On the performance of 1-level LDPC lattices

The low-density parity-check (LDPC) lattices perform very well in high dimensions under generalized min-sum iterative decoding algorithm. In this work we focus on 1-level LDPC lattices. We show that these lattices are the same as lattices constructed based on Construction A and low-density lattice-code (LDLC) lattices. In spite of having slightly lower coding gain, 1-level regular LDPC lattices have remarkable performances. The lower complexity nature of the decoding algorithm for these type of lattices allows us to run it for higher dimensions easily. Our simulation results show that a 1-level LDPC lattice of size 10000 can work as close as 1.1 dB at normalized error probability (NEP) of $10^{-5}$.This can also be reported as 0.6 dB at symbol error rate (SER) of $10^{-5}$ with sum-product algorithm.Comment: 1 figure, submitted to IWCIT 201

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

Coding with Scrambling, Concatenation, and HARQ for the AWGN Wire-Tap Channel: A Security Gap Analysis

This study examines the use of nonsystematic channel codes to obtain secure transmissions over the additive white Gaussian noise (AWGN) wire-tap channel. Unlike the previous approaches, we propose to implement nonsystematic coded transmission by scrambling the information bits, and characterize the bit error rate of scrambled transmissions through theoretical arguments and numerical simulations. We have focused on some examples of Bose-Chaudhuri-Hocquenghem (BCH) and low-density parity-check (LDPC) codes to estimate the security gap, which we have used as a measure of physical layer security, in addition to the bit error rate. Based on a number of numerical examples, we found that such a transmission technique can outperform alternative solutions. In fact, when an eavesdropper (Eve) has a worse channel than the authorized user (Bob), the security gap required to reach a given level of security is very small. The amount of degradation of Eve's channel with respect to Bob's that is needed to achieve sufficient security can be further reduced by implementing scrambling and descrambling operations on blocks of frames, rather than on single frames. While Eve's channel has a quality equal to or better than that of Bob's channel, we have shown that the use of a hybrid automatic repeat-request (HARQ) protocol with authentication still allows achieving a sufficient level of security. Finally, the secrecy performance of some practical schemes has also been measured in terms of the equivocation rate about the message at the eavesdropper and compared with that of ideal codes.Comment: 29 pages, 10 figure