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IFIP International Conference on Wireless and Optical Communications Networks (WOCN)

A new modified UMP BP decoding algorithm of quasi-cyclic LDPC codes based on oscillation estimation

Fa Xun Zhang, Fa Xia Yang, Meng Dong

Published Jul 1, 2013• 0 citations
Publisher

Abstract

A modified algorithm based on the Uniformly Most Powerful Belief Propagation (UMP BP) algorithm are studied for decoding implementation of regular QC-LDPC codes by introducing two factors of mean square difference and ratio in check processing. The decoding algorithm is a combination of soft decision and hard decision to adaptively decrease the oscillation caused by the change of ex-LLRs sign, further to reduce the errors of UMP BP algorithm caused in first iteration, Simulation result shows that implementation of improved DARBFMS algorithm outperform conventional algorithms. Compared with the improved algorithm in irregular LDPC codes, performance in QC-LDPC codes seems better.

DOI
10.1109/wocn.2013.6616219

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A modified algorithm based on the Uniformly Most Powerful Belief Propagation (UMP BP) algorithm are studied for decoding implementation of regular QC-LDPC codes by introducing two factors of mean square difference and ratio in check processing. The decoding algorithm is a combination of soft decision and hard decision to adaptively decrease the oscillation caused by the change of ex-LLRs sign, further to reduce the errors of UMP BP algorithm caused in first iteration, Simulation result shows that implementation of improved DARBFMS algorithm outperform conventional algorithms. Compared with the improved algorithm in irregular LDPC codes, performance in QC-LDPC codes seems better.
In this paper, we propose the modified uniformly most powerful (UMP) belief-propagation (BP)-based decoding algorithm which utilizes multiplicative and additive factors to diminish the errors introduced by the approximation of the soft values given by a previously proposed UMP BP-based algorithm. This modified UMP BP-based algorithm shows better performance than that of the normalized UMP BP-based algorithm, i.e., it has an error performance closer to BP than that of the normalized UMP BP-based algorithm on the additive white Gaussian noise channel for low density parity check codes. Also, this algorithm has the same complexity in its implementation as the normalized UMP BP-based algorithm.
In order to reduce the performance loss of UMP BP-based decoding algorithm relative to LLR-BP decoding algorithm,an improved UMP BP-based decoding algorithm is proposed.When the check nodes process the message,the normalized BP-based decoding algorithm and offset BP-based decoding algorithm are integrated effectively by setting a correction factor and an offset factor reasonably.When the variable nodes process the message,an oscillation compensation algorithm based on LLR-BP decoding algorithm is introduced.Simulation results show that based on the irregular LDPC codes and under the condition of the same bit error rate within a certain range,the improved UMP BP-based decoding algorithm improves the decoding performance greatly compared with the three decoding algorithms which are based on UMP BP,normalized BP and offset BP decoding algorithms,respectively,and therefore quite efficiently approaches to the LLR-BP decoding algorithm which has excellent performance.
An improved decoding algorithm based on minimum mean square error(MMSE) for low-density parity-check(LDPC) codes is proposed.The new algorithm combines processing methods of two modified uniformly most powerful(UMP) BP-based algorithms(normalized UMP BP-based algorithm and offset UMP BP-based algorithm) and attains the corresponding normalization factor and offset factor according to MMSE criterion.Simulations indicate that,compared with the two above-mentioned algorithms,a gain of 0.03 dB can be achieved at bit error rate(BER) of 10-6 with the proposed algorithm when a(3,6) regular LDPC code of code length 1 008 and code rate 1/2 is used.
A low-density parity check (LDPC) code with the belief propagation (BP) or the log-likelihood ratio belief propagation (LLR-BP) can achieve good bit error rate (BER) performance approaching the Shannon limit. When a parity check matrix of the LDPC code has the cycle, the BP and LLR-BP decoding algorithms achieve approximate maximum a posterior probability (MAP) decoding. Although the decoding algorithms are approximate MAP decoding, LDPC codes can achieve very good BER. For the short and middle length LDPC codes, BER and block error rate (BLER) performances are affected by cycle largely. In each iteration, the magnitudes of a posterior LLRs of some bits oscillate owing to cycles. The oscillation is the dominant error factor in the high Eb/Noregion for short and middle length LDPC codes. In this paper, we extend the definition of oscillation to extrinsic LLR (ex-LLR) derived in the bit node process and propose the modified LLR-BP and the modified UMP-BP decoding algorithms. To reduce effects of oscillating ex-LLRs on decoding, for oscillating ex-LLRs, we add the previous ex-LLR to the current ex-LLR. From the computer simulation, we show that for short and middle length LDPC codes, with a simple modification, our proposed decoding algorithms can improve the conventional LLR-BP and UMP-BP decoding algorithms. In particular, we show that the modified UMP-BP decoding algorithm with low complexity can achieve better BER and BLER than the conventional LLR-BP decoding algorithm
A uniformly most powerful (UMP) belief propagation (BP) based algorithm is referred to as a simplified version of a BP algorithm with reduced complexity but performance loss for low density parity check (LDPC) codes. To compensate the performance loss, the normalized BP based algorithm was proposed, where the normalization factor was derived by mean ratio or by minimizing the mean square error. In this paper, an improved novel normalized BP based algorithm is proposed. The normalization uses multiplicative factor instead of divisional factor. The novel scheme shows better performance than the existing normalized BP based algorithms while keeping the same implementation complexity. The simulation is done for two kinds of LDPC codes: random constructed codes and finite geometry codes. At high signal-to-noise ratio (SNR) region, the proposed scheme can achieve even better performance than BP algorithm for short length random constructed LDPC codes.
According to no-convergence of falsely oscillating iteration in the low-density parity-check(LDPC) decoding at the range from medium to high SNRs(Signal to Noise Ratios),we propose a modified LDPC belief propagation(BP) decoding algorithm,i.e.soft value zero-forcing BP algorithm.By setting extrinsic information of the oscillating iteration bit nodes into zero,the impact on the iteratively decoding from false channel information is greatly reduced.And it also improves the performance of the decoding algorithm.Furthermore,a decision criterion of oscillating iteration nodes is presented to increase the accuracy of the decision.Simulation results show that the proposed algorithm has better decoding performance than that of the BP algorithm with the same iterations at medium and high SNRs.