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

A Novel Interleaving Scheme for Polar Codes

It's known that the bit errors of polar codes with successive cancellation (SC) decoding are coupled. We call the coupled information bits the correlated bits. In this paper, concatenation schemes are studied for polar codes (as inner codes) and LDPC codes (as outer codes). In a conventional concatenation scheme, to achieve a better BER performance, one can divide all $N_l$ bits in a LDPC block into $N_l$ polar blocks to completely de-correlate the possible coupled errors. In this paper, we propose a novel interleaving scheme between a LDPC code and a polar code which breaks the correlation of the errors among the correlated bits. This interleaving scheme still keeps the simple SC decoding of polar codes while achieves a comparable BER performance at a much smaller delay compared with a $N_l$-block delay scheme

Polar Coding for the Large Hadron Collider: Challenges in Code Concatenation

In this work, we present a concatenated repetition-polar coding scheme that is aimed at applications requiring highly unbalanced unequal bit-error protection, such as the Beam Interlock System of the Large Hadron Collider at CERN. Even though this concatenation scheme is simple, it reveals significant challenges that may be encountered when designing a concatenated scheme that uses a polar code as an inner code, such as error correlation and unusual decision log-likelihood ratio distributions. We explain and analyze these challenges and we propose two ways to overcome them.Comment: Presented at the 51st Asilomar Conference on Signals, Systems, and Computers, November 201