arXiv subjects

Ahmed Elkelesh

Publications and source records attributed to Ahmed Elkelesh.

21 records · Page 2Linked to original sources

arXiv2018

Scattered EXIT Charts for Finite Length LDPC Code Design

We introduce the Scattered Extrinsic Information Transfer (S-EXIT) chart as a tool for optimizing degree profiles of short length Low-Density Parity-Check (LDPC) codes under iterative decoding. As degree profile optimization is typically done in the asymptotic length regime, there is space for further improvement when considering the finite length behavior. We propose to consider the average extrinsic information as a random variable, exploiting its specific distribution properties for guiding code design. We explain, step-by-step, how to generate an S-EXIT chart for short-length LDPC codes. We show that this approach achieves gains in terms of bit error rate (BER) of 0.5 dB and 0.6 dB over the additive white Gaussian noise (AWGN) channel for codeword lengths of 128 and 180 bits, respectively, at a target BER of $10^{-4}$ when compared to conventional Extrinsic Information Transfer (EXIT) chart-based optimization. Also, a performance gain for the Binary Erasure Channel (BEC) for a block (i.e., codeword) length of 180 bits is shown.

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arXiv2018

Belief Propagation Decoding of Polar Codes on Permuted Factor Graphs

We show that the performance of iterative belief propagation (BP) decoding of polar codes can be enhanced by decoding over different carefully chosen factor graph realizations. With a genie-aided stopping condition, it can achieve the successive cancellation list (SCL) decoding performance which has already been shown to achieve the maximum likelihood (ML) bound provided that the list size is sufficiently large. The proposed decoder is based on different realizations of the polar code factor graph with randomly permuted stages during decoding. Additionally, a different way of visualizing the polar code factor graph is presented, facilitating the analysis of the underlying factor graph and the comparison of different graph permutations. In our proposed decoder, a high rate Cyclic Redundancy Check (CRC) code is concatenated with a polar code and used as an iteration stopping criterion (i.e., genie) to even outperform the SCL decoder of the plain polar code (without the CRC-aid). Although our permuted factor graph-based decoder does not outperform the SCL-CRC decoder, it achieves, to the best of our knowledge, the best performance of all iterative polar decoders presented thus far.

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arXiv2017

Mitigating Clipping Effects on Error Floors under Belief Propagation Decoding of Polar Codes

In this work, we show that polar belief propagation (BP) decoding exhibits an error floor behavior which is caused by clipping of the log-likelihood ratios (LLR). The error floor becomes more pronounced for clipping to smaller LLR-values. We introduce a single-value measure quantifying a "relative error floor", showing, by exhaustive simulations for different lengths, that the error floor is mainly caused by inadequate clipping values. We propose four modifications to the conventional BP decoding algorithm to mitigate this error floor behavior, demonstrating that the error floor is a decoder property, and not a code property. The results agree with the fact that polar codes are theoretically proven to not suffer from error floors. Finally, we show that another cause of error floors can be an improper selection of frozen bit positions.

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