Design of Non-Binary Quasi-Cyclic LDPC Codes by ACE Optimization

An algorithm for constructing Tanner graphs of non-binary irregular quasi-cyclic LDPC codes is introduced. It employs a new method for selection of edge labels allowing control over the code's non-binary ACE spectrum and resulting in low error-floor. The efficiency of the algorithm is demonstrated by generating good codes of short to moderate length over small fields, outperforming codes generated by the known methods.Comment: Accepted to 2013 IEEE Information Theory Worksho

Performance of polar codes for quantum and private classical communication

We analyze the practical performance of quantum polar codes, by computing rigorous bounds on block error probability and by numerically simulating them. We evaluate our bounds for quantum erasure channels with coding block lengths between 2^10 and 2^20, and we report the results of simulations for quantum erasure channels, quantum depolarizing channels, and "BB84" channels with coding block lengths up to N = 1024. For quantum erasure channels, we observe that high quantum data rates can be achieved for block error rates less than 10^(-4) and that somewhat lower quantum data rates can be achieved for quantum depolarizing and BB84 channels. Our results here also serve as bounds for and simulations of private classical data transmission over these channels, essentially due to Renes' duality bounds for privacy amplification and classical data transmission of complementary observables. Future work might be able to improve upon our numerical results for quantum depolarizing and BB84 channels by employing a polar coding rule other than the heuristic used here.Comment: 8 pages, 6 figures, submission to the 50th Annual Allerton Conference on Communication, Control, and Computing 201

On Maximum Contention-Free Interleavers and Permutation Polynomials over Integer Rings

An interleaver is a critical component for the channel coding performance of turbo codes. Algebraic constructions are of particular interest because they admit analytical designs and simple, practical hardware implementation. Contention-free interleavers have been recently shown to be suitable for parallel decoding of turbo codes. In this correspondence, it is shown that permutation polynomials generate maximum contention-free interleavers, i.e., every factor of the interleaver length becomes a possible degree of parallel processing of the decoder. Further, it is shown by computer simulations that turbo codes using these interleavers perform very well for the 3rd Generation Partnership Project (3GPP) standard.Comment: 13 pages, 2 figures, submitted as a correspondence to the IEEE Transactions on Information Theory, revised versio

Variable-to-Fixed Length Homophonic Coding Suitable for Asymmetric Channel Coding

In communication through asymmetric channels the capacity-achieving input distribution is not uniform in general. Homophonic coding is a framework to invertibly convert a (usually uniform) message into a sequence with some target distribution, and is a promising candidate to generate codewords with the nonuniform target distribution for asymmetric channels. In particular, a Variable-to-Fixed length (VF) homophonic code can be used as a suitable component for channel codes to avoid decoding error propagation. However, the existing VF homophonic code requires the knowledge of the maximum relative gap of probabilities between two adjacent sequences beforehand, which is an unrealistic assumption for long block codes. In this paper we propose a new VF homophonic code without such a requirement by allowing one-symbol decoding delay. We evaluate this code theoretically and experimentally to verify its asymptotic optimality.Comment: Full version of the paper to appear in 2017 IEEE International Symposium on Information Theory (ISIT2017