis of PCs introduced by Elias in 1954 is also established. Furthermore, bounds on the block error probability under SC decoding are provided, and compared to the bounds under the original decoding algorithm proposed by Elias. It is shown that SC decoding of SPC-PCs achieves a lower block error probability than Elias decoding.
Consider transmission over a binary additive white gaussian noise channel using a fixed low-density parity check code. We consider the posterior measure over the code bits and the corresponding correlation between two codebits, averaged over the noise realizations. We show that for low enough noise variance this average correlation decays exponentially fast with the graph distance between the code bits. One consequence of this result is that for low enough noise variance the GEXIT functions (further averaged over a standard code ensemble) of the belief propagation and optimal decoders are the same.
An efficient decoding algorithm for horizontally u-interleaved LRPC codes is proposed and analyzed. Upper bounds on the decoding failure rate and the computational complexity of the algorithm are derived. It is shown that interleaving reduces the decoding failure rate exponentially in the interleaving order u whereas the computational complexity grows linearly.
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