A multistage scheduled decoder for short block length low-density parity-check codes

Recent advances in coding theory have uncovered the previously forgotten power of Low-Density Parity-Check (LDPC) codes. Their popularity can be related to their relatively simple iterative decoders and their potential to achieve high performance close to shannon limit. These make them an attractive candidate for error correcting application in communication systems. In this thesis, we focus our research on the iterative decoding algorithms for Low-Density Parity-Check codes and present an improved decoding algorithm. First, the graph structure of LDPC codes is studied and a graph-based search algorithm to find the shortest closed walk and shortest cycle for each node of the graph is proposed. Then, the Deterministic schedule is applied on nodes of the graph with the objective of preserving the optimality of the algorithms. Finally, Hybrid Switch-Type technique is applied on the improved algorithms to provide a desirable complexity/performance trade-off. Hybrid Technique and Deterministic schedule are combined for decoding regular and irregular LDPC codes. The performance and complexity of the decoder is studied for Sum-Product and Gallager A algorithms. The result is a flexible decoder for any available LDPC code and any combination of decoding algorithms based on the communication systems need. In this technique, we benefit the high performance of soft-decision algorithms and low complexity of hard-decision algorithms by changing the decoding rule after a few iterations. Hence, a desirable performance can be obtained with less average number of soft iterations. Moreover, all the nodes do not update messages in each iteration. As a result, the total number of computations is reduced considerabl

Spatially Coupled Codes and Optical Fiber Communications: An Ideal Match?

In this paper, we highlight the class of spatially coupled codes and discuss their applicability to long-haul and submarine optical communication systems. We first demonstrate how to optimize irregular spatially coupled LDPC codes for their use in optical communications with limited decoding hardware complexity and then present simulation results with an FPGA-based decoder where we show that very low error rates can be achieved and that conventional block-based LDPC codes can be outperformed. In the second part of the paper, we focus on the combination of spatially coupled LDPC codes with different demodulators and detectors, important for future systems with adaptive modulation and for varying channel characteristics. We demonstrate that SC codes can be employed as universal, channel-agnostic coding schemes.Comment: Invited paper to be presented in the special session on "Signal Processing, Coding, and Information Theory for Optical Communications" at IEEE SPAWC 201

Bilayer Low-Density Parity-Check Codes for Decode-and-Forward in Relay Channels

This paper describes an efficient implementation of binning for the relay channel using low-density parity-check (LDPC) codes. We devise bilayer LDPC codes to approach the theoretically promised rate of the decode-and-forward relaying strategy by incorporating relay-generated information bits in specially designed bilayer graphical code structures. While conventional LDPC codes are sensitively tuned to operate efficiently at a certain channel parameter, the proposed bilayer LDPC codes are capable of working at two different channel parameters and two different rates: that at the relay and at the destination. To analyze the performance of bilayer LDPC codes, bilayer density evolution is devised as an extension of the standard density evolution algorithm. Based on bilayer density evolution, a design methodology is developed for the bilayer codes in which the degree distribution is iteratively improved using linear programming. Further, in order to approach the theoretical decode-and-forward rate for a wide range of channel parameters, this paper proposes two different forms bilayer codes, the bilayer-expurgated and bilayer-lengthened codes. It is demonstrated that a properly designed bilayer LDPC code can achieve an asymptotic infinite-length threshold within 0.24 dB gap to the Shannon limits of two different channels simultaneously for a wide range of channel parameters. By practical code construction, finite-length bilayer codes are shown to be able to approach within a 0.6 dB gap to the theoretical decode-and-forward rate of the relay channel at a block length of $10^5$ and a bit-error probability (BER) of $10^{-4}$. Finally, it is demonstrated that a generalized version of the proposed bilayer code construction is applicable to relay networks with multiple relays.Comment: Submitted to IEEE Trans. Info. Theor

Binary Message Passing Decoding of Product-like Codes

We propose a novel binary message passing decoding algorithm for product-like codes based on bounded distance decoding (BDD) of the component codes. The algorithm, dubbed iterative BDD with scaled reliability (iBDD-SR), exploits the channel reliabilities and is therefore soft in nature. However, the messages exchanged by the component decoders are binary (hard) messages, which significantly reduces the decoder data flow. The exchanged binary messages are obtained by combining the channel reliability with the BDD decoder output reliabilities, properly conveyed by a scaling factor applied to the BDD decisions. We perform a density evolution analysis for generalized low-density parity-check (GLDPC) code ensembles and spatially coupled GLDPC code ensembles, from which the scaling factors of the iBDD-SR for product and staircase codes, respectively, can be obtained. For the white additive Gaussian noise channel, we show performance gains up to $0.29$ dB and $0.31$ dB for product and staircase codes compared to conventional iterative BDD (iBDD) with the same decoder data flow. Furthermore, we show that iBDD-SR approaches the performance of ideal iBDD that prevents miscorrections.Comment: Accepted for publication in the IEEE Transactions on Communication

Check-hybrid GLDPC Codes: Systematic Elimination of Trapping Sets and Guaranteed Error Correction Capability

In this paper, we propose a new approach to construct a class of check-hybrid generalized low-density parity-check (CH-GLDPC) codes which are free of small trapping sets. The approach is based on converting some selected check nodes involving a trapping set into super checks corresponding to a 2-error correcting component code. Specifically, we follow two main purposes to construct the check-hybrid codes; first, based on the knowledge of the trapping sets of the global LDPC code, single parity checks are replaced by super checks to disable the trapping sets. We show that by converting specified single check nodes, denoted as critical checks, to super checks in a trapping set, the parallel bit flipping (PBF) decoder corrects the errors on a trapping set and hence eliminates the trapping set. The second purpose is to minimize the rate loss caused by replacing the super checks through finding the minimum number of such critical checks. We also present an algorithm to find critical checks in a trapping set of column-weight 3 LDPC code and then provide upper bounds on the minimum number of such critical checks such that the decoder corrects all error patterns on elementary trapping sets. Moreover, we provide a fixed set for a class of constructed check-hybrid codes. The guaranteed error correction capability of the CH-GLDPC codes is also studied. We show that a CH-GLDPC code in which each variable node is connected to 2 super checks corresponding to a 2-error correcting component code corrects up to 5 errors. The results are also extended to column-weight 4 LDPC codes. Finally, we investigate the eliminating of trapping sets of a column-weight 3 LDPC code using the Gallager B decoding algorithm and generalize the results obtained for the PBF for the Gallager B decoding algorithm