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Register a new userSpatially Coupled Generalized LDPC Codes: Asymptotic Analysis and Finite Length Scaling
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Added by
David G. M. Mitchell
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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Generalized low-density parity-check (GLDPC) codes are a class of LDPC codes in which the standard single parity check (SPC) constraints are replaced by constraints defined by a linear block code. These stronger constraints typically result in improved error floor performance, due to better minimum distance and trapping set properties, at a cost of some increased decoding complexity. In this paper, we study spatially coupled generalized low-density parity-check (SC-GLDPC) codes and present a comprehensive analysis of these codes, including: (1) an iterative decoding threshold analysis of SC-GLDPC code ensembles demonstrating capacity approaching thresholds via the threshold saturation effect; (2) an asymptotic analysis of the minimum distance and free distance properties of SC-GLDPC code ensembles, demonstrating that the ensembles are asymptotically good; and (3) an analysis of the finite-length scaling behavior of both GLDPC block codes and SC-GLDPC codes based on a peeling decoder (PD) operating on a binary erasure channel (BEC). Results are compared to GLDPC block codes, and the advantages and disadvantages of SC-GLDPC codes are discussed.
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SC-LDPC codes with sub-block locality can be decoded locally at the level of sub-blocks that are much smaller than the full code block, thus providing fast access to the coded information. The same code can also be decoded globally using the entire code block, for increased data reliability. In this paper, we pursue the analysis and design of such codes from both finite-length and asymptotic lenses. This mixed approach has rarely been applied in designing SC codes, but it is beneficial for optimizing code graphs for local and global performance simultaneously. Our proposed framework consists of two steps: 1) designing the local code for both threshold and cycle counts, and 2) designing the coupling of local codes for best cycle count in the global design.
Spatially-coupled (SC) LDPC codes have recently emerged as an excellent choice for error correction in modern data storage and communication systems due to their outstanding performance. It has long been known that irregular graph codes offer performance advantage over their regular counterparts. In this paper, we present a novel combinatorial framework for designing finite-length irregular SC LDPC codes. Our irregular SC codes have the desirable properties of regular SC codes thanks to their structure while offering significant performance benefits that come with the node degree irregularity. Coding constructions proposed in this work contribute to the existing portfolio of finite-length graph code designs.
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 tradeoff 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.
A new type of spatially coupled low-density parity-check (SC-LDPC) codes motivated by practical storage applications is presented. SC-LDPCL codes (suffix L stands for locality) can be decoded locally at the level of sub-blocks that are much smaller than the full code block, thus offering flexible access to the coded information alongside the strong reliability of the global full-block decoding. Toward that, we propose constructions of SC-LDPCL codes that allow controlling the trade-off between local and global correction performance. In addition to local and global decoding, the paper develops a density-evolution analysis for a decoding mode we call semi-global decoding, in which the decoder has access to the requested sub-block plus a prescribed number of sub-blocks around it. SC-LDPCL codes are also studied under a channel model with variability across sub-blocks, for which decoding-performance lower bounds are derived.
As a typical example of bandwidth-efficient techniques, bit-interleaved coded modulation with iterative decoding (BICM-ID) provides desirable spectral efficiencies in various wireless communication scenarios. In this paper, we carry out a comprehensive investigation on tail-biting (TB) spatially coupled protograph (SCP) low-density parity-check (LDPC) codes in BICM-ID systems. Specifically, we first develop a two-step design method to formulate a novel type of constellation mappers, referred to as labeling-bit-partial-match (LBPM) constellation mappers, for SC-P-based BICM-ID systems. The LBPM constellation mappers can be seamlessly combined with high-order modulations, such as M-ary phase-shift keying (PSK) and M-ary quadrature amplitude modulation (QAM). Furthermore, we conceive a new bit-level interleaving scheme, referred to as variable node matched mapping (VNMM) scheme, which can substantially exploit the structure feature of SC-P codes and the unequal protection-degree property of labeling bits to trigger the wave-like convergence for TB-SC-P codes. In addition, we propose a hierarchical extrinsic information transfer (EXIT) algorithm to predict the convergence performance (i.e., decoding thresholds) of the proposed SC-P-based BICM-ID systems. Theoretical analyses and simulation results illustrate that the LBPM-mapped SC-P-based BICM-ID systems are remarkably superior to the state-of-the-art mapped counterparts. Moreover, the proposed SC-P-based BICM-ID systems can achieve even better error performance with the aid of the VNMM scheme. As a consequence, the proposed LBPM constellation mappers and VNMM scheme make the SC-P-based BICM-ID systems a favorable choice for the future-generation wireless communication systems.
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