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IEICE Proceedings Series

Error Floor Estimation of Spatially-Coupled Irregular LDPC Code Ensembles

Kengo Shibata, Shan Lu, M. Yoshida, Krishna R. Narayanan, Jun Cheng

Published Oct 18, 2018• 0 citations
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Abstract

The frame error rate (FER) of spatially-coupled irregular low-density parity-check (SC-iLDPC) code ensemble in error floor region is estimated. First, the number of codewords of each weight is calculated by the permutations of all the sub-codewords at their coupling positions. Second, the FER is estimated by these numbers of the codewords of each weight. Numerical results show that the FER performances in the error floor regions of the SC-iLDPC code ensembles are superior to the conventional irregular LDPC code ensembles at almost identical belief-propagation (BP) thresholds.

Related papers

Error Floor Estimation of Spatially-Coupled Irregular LDPC Code Ensembles

Kengo Shibata, Shan Lu, M. Yoshida +2 more

The frame error rate (FER) of spatially-coupled irregular low-density parity-check (SC-iLDPC) code ensemble in error floor region is estimated. First, the number of codewords of each weight is calculated by the permutations of all the sub-codewords at their coupling positions. Second, the FER is estimated by these numbers of the codewords of each weight. Numerical results show that the FER performances in the error floor regions of the SC-iLDPC code ensembles are superior to the conventional irregular LDPC code ensembles at almost identical belief-propagation (BP) thresholds.

International Symposium on Information Theory and its Applications•Oct 1, 2018•0 citations

Lowering Error Floor of Irregular LDPC Codes by CRC and OSD Algorithm

Satoshi Gounai

Irregular Low-Density Parity-Check (LDPC) codes generally achieve better performance than regular LDPC codes at low E b /N 0 values. They have, however, higher error floors than regular LDPC codes. With respect to the construction of the irregular LDPC code, it can achieve the trade-off between the performance degradation of low E b /N 0 region and lowering error floor. It is known that a decoding algorithm can achieve very good performance if it combines the Ordered Statistic Decoding (OSD) algorithm and the Log Likelihood Ratio-Belief Propagation (LLR-BP) decoding algorithm. Unfortunately, all the codewords obtained by the OSD algorithm satisfy the parity check equation of the LDPC code. While we can not use the parity check equation of the LDPC code to stop the decoding process, the wrong codeword that satisfies the parity check equation raises the error floor. Once a codeword that satisfies the parity check equation is generated by the LLR-BP decoding algorithm, we regard that codeword as the final estimate and halt decoding; the OSD algorithm is not performed. In this paper, we propose a new encoding/decoding scheme to lower the error floor created by irregular LDPC codes. The proposed encoding scheme encodes information bits by Cyclic Redundancy Check (CRC) and LDPC code. The proposed decoding scheme, which consists of the LLR-BP decoding, CRC check, and OSD decoding, detects errors in the codewords obtained by the LLR-BP decoding algorithm and the OSD decoding algorithm using the parity check equations of LDPC codes and CRC. Computer simulations show that the proposed encoding/decoding scheme can lower the error floor of irregular LDPC codes.

IEICE Transactions on Communications•Jan 1, 2006•6 citations

Estimation of Bit and Frame Error Rates of Low-Density Parity-Check Codes on Binary Symmetric Channels

Hua Xiao, Amir H. Banihashemi

A method for estimating the performance of low-density parity-check (LDPC) codes decoded by hard-decision iterative decoding algorithms on binary symmetric channels (BSC) is proposed. Based on the enumeration of the smallest weight error patterns that cannot be all corrected by the decoder, this method estimates both the frame error rate (FER) and the bit error rate (BER) of a given LDPC code with very good precision for all crossover probabilities of practical interest. Through a number of examples, we show that the proposed method can be effectively applied to both regular and irregular LDPC codes and to a variety of hard-decision iterative decoding algorithms. Compared with the conventional Monte Carlo simulation, the proposed method has a much smaller computational complexity, particularly for lower error rates.

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Estimation of Bit and Frame Error Rates of Finite-Length Low-Density Parity-Check Codes on Binary Symmetric Channels

Hua Xiao, Amir H. Banihashemi

A method for estimating the performance of low-density parity-check (LDPC) codes decoded by hard-decision iterative decoding algorithms on binary symmetric channels (BSCs) is proposed. Based on the enumeration of the smallest weight error patterns that cannot be all corrected by the decoder, this method estimates both the frame error rate (FER) and the bit error rate (BER) of a given LDPC code with very good precision for all crossover probabilities of practical interest. Through a number of examples, we show that the proposed method can be effectively applied to both regular and irregular LDPC codes and to a variety of hard-decision iterative decoding algorithms. Compared with the conventional Monte Carlo simulation, the proposed method has a much smaller computational complexity, particularly for lower error rates.

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Finite-Length Scaling of Spatially Coupled LDPC Codes Under Window Decoding Over the BEC

Roman Sokolovskii, Alexandre Graell i Amat, Fredrik Brännström

We analyze the finite-length performance of spatially coupled low-density parity-check (SC-LDPC) codes under window decoding over the binary erasure channel. In particular, we propose a refinement of the scaling law by Olmos and Urbanke for the frame error rate (FER) of terminated SC-LDPC ensembles under full belief propagation (BP) decoding. The refined scaling law models the decoding process as two independent Ornstein-Uhlenbeck processes, in correspondence to the two decoding waves that propagate toward the center of the coupled chain for terminated SC-LDPC codes. We then extend the proposed scaling law to predict the performance of (terminated) SC-LDPC code ensembles under the more practical sliding window decoding. Finally, we extend this framework to predict the bit error rate (BER) and block error rate (BLER) of SC-LDPC code ensembles. The proposed scaling law yields very accurate predictions of the FER, BLER, and BER for both full BP and window decoding.

arXiv:2003.04421•IEEE Transactions on Communications•Jul 21, 2020•10 citations

On the Dependence of Error Performance of Spatially Coupled LDPC Codes on Their Design Parameters

Ihara Hiroyuki, Tomoharu Shibuya

Spatially coupled (SC) low-density parity-check (LDPC) codes are defined by bipartite graphs that are obtained by assembling prototype graphs. The combination and connection of prototype graphs are designated by specifying some parameters, and Kudekar et al. showed that BP threshold of the ensemble of SC LDPC codes agrees with MAP threshold of the ensemble of regular LDPC codes when those parameters are grown up so that the code length tends to infinity. When we design SC LDPC codes with practical code length, however, it is not clear how to set those parameters to enhance the performance of SC LDPC codes. In this paper, we provide the result of numerical experiments that suggest the dependence of error performance of SC LDPC codes over BEC on their design parameters.

IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences•Jan 1, 2013•0 citations
The frame error rate (FER) of spatially-coupled irregular low-density parity-check (SC-iLDPC) code ensemble in error floor region is estimated. First, the number of codewords of each weight is calculated by the permutations of all the sub-codewords at their coupling positions. Second, the FER is estimated by these numbers of the codewords of each weight. Numerical results show that the FER performances in the error floor regions of the SC-iLDPC code ensembles are superior to the conventional irregular LDPC code ensembles at almost identical belief-propagation (BP) thresholds.
The frame error rate (FER) of spatially-coupled irregular low-density parity-check (SC-iLDPC) code ensemble in error floor region is estimated. First, the number of codewords of each weight is calculated by the permutations of all the sub-codewords at their coupling positions. Second, the FER is estimated by these numbers of the codewords of each weight. Numerical results show that the FER performances in the error floor regions of the SC-iLDPC code ensembles are superior to the conventional irregular LDPC code ensembles at almost identical belief-propagation (BP) thresholds.
Irregular Low-Density Parity-Check (LDPC) codes generally achieve better performance than regular LDPC codes at low E b /N 0 values. They have, however, higher error floors than regular LDPC codes. With respect to the construction of the irregular LDPC code, it can achieve the trade-off between the performance degradation of low E b /N 0 region and lowering error floor. It is known that a decoding algorithm can achieve very good performance if it combines the Ordered Statistic Decoding (OSD) algorithm and the Log Likelihood Ratio-Belief Propagation (LLR-BP) decoding algorithm. Unfortunately, all the codewords obtained by the OSD algorithm satisfy the parity check equation of the LDPC code. While we can not use the parity check equation of the LDPC code to stop the decoding process, the wrong codeword that satisfies the parity check equation raises the error floor. Once a codeword that satisfies the parity check equation is generated by the LLR-BP decoding algorithm, we regard that codeword as the final estimate and halt decoding; the OSD algorithm is not performed. In this paper, we propose a new encoding/decoding scheme to lower the error floor created by irregular LDPC codes. The proposed encoding scheme encodes information bits by Cyclic Redundancy Check (CRC) and LDPC code. The proposed decoding scheme, which consists of the LLR-BP decoding, CRC check, and OSD decoding, detects errors in the codewords obtained by the LLR-BP decoding algorithm and the OSD decoding algorithm using the parity check equations of LDPC codes and CRC. Computer simulations show that the proposed encoding/decoding scheme can lower the error floor of irregular LDPC codes.
A method for estimating the performance of low-density parity-check (LDPC) codes decoded by hard-decision iterative decoding algorithms on binary symmetric channels (BSC) is proposed. Based on the enumeration of the smallest weight error patterns that cannot be all corrected by the decoder, this method estimates both the frame error rate (FER) and the bit error rate (BER) of a given LDPC code with very good precision for all crossover probabilities of practical interest. Through a number of examples, we show that the proposed method can be effectively applied to both regular and irregular LDPC codes and to a variety of hard-decision iterative decoding algorithms. Compared with the conventional Monte Carlo simulation, the proposed method has a much smaller computational complexity, particularly for lower error rates.
A method for estimating the performance of low-density parity-check (LDPC) codes decoded by hard-decision iterative decoding algorithms on binary symmetric channels (BSCs) is proposed. Based on the enumeration of the smallest weight error patterns that cannot be all corrected by the decoder, this method estimates both the frame error rate (FER) and the bit error rate (BER) of a given LDPC code with very good precision for all crossover probabilities of practical interest. Through a number of examples, we show that the proposed method can be effectively applied to both regular and irregular LDPC codes and to a variety of hard-decision iterative decoding algorithms. Compared with the conventional Monte Carlo simulation, the proposed method has a much smaller computational complexity, particularly for lower error rates.
We analyze the finite-length performance of spatially coupled low-density parity-check (SC-LDPC) codes under window decoding over the binary erasure channel. In particular, we propose a refinement of the scaling law by Olmos and Urbanke for the frame error rate (FER) of terminated SC-LDPC ensembles under full belief propagation (BP) decoding. The refined scaling law models the decoding process as two independent Ornstein-Uhlenbeck processes, in correspondence to the two decoding waves that propagate toward the center of the coupled chain for terminated SC-LDPC codes. We then extend the proposed scaling law to predict the performance of (terminated) SC-LDPC code ensembles under the more practical sliding window decoding. Finally, we extend this framework to predict the bit error rate (BER) and block error rate (BLER) of SC-LDPC code ensembles. The proposed scaling law yields very accurate predictions of the FER, BLER, and BER for both full BP and window decoding.
Spatially coupled (SC) low-density parity-check (LDPC) codes are defined by bipartite graphs that are obtained by assembling prototype graphs. The combination and connection of prototype graphs are designated by specifying some parameters, and Kudekar et al. showed that BP threshold of the ensemble of SC LDPC codes agrees with MAP threshold of the ensemble of regular LDPC codes when those parameters are grown up so that the code length tends to infinity. When we design SC LDPC codes with practical code length, however, it is not clear how to set those parameters to enhance the performance of SC LDPC codes. In this paper, we provide the result of numerical experiments that suggest the dependence of error performance of SC LDPC codes over BEC on their design parameters.