Error Floor Approximation for LDPC Codes in the AWGN Channel
Brian K. Butler,Paul H. Siegel +1 more
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This paper addresses the prediction of error floors of low-density parity-check codes transmitted over the additive white Gaussian noise channel with modifications that account for the behavior of a nonsaturating decoder and presents the resulting error floor estimates for the Margulis code.Abstract:
This paper addresses the prediction of error floors of low-density parity-check codes transmitted over the additive white Gaussian noise channel. Using a linear state-space model to estimate the behavior of the sum-product algorithm (SPA) decoder in the vicinity of trapping sets (TSs), we study the performance of the SPA decoder in the log-likelihood ratio (LLR) domain as a function of the LLR saturation level. When applied to several widely studied codes, the model accurately predicts a significant decrease in the error floor as the saturation level is allowed to increase. For nonsaturating decoders, however, we find that the state-space model breaks down after a small number of iterations due to the strong correlation of LLR messages. We then revisit Richardson's importance-sampling methodology for estimating error floors due to TSs when those floors are too low for Monte Carlo simulation. We propose modifications that account for the behavior of a nonsaturating decoder and present the resulting error floor estimates for the Margulis code. These estimates are much lower, significantly steeper, and more sensitive to iteration count than those previously reported.read more
Citations
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Finite Alphabet Iterative Decoders—Part I: Decoding Beyond Belief Propagation on the Binary Symmetric Channel
TL;DR: It is shown that there exist FAIDs that surpass the floating-point BP decoder in the error floor region while requiring only three bits of precision for the representation of the messages, and FAIDs are able to achieve a superior performance at much lower complexity.
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The ADMM Penalized Decoder for LDPC Codes
Xishuo Liu,Stark C. Draper +1 more
TL;DR: A new class of decoders obtained by applying the alternating direction method of multipliers (ADMM) algorithm to a set of non-convex optimization problems are constructed by adding a penalty term to the objective of LP decoding to make pseudocodewords, which are non-integer vertices of the LP relaxation, more costly.
Journal ArticleDOI
New Characterization and Efficient Exhaustive Search Algorithm for Leafless Elementary Trapping Sets of Variable-Regular LDPC Codes
TL;DR: It is proved that using the three expansion techniques, any LETS structure can be obtained starting from a simple cycle, no matter how large the size of the structure a or the number of its unsatisfied check nodes b are, and that for the proposed characterization/ search to exhaustively cover all the LETS structures within the (a, b) classes, the length of the short cycles required to be enumerated is less than that of the LSS-based characterization/search.
Posted Content
Quantized Iterative Message Passing Decoders with Low Error Floor for LDPC Codes
Xiaojie Zhang,Paul H. Siegel +1 more
TL;DR: In this article, the authors proposed a (q+1)-bit quasi-uniform quantization method to increase the dynamic range of messages, thereby overcoming a limitation of conventional quantization schemes.
Proceedings ArticleDOI
Quantized min-sum decoders with low error floor for LDPC codes
Xiaojie Zhang,Paul H. Siegel +1 more
TL;DR: It is shown that one source of the error floors observed in the literature may be the message quantization rule used in the iterative decoder implementation, and a new quantization method is proposed to overcome the limitations of standard quantization rules.
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