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.Comment: in IEEE Wireless Commun. and Networking Conf. (WCNC), April 201

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.Comment: in IEEE International Conference on Communications (ICC), May 201