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IET International Conference on Information and Communications Technologies (IETICT)

Serial FFT-BP LDPC decoding based on unsymmetrical message transmission

Xin Chen, Shenyang Li

Published Jan 1, 2013• 0 citations
Publisher

Abstract

A low complexity serial Fast Fourier Transform Belief Propagation (FFT-BP) algorithm for decoding non-binary low-density parity-check (LDPC) codes use unsymmetrical message transmission scheme between bit nodes and check nodes is presented. Before each step of iteration, every symbol node's reliability was evaluated based on high reliable check number and pseudo a posterior probability (APP). The variable nodes with high reliability will just send messages to its neighbour and avoid the messages from them. Compared to the previous traditional message transmission method, it can use the messages adaptively, and therefore provide better decoding quality and computation complexity reduction. Simulations show that the proposed method could improve performance and reduce complexity at the same time compared with the conventional FFT-BP decoding algorithm.

DOI
10.1049/cp.2013.0090

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A low complexity serial Fast Fourier Transform Belief Propagation (FFT-BP) algorithm for decoding non-binary low-density parity-check (LDPC) codes use unsymmetrical message transmission scheme between bit nodes and check nodes is presented. Before each step of iteration, every symbol node's reliability was evaluated based on high reliable check number and pseudo a posterior probability (APP). The variable nodes with high reliability will just send messages to its neighbour and avoid the messages from them. Compared to the previous traditional message transmission method, it can use the messages adaptively, and therefore provide better decoding quality and computation complexity reduction. Simulations show that the proposed method could improve performance and reduce complexity at the same time compared with the conventional FFT-BP decoding algorithm.
An improved belief propagation(BP) decoding scheme was put forward to solve the high complexity and low decoding efficiency problem of BP in low density parity check(LDPC) codes.Because different bit nodes and check nodes have different reliability and contribute differently to BP decoding;the proposed decoding scheme employs a differentiate rule based on lawless check number and pseudo posterior probability to evaluate every bit's reliability before each step of iteration;The nodes have little lawless check number and large pseudo posterior probability are supposed to have higher reliability.The bits with high reliability need not to be updated by the decoder.Simulation shows that the proposed BP decoding algorithm can reduce the computational load and increase the decoding efficiency significantly.
Abstract A serial Fast Fourier Transform Belief Propagation (FFT-BP) algorithm with low complexity of non-binary LDPC codes decoding is presented in this paper to reduce the effects of short girth. During iteration, part of the variable nodes with short girths will just send messages to its neighbor, which are in the same short girth and avoid the messages from them. In the next iteration decoding, this part of the nodes updates and the newly updated node with sort girth stops updating. Simulations show that the proposed algorithm achieves a better gain to the standard algorithm and reduces complexity at the same time.
Variant belief propagation (BP) algorithms are applied to low-density parity-check (LDPC) codes. However, conventional decoders suffer from a large resource consumption due to gathering messages from all the neighbour variable-nodes and/or check-nodes through cumulative calculations. In this paper, a check-belief propagation (CBP) decoding algorithm is proposed. Check-belief is used as the probability that the corresponding parity-check is satisfied. All check-beliefs are iteratively enlarged in a sequential recursive order, and successful decoding will be achieved after the check-beliefs are all big enough. Compared to previous algorithms employing a large number of cumulative calculations to gather all the neighbour messages, CBP decoding can renew each check-belief by propagating it from one check-node to another through only one variable-node, resulting in a low complexity decoding with no cumulative calculations. The simulation results and analyses show that the CBP algorithm provides little error-rate performance loss in contrast with the previous BP algorithms, but consumes much fewer calculations and memories than them. It earns a big benefit in terms of complexity.
Low-density parity-check (LDPC) codes over finite fields GF(q) have a better performance than those of the binary low-density parity-check codes, at short and medium block lengths, but the decoder of GF(q)-LDPC has more complexity. In this paper, we present a new reduced-complexity belief propagation (BP) decoding algorithm for GF(q)-LDPC codes by analyzing the reliability of code symbols. Instead of update all the variable nodes during iteration, we just update variable nodes which are mostly to be in an error. The algorithm also shows a property to reduce the effects of oscillating on decoding. The simulations prove that we could improve performance and reduce complexity at the same time for short and medium GF(q)-LDPC codes.
In this paper, an improved decoding algorithm for Non-binary low density parity check (NB-LDPC) codes with low decoding complexity and suitable for field-programmable gate array (FPGA) implementation is proposed, which is a mixed logarithmic domain FFT-BP decoding algorithm (Mixed Log-FFT-BP) for the problem of high complexity of the existing decoding algorithms for Non-binary LDPC codes. The algorithm combines the traditional Log-BP algorithm with the FFT-BP algorithm, and simplifies the update of the check nodes in the iterative decoding process. A large number of convolution operations are converted into multiplication operations in frequency domain by using FFT transform and IFFT transform. The multiplication of the original FFT-BP algorithm is converted into the addition and look-up table operations in the logarithmic domain. Then, the logarithm of the probability information is directly solved, so that it can be decoded in the logarithmic domain, which saves the computation of the log likelihood ratio, and then reduces the complexity. Simulation results show that under the additive Gauss white noise channel, when the bit error rate is 10-5, compared with BP algorithm, Log-Bp algorithm and FFT-BP algorithm, the performance of Mixed Log-FFT-BP algorithm is not decreased, and all of them remain within the range of 0.1-0.2dB.
Compared to classic channel coding,Low-density parity-check(LDPC) codes have proved to be very powerful channel coding schemes with a broad range of applications.However,as maximum-likelihood decoding is too complex to implement,suboptimal decoders have to be employed.One of the most popular decoding algorithms of LDPC codes is belief propagation(BP) decoding.Informed Dynamic Scheduling(IDS) can provide a better BER performance,but hard to implement due to high computational complexity increased.In order to improve the convergence,a simple low-complexity sequential check-node-based scheduling strategy is proposed.A new check-node-based reliability measure is defined,which represents the degree of reliability approximately.The reliability measure is used for ordering while the actual message updates still use the exact BP equations.During an iteration,the schedule strategy finds an update sequence,which is arranged by the new defined reliability measure in ascending order.Complexity is compared among those algorithms.Mechanism why the new strategy works effective is presented.Simulation shows that the new approach significantly improves the BER performance using short-length block LDPC codes and reduces iterations.