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International Conference on Advanced Communication Technology

A study on adaptive thresholds for reduced complexity bit-flip decoding

Julian L. Webber, Toshihiko Nishimura, Takeo Ohgane, Yasutaka Ogawa

Published Jan 1, 2012• 5 citations
OpenAlex

Abstract

Low-density parity-check (LDPC) codes are capacity approaching codes that have rapidly been adopted in modern systems such as the IEEE 802.11n and long term evolution advanced (LTE-A) communications standards. The decoders based on the iterative belief propagation offer exceedingly high performance but unfortunately have high computational complexity. Therefore significant research has focused on lower complexity architectures based on the family of so-called bit-flipping algorithms. In the basic bit-flipping algorithm the number of failed parity checks for each bit is calculated and the sign of the bit with the maximum failed checks is inverted. Inverting bits above a certain threshold removes the complexity of calculating a maximum function and adaptive thresholds on each bit further simplifies the design. The choice of threshold updates directly affects the error and convergence performances. Here we describe a simple architecture that has two decoders with different scaling factors and select the branch with the lowest syndrome sum. It is shown that the addition of a random uniform perturbation to the threshold can reduce the average iteration count further by providing an escape from stuck decoding states.

Related papers

Performance investigation of reduced complexity bit-flipping using variable thresholds and noise perturbation

Julian L. Webber, Toshihiko Nishimura, Takeo Ohgane +1 more

The near Shannon capacity approaching low-density parity-check (LDPC) linear block codes are now in widespread use in modern systems including the long term evolution advanced (LTE-A) cellular, 802.11η Wi-Fi and DVB-S2 satellite communications standards. The decoders based on the iterative belief propagation algorithm provide near optimum performance but also have very high computational complexity. Therefore significant research has recently focused on reduced complexity architectures based on the group of so-called bit-flipping algorithms. In the basic bit-flipping algorithm the number of failed parity checks for each bit is computed and the bit with the maximum failed parity checks is inverted. Inverting bits above a certain threshold removes the complexity involved with a maximum-search and, adaptive thresholds on each bit can further reduce the computation overhead. The criterion for the threshold update affects the error and convergence performances. Here, we describe a low-complexity architecture that has two (or more) decoder branches each with a different threshold scaling factor and select the threshold and bits at each iteration from the branch with the lowest syndrome sum. We then investigate the effect of adding a random Uniform or Gaussian noise perturbation to the threshold in order to reduce the average iteration count further in order to provide the opportunity to escape from stuck decoding states.

International Conference on Advanced Communication Technology•Feb 1, 2014•1 citation

Investigation of simple threshold shifting for bit-flip decoding

Julian L. Webber, Toshihiko Nishimura, Takeo Ohgane +1 more

Remarkably low error rates can be obtained using low-density parity-check (LDPC) codes and their use is now an increasingly common option in communications standards. The classic decoders based on belief propagation offer very high performance but have high implementation complexity. Therefore over the last decade simpler architectures such as the bit flipping class of algorithms have been researched. Recently, a number of adaptive threshold algorithms have been proposed in which at each iteration a bit is either flipped if it is below an inversion threshold, or the threshold is lowered. By choosing certain values of the scaling factor, the scaling can be efficiently implemented using a small number of shift and add operations. This work looks at how the scaling factor affects the convergence and error performance, and investigates an algorithm that switches between two scaling values based on the syndrome sum. The dual scaling method maintained the error performance compared to that with a single scaling but the iteration count was significantly reduced.

International Symposium on Wireless Personal Multimedia Communications (WPMC)•Jan 1, 2011•2 citations

Adaptive Threshold Technique for Bit-Flipping Decoding of Low-Density Parity-Check Codes

Junho Cho, Wonyong Sung

The bit-flipping (BF) algorithm for decoding of low-density parity-check (LDPC) codes requires less complex hardware than other decoding algorithms, but its error correcting performance needs to be improved. In this letter, a threshold adaptation scheme is applied to BF algorithm based decoding of LDPC codes. Our experiments show that the optimal threshold value for BF depends on the error conditions, and threshold adjustment during decoding helps to prevent meaningless no-flipping iterations. Based on these statistical observations, the adaptive threshold technique is proposed to pursue both the maximum error correcting capability and the fastest decoding convergence.

IEEE Communications Letters•Aug 5, 2010•32 citations

Modified Bit-Flipping Decoding of Low-Density Parity-Check Codes

Yuan Hua Liu, Mei Ling Zhang

A novel bit-flipping (BF) algorithm with low complexity for high-throughput decoding of low-density parity-check (LDPC) codes is presented. At each iteration, a novel threshold pattern is used to determine the code bits whether to be flipped or not, and the flipping error probability is effectively decreased. Compared with the weighted BF algorithm and its modifications, the modified BF algorithm has significantly lower complexity and decoding time. Through simulations the proposed BF algorithm is shown to achieve excellent performance and fast convergence speed while maintaining significantly low complexity thus facilitating high-throughput decoding.

Advanced materials research•Jun 1, 2013•0 citations

An Improved Iterative Bit-flipping Decoding Algorithm for Low-density Parity-check Codes

Meiling Zhang

An improved iterative bit-flipping(BF) algorithm adapted for decoding low-density parity-check(LDPC) codes is proposed to improve the performance of the hard-decision BF decoding algorithm.The new algorithm uses an alternating threshold pattern to determine the bits whether to be flipped or not,and the flipping error probability is effectively decreased.Simulation results show that compared with BF algorithm,the improved BF algorithm improves both the error-correction performance and the convergence speed while maintaining the low computational complexity.

Telecommunication Engineering•Jan 1, 2012•0 citations

On the modification of bit-flipping decoder of LDPC-codes

S. S. Gurskiy, N. S. Mogilevskaya

Introduction. In all types of digital communication, error control coding techniques are used. Many digital communication standards, such as Wi-Fi and 5G, use low density parity check (LDPC) codes. These codes are popular because they provide building encoders and decoders with low computational complexity. This work objective is to increase the error correcting capability of the well-known bit-flipping decoder (BF) of LDPC-codes. For this purpose, a modification of the decoder is built, which enables to dynamically control one of its main parameters whose choice affects significantly the quality of decoding. Materials and Methods. The well-known bit-flipping decoder of binary LDPC-codes is considered. This decoder has several parameters that are not rigidly bound with the code parameters. The dependence of the decoding quality on the selection of the output parameters of the bit-flipping decoder was investigated through simulation modeling. It is shown that the decoding results in this case are significantly affected by the input parameter of the decoder — threshold T. A modification of the BF-decoder of binary LDPC-codes has been developed, in which it is proposed to set the threshold dynamically during the execution of the algorithm depending on the error rate. A comparative analysis of the error- correcting capability of decoders is carried out by the simulation modeling method. Results. A lemma on the maximum value of the decoder threshold T is formulated and proved. Upper bounds for the number of operations are found for the original and modified decoders. A simulation model that implements a digital noise-immune communication channel has been built. In the model, the initial data is encoded with a given LDPC-code, then it is made noisy by additive uniformly distributed errors, and thereafter, it is decoded in turn by the bit-flipping algorithm with different threshold T parameters, as well as by a modified decoder. Based on the input and output data, the correction capacity of the decoders used is estimated. Experiments have shown that the error-correcting capability of the modified decoder in the range of the real error rate is higher than that of the original decoder, regardless of the selection of its parameters. Discussion and Conclusions. The lemma, proved in the paper, sets the upper bound on the threshold value in the original decoder, which simplifies its adjustment. The developed modification of the decoder has a better error- correcting capability compared to the original decoder. Nevertheless, the complexity of the modification is slightly increased compared to the original algorithm. It has been pointed out that the decoding quality of a modified decoder develops with a decrease in the number of cycles in the Tanner graph and an increase in the length of the code.

Advanced Engineering Research•Apr 4, 2021•0 citations
Low-density parity-check (LDPC) codes are capacity approaching codes that have rapidly been adopted in modern systems such as the IEEE 802.11n and long term evolution advanced (LTE-A) communications standards. The decoders based on the iterative belief propagation offer exceedingly high performance but unfortunately have high computational complexity. Therefore significant research has focused on lower complexity architectures based on the family of so-called bit-flipping algorithms. In the basic bit-flipping algorithm the number of failed parity checks for each bit is calculated and the sign of the bit with the maximum failed checks is inverted. Inverting bits above a certain threshold removes the complexity of calculating a maximum function and adaptive thresholds on each bit further simplifies the design. The choice of threshold updates directly affects the error and convergence performances. Here we describe a simple architecture that has two decoders with different scaling factors and select the branch with the lowest syndrome sum. It is shown that the addition of a random uniform perturbation to the threshold can reduce the average iteration count further by providing an escape from stuck decoding states.
The near Shannon capacity approaching low-density parity-check (LDPC) linear block codes are now in widespread use in modern systems including the long term evolution advanced (LTE-A) cellular, 802.11η Wi-Fi and DVB-S2 satellite communications standards. The decoders based on the iterative belief propagation algorithm provide near optimum performance but also have very high computational complexity. Therefore significant research has recently focused on reduced complexity architectures based on the group of so-called bit-flipping algorithms. In the basic bit-flipping algorithm the number of failed parity checks for each bit is computed and the bit with the maximum failed parity checks is inverted. Inverting bits above a certain threshold removes the complexity involved with a maximum-search and, adaptive thresholds on each bit can further reduce the computation overhead. The criterion for the threshold update affects the error and convergence performances. Here, we describe a low-complexity architecture that has two (or more) decoder branches each with a different threshold scaling factor and select the threshold and bits at each iteration from the branch with the lowest syndrome sum. We then investigate the effect of adding a random Uniform or Gaussian noise perturbation to the threshold in order to reduce the average iteration count further in order to provide the opportunity to escape from stuck decoding states.
Remarkably low error rates can be obtained using low-density parity-check (LDPC) codes and their use is now an increasingly common option in communications standards. The classic decoders based on belief propagation offer very high performance but have high implementation complexity. Therefore over the last decade simpler architectures such as the bit flipping class of algorithms have been researched. Recently, a number of adaptive threshold algorithms have been proposed in which at each iteration a bit is either flipped if it is below an inversion threshold, or the threshold is lowered. By choosing certain values of the scaling factor, the scaling can be efficiently implemented using a small number of shift and add operations. This work looks at how the scaling factor affects the convergence and error performance, and investigates an algorithm that switches between two scaling values based on the syndrome sum. The dual scaling method maintained the error performance compared to that with a single scaling but the iteration count was significantly reduced.
The bit-flipping (BF) algorithm for decoding of low-density parity-check (LDPC) codes requires less complex hardware than other decoding algorithms, but its error correcting performance needs to be improved. In this letter, a threshold adaptation scheme is applied to BF algorithm based decoding of LDPC codes. Our experiments show that the optimal threshold value for BF depends on the error conditions, and threshold adjustment during decoding helps to prevent meaningless no-flipping iterations. Based on these statistical observations, the adaptive threshold technique is proposed to pursue both the maximum error correcting capability and the fastest decoding convergence.
A novel bit-flipping (BF) algorithm with low complexity for high-throughput decoding of low-density parity-check (LDPC) codes is presented. At each iteration, a novel threshold pattern is used to determine the code bits whether to be flipped or not, and the flipping error probability is effectively decreased. Compared with the weighted BF algorithm and its modifications, the modified BF algorithm has significantly lower complexity and decoding time. Through simulations the proposed BF algorithm is shown to achieve excellent performance and fast convergence speed while maintaining significantly low complexity thus facilitating high-throughput decoding.
An improved iterative bit-flipping(BF) algorithm adapted for decoding low-density parity-check(LDPC) codes is proposed to improve the performance of the hard-decision BF decoding algorithm.The new algorithm uses an alternating threshold pattern to determine the bits whether to be flipped or not,and the flipping error probability is effectively decreased.Simulation results show that compared with BF algorithm,the improved BF algorithm improves both the error-correction performance and the convergence speed while maintaining the low computational complexity.
Introduction. In all types of digital communication, error control coding techniques are used. Many digital communication standards, such as Wi-Fi and 5G, use low density parity check (LDPC) codes. These codes are popular because they provide building encoders and decoders with low computational complexity. This work objective is to increase the error correcting capability of the well-known bit-flipping decoder (BF) of LDPC-codes. For this purpose, a modification of the decoder is built, which enables to dynamically control one of its main parameters whose choice affects significantly the quality of decoding. Materials and Methods. The well-known bit-flipping decoder of binary LDPC-codes is considered. This decoder has several parameters that are not rigidly bound with the code parameters. The dependence of the decoding quality on the selection of the output parameters of the bit-flipping decoder was investigated through simulation modeling. It is shown that the decoding results in this case are significantly affected by the input parameter of the decoder — threshold T. A modification of the BF-decoder of binary LDPC-codes has been developed, in which it is proposed to set the threshold dynamically during the execution of the algorithm depending on the error rate. A comparative analysis of the error- correcting capability of decoders is carried out by the simulation modeling method. Results. A lemma on the maximum value of the decoder threshold T is formulated and proved. Upper bounds for the number of operations are found for the original and modified decoders. A simulation model that implements a digital noise-immune communication channel has been built. In the model, the initial data is encoded with a given LDPC-code, then it is made noisy by additive uniformly distributed errors, and thereafter, it is decoded in turn by the bit-flipping algorithm with different threshold T parameters, as well as by a modified decoder. Based on the input and output data, the correction capacity of the decoders used is estimated. Experiments have shown that the error-correcting capability of the modified decoder in the range of the real error rate is higher than that of the original decoder, regardless of the selection of its parameters. Discussion and Conclusions. The lemma, proved in the paper, sets the upper bound on the threshold value in the original decoder, which simplifies its adjustment. The developed modification of the decoder has a better error- correcting capability compared to the original decoder. Nevertheless, the complexity of the modification is slightly increased compared to the original algorithm. It has been pointed out that the decoding quality of a modified decoder develops with a decrease in the number of cycles in the Tanner graph and an increase in the length of the code.