On the Construction and Decoding of Concatenated Polar Codes

A scheme for concatenating the recently invented polar codes with interleaved block codes is considered. By concatenating binary polar codes with interleaved Reed-Solomon codes, we prove that the proposed concatenation scheme captures the capacity-achieving property of polar codes, while having a significantly better error-decay rate. We show that for any $\epsilon > 0$, and total frame length $N$, the parameters of the scheme can be set such that the frame error probability is less than $2^{-N^{1-\epsilon}}$, while the scheme is still capacity achieving. This improves upon 2^{-N^{0.5-\eps}}, the frame error probability of Arikan's polar codes. We also propose decoding algorithms for concatenated polar codes, which significantly improve the error-rate performance at finite block lengths while preserving the low decoding complexity

Design and optimization of joint iterative detection and decoding receiver for uplink polar coded SCMA system

SCMA and polar coding are possible candidates for 5G systems. In this paper, we firstly propose the joint iterative detection and decoding (JIDD) receiver for the uplink polar coded sparse code multiple access (PC-SCMA) system. Then, the EXIT chart is used to investigate the performance of the JIDD receiver. Additionally, we optimize the system design and polar code construction based on the EXIT chart analysis. The proposed receiver integrates the factor graph of SCMA detector and polar soft-output decoder into a joint factor graph, which enables the exchange of messages between SCMA detector and polar decoder iteratively. Simulation results demonstrate that the JIDD receiver has better BER performance and lower complexity than the separate scheme. Specifically, when polar code length N=256 and code rate R=1/2 , JIDD outperforms the separate scheme 4.8 and 6 dB over AWGN channel and Rayleigh fading channel, respectively. It also shows that, under 150% system loading, the JIDD receiver only has 0.3 dB performance loss compared to the single user uplink PC-SCMA over AWGN channel and 0.6 dB performance loss over Rayleigh fading channel

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