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1. On Sparse Regression LDPC Codes

   https://doi.org/10.1109/ISIT54713.2023.10206818  

   Ebert, Jamison R; Chamberland, Jean-Francois; Narayanan, Krishna R (August 2023, IEEE)

   Iterative decoding of graph-based codes and sparse recovery through approximate message passing (AMP) are two research areas that have seen monumental progress in recent decades. Inspired by these advances, this article introduces sparse regression LDPC codes (SR-LDPC codes) and their decoding. Sparse regression codes (SPARCs) are a class of error correcting codes that build on ideas from compressed sensing and can be decoded using AMP. In certain settings, SPARCs are known to achieve capacity; yet, their performance suffers at finite block lengths. Likewise, low-density parity-check (LDPC) codes can be decoded efficiently using belief propagation and can also be capacity achieving. This article introduces a novel concatenated coding structure that combines an LDPC outer code with a SPARC-inspired inner code. Efficient decoding for such a code can be achieved using AMP with a denoiser that performs belief propagation on the factor graph of the outer LDPC code. The proposed framework exhibits performance improvements over SPARCs and standard LDPC codes for finite block lengths and results in a steep waterfall in error performance, a phenomenon not observed in uncoded SPARCs. 

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2. Optimization of Nested Array-based LDPC Codes Via Spatial Coupling

   https://doi.org/10.1109/ITW44776.2019.8989313  

   Habib, Salman; Mitchell, David G.; Kliewer, Jorg (August 2019, 2019 IEEE Information Theory Workshop (ITW))

   Linear nested codes, where two or more subcodes are nested in a global code, have been proposed as candidates for reliable multi-terminal communication. In this paper, we consider nested array-based spatially coupled LDPC codes and propose a line-counting based optimization scheme for minimizing the number of dominant absorbing sets in order to improve its performance in the high signal-to-noise ratio regime. The presented multi-step optimization process is applied first to one of the nested codes, then an optimization of the remaining nested codes is carried out based on these code constraints. We also show that for certain code parameters, dominant absorbing sets in the Tanner graphs of all nested codes can be completely removed using our proposed optimization strategy. 

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3. Suppressing Error Floors in SCPPM via an Efficient CRC-aided List Viterbi Decoding Algorithm

   https://doi.org/10.1109/ISTC57237.2023.10273548  

   Antonini, A.; Sui, W.; Towell, B.; Divsalar, D.; Hamkins, J.; Wesel, R. D. (September 2023, IEEE International Symposium on Topics in Coding)

   List Viterbi decoders are a very effective way to improve the performance of block codes in combination with an error detection outer code. In this work, we combine an efficient serial list Viterbi decoder design with an existing serially concatenated, convolutionally-encoded, pulse position modulated code (SCPPM) used in space communication, that exhibits poor performance because of an error floor. The SCPPM code features a 32-bit CRC that provides powerful error detection capability and an outer four-state convolutional code that makes it suitable for a list Viterbi decoder. The system’s code is very long, consisting of 15, 120 bits, which renders a high complexity decoder impractical, while the high error detection allows for a list decoder with very low undetected error probability. We use a very efficient list Viterbi decoder algorithm to avoid most of the redundant operations to produce low complexity serial list Viterbi decoder. The combined system reduces the error floor, moderately for the original version of the system, and completely suppresses it when the code length is increased to four times longer. 

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4. Nested Array-Based Spatially Coupled LDPC Codes

   https://doi.org/10.1109/TCOMM.2021.3061689  

   Habib, Salman; Mitchell, David G.; Kliewer, Jorg (January 2021, IEEE Transactions on Communications)

   null (Ed.)

   Linear nested codes, where two or more sub-codes are nested in a global code, have been proposed as candidates for reliable multi-terminal communication. In this paper, we consider nested array-based spatially coupled low-density parity-check (SC-LDPC) codes and propose a line-counting based optimization scheme for minimizing the number of dominant absorbing sets in order to improve its performance in the high signal-to-noise ratio regime. Since the parity-check matrices of different nested sub-codes partially overlap, the optimization of one nested sub-code imposes constraints on the optimization of the other sub-codes. To tackle these constraints, a multi-step optimization process is applied first to one of the nested codes, then sequential optimization of the remaining nested codes is carried out based on the constraints imposed by the previously optimized sub-codes. Results show that the order of optimization has a significant impact on the number of dominant absorbing sets in the Tanner graph of the code, resulting in a trade-off between the performance of a nested code structure and its optimization sequence: the code which is optimized without constraints has fewer harmful structures than the code which is optimized with constraints. We also show that for certain code parameters, dominant absorbing sets in the Tanner graphs of all nested codes are completely removed using our proposed optimization strategy. 

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5. Window code parameters of spatially-coupled LDPC codes

   https://doi.org/10.1142/S0219498825501270  

   McMillon, Emily; Kelley, Christine A (June 2024, Journal of Algebra and Its Applications)

   In this paper, we define a window code to be the portion of a Spatially-coupled low-density parity check (SC-LDPC) code seen by a single iteration of a windowed decoder. We consider the design of SC-LDPC codes for windowed decoding via optimization of the window code. In particular, because iterative decoding is optimal on codes with cycle-free graph representations, we ask fundamental questions about the construction and parameters of cycle-free window codes. We show that it is possible to have an SC-LDPC code with cycles and with cycle-free window codes. We consider the relationship between the distance of the window code and the distance of the SC-LDPC code. Further, we show that SC-LDPC codes with MDS window codes exist, and all such codes are asymptotically bad. This work gives insight into the tradeoffs between window code parameters and performance of the SC-LDPC code. 

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