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Error Floors of LDPC Codes

Tom Richardson

Published Jan 1, 2003• 686 citations
OpenAlex

Abstract

We introduce a computational technique that accurately predicts performance for a given LDPC code in the error floor region. We present some results obtained by applying the technique and describe certain aspects of it. 1

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Advances of the error-floor study of LDPC codes

Jiwen Zeng

Low-density parity check(LDPC)codes are known to perform very well under iterative decoding.However,these codes often exhibit an error floor phenomenon in the high signal-to-noise(SNR)region.This paper provides a comprehensive description of the cause of the error floor phenomenon of LDPC codes.It presents a detailed description of the trapping sets,describes the methods to estimate and reduce the error floor of LDPC codes.Finally,it proposes the future development of the error floor of LDPC codes.

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Error floors in LDPC codes: Fast simulation, bounds and hardware emulation

Pamela Lee, Lara Dolecek, Zhengya Zhang +3 more

Abstract — The error-correcting performance of low-density parity check (LDPC) codes, when decoded using practical iterative decoding, is known to approach Shannon limits in the asymptotic limit of large blocklengths. A substantial limitation to the use of finite-length LDPC codes is the presence of an error floor in the low frame error rate (FER) region. This paper develops a method, based on importance sampling and high SNR asymptotics as applied to suitably defined absorbing structures within the LDPC code, to predict error floors. Our results are in very close agreement with hardware-based experimental results, and moreover extend the prediction of the error probability to even lower regions. We compute both importance sampling estimates of error probabilities and deterministic estimates that are guaranteed to lower bound the error probability in the high SNR regime. I.

IEEE International Symposium on Information Theory (ISIT)•Jul 1, 2008•12 citations

A survey of error floor of LDPC codes

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Lowering Error Floor of LDPC Codes: A Machine Learning Approach

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•Mar 10, 2019•0 citations

An Upper Bounding Technique on the Error Floor Performance of LDPC Codes

Santhosh Kumar, Ravi Motwani

Low-density parity-check (LDPC) codes have higher coding gains compared to algebraic codes in several configurations. However, unlike algebraic codes whose performance can be easily determined generally, the block error rate performance of an LDPC code needs to be obtained by simulations. While there are analytical methods for some structured LDPC codes that predict this performance in the low error rate regime, these provide little insight into the error floor of other (less structured) LDPC codes. In this article, we present a simple method to upper bound the error floor of LDPC codes based on a certain monotonicity assumption on the decoder. This upper bound is general enough so that under the monotonicity assumption it is valid for any error-correcting code. This upper bounding technique is useful when projecting very low block error rates (such as below 1E-14) for LDPC codes and there is no knowledge of the trapping sets.

Globecom•Dec 1, 2017•0 citations

Error Floors of LDPC Codes and Related Topics

Brian K. Butler

Since their rediscovery in the late 1990s, low-density parity-check (LDPC) codes have rapidly become one the most important classes of error correcting codes. LDPC codes have a graphical description and are generally decoded iteratively. The graph of an iteratively decoded code's error rate performance versus the channel quality is typically divided into two regions. The error floor region appears at higher channel quality and is characterized by a more gradual decrease in error rate as channel quality improves. For iterative decoders the error floor is apparently determined by small structures within the code that are specific to the selected graphical description of the code and subtle details of the decoding algorithm. This thesis addresses several issues of LDPC error floors in the additive white Gaussian noise channel. First, we find the source of several well publicized error floors to be numerical issues within the message-passing decoder. We propose numerical improvements to several decoding formulations which substantially lower error floors. Next, we examine and refine error-floor prediction models. A time-variant linear state-space model is presented and analyzed. Graph theory is applied to analyze the small error-prone structures within the code. While we find our techniques encounter considerable problems in determining the error floors for iterative decoders with unrestricted dynamic range, their predictions are quite accurate when significant range restrictions are present. The final issue of LDPC error floors which we address relates to the minimum distance of quasi-cyclic (QC) LDPC codes. We derive improved minimum distance upper bounds for codes which are punctured and codes which contain a significant number of zeros in their protomatrices. These bound are then applied to a family of protograph-based LDPC codes standardized for use in deep-space communications. In the case of the rate-1/2 code, our upper bounds demonstrate that the previously promulgated ensemble lower bounds do not apply to QC constructions at block lengths beyond 4400 bits. The last part of this dissertation is a fairly separate piece of work on bounding the spectral radius of a large class of nonnegative matrices. We apply these bounds to digraphs and derive several associated equality conditions.</

•Jan 1, 2013•1 citation
Low-density parity check(LDPC)codes are known to perform very well under iterative decoding.However,these codes often exhibit an error floor phenomenon in the high signal-to-noise(SNR)region.This paper provides a comprehensive description of the cause of the error floor phenomenon of LDPC codes.It presents a detailed description of the trapping sets,describes the methods to estimate and reduce the error floor of LDPC codes.Finally,it proposes the future development of the error floor of LDPC codes.
Abstract — The error-correcting performance of low-density parity check (LDPC) codes, when decoded using practical iterative decoding, is known to approach Shannon limits in the asymptotic limit of large blocklengths. A substantial limitation to the use of finite-length LDPC codes is the presence of an error floor in the low frame error rate (FER) region. This paper develops a method, based on importance sampling and high SNR asymptotics as applied to suitably defined absorbing structures within the LDPC code, to predict error floors. Our results are in very close agreement with hardware-based experimental results, and moreover extend the prediction of the error probability to even lower regions. We compute both importance sampling estimates of error probabilities and deterministic estimates that are guaranteed to lower bound the error probability in the high SNR regime. I.
Low-density parity-check (LDPC) codes have higher coding gains compared to algebraic codes in several configurations. However, unlike algebraic codes whose performance can be easily determined generally, the block error rate performance of an LDPC code needs to be obtained by simulations. While there are analytical methods for some structured LDPC codes that predict this performance in the low error rate regime, these provide little insight into the error floor of other (less structured) LDPC codes. In this article, we present a simple method to upper bound the error floor of LDPC codes based on a certain monotonicity assumption on the decoder. This upper bound is general enough so that under the monotonicity assumption it is valid for any error-correcting code. This upper bounding technique is useful when projecting very low block error rates (such as below 1E-14) for LDPC codes and there is no knowledge of the trapping sets.
Since their rediscovery in the late 1990s, low-density parity-check (LDPC) codes have rapidly become one the most important classes of error correcting codes. LDPC codes have a graphical description and are generally decoded iteratively. The graph of an iteratively decoded code's error rate performance versus the channel quality is typically divided into two regions. The error floor region appears at higher channel quality and is characterized by a more gradual decrease in error rate as channel quality improves. For iterative decoders the error floor is apparently determined by small structures within the code that are specific to the selected graphical description of the code and subtle details of the decoding algorithm. This thesis addresses several issues of LDPC error floors in the additive white Gaussian noise channel. First, we find the source of several well publicized error floors to be numerical issues within the message-passing decoder. We propose numerical improvements to several decoding formulations which substantially lower error floors. Next, we examine and refine error-floor prediction models. A time-variant linear state-space model is presented and analyzed. Graph theory is applied to analyze the small error-prone structures within the code. While we find our techniques encounter considerable problems in determining the error floors for iterative decoders with unrestricted dynamic range, their predictions are quite accurate when significant range restrictions are present. The final issue of LDPC error floors which we address relates to the minimum distance of quasi-cyclic (QC) LDPC codes. We derive improved minimum distance upper bounds for codes which are punctured and codes which contain a significant number of zeros in their protomatrices. These bound are then applied to a family of protograph-based LDPC codes standardized for use in deep-space communications. In the case of the rate-1/2 code, our upper bounds demonstrate that the previously promulgated ensemble lower bounds do not apply to QC constructions at block lengths beyond 4400 bits. The last part of this dissertation is a fairly separate piece of work on bounding the spectral radius of a large class of nonnegative matrices. We apply these bounds to digraphs and derive several associated equality conditions.</