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Journal of Communications

A Classified Normalized BP-Based Algorithm with 2-Dimensional Correction for LDPC Codes

Zhou Zhong, Shuming Guo, Xiangyang Xu, Huiqing Bai

Published Jan 1, 2013• 5 citations
Publisher

Abstract

A BP-based algorithm with 2-dimensional classified normalized correction is developed to reduce the complexity and improve the performance of decoding algorithm for the low density parity check (LDPC) codes. The algorithm first utilizes classification according to the absolute values of incoming messages in check nodes. Then it uses 2-dimensional normalization to correct the minimum and sub-minimum values. The 2-dimensional normalized factors can be calculated respectively by using probability and statistic theory in the initialization step. Simulation results illustrate that the proposed algorithm achieves better performance in bit error ratio (BER) and average iteration number than normalized BP-based algorithm in the high signal noise ratio (SNR) region, i.e., it can achieve 0.4 dB SNR gain and reduce 20% number of iterations at BER= 5 10  , whose complexity is also much less than that of belief propagation (BP) algorithm. It is concluded that the proposed algorithm offers better tradeoff between performance and complexity.  Index Terms—channel coding theory, density evolution, Iterative decoding algorithm

DOI
10.12720/jcm.8.5.315-321

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A BP-based algorithm with 2-dimensional classified normalized correction is developed to reduce the complexity and improve the performance of decoding algorithm for the low density parity check (LDPC) codes. The algorithm first utilizes classification according to the absolute values of incoming messages in check nodes. Then it uses 2-dimensional normalization to correct the minimum and sub-minimum values. The 2-dimensional normalized factors can be calculated respectively by using probability and statistic theory in the initialization step. Simulation results illustrate that the proposed algorithm achieves better performance in bit error ratio (BER) and average iteration number than normalized BP-based algorithm in the high signal noise ratio (SNR) region, i.e., it can achieve 0.4 dB SNR gain and reduce 20% number of iterations at BER= 5 10  , whose complexity is also much less than that of belief propagation (BP) algorithm. It is concluded that the proposed algorithm offers better tradeoff between performance and complexity.  Index Terms—channel coding theory, density evolution, Iterative decoding algorithm
A check node degree-based modified min-sum algorithm which classifies the codes was developed to reduce the complexity and improve the performance of decoding algorithm for low-density parity-check(LDPC) codes.The algorithm corrects both the minimum and sub-minimum absolute values of incoming messages in the check nodes.Two correction factors are obtained by calculating the offset between the belief propagation(BP) algorithm and the min-sum algorithm based on the check node degree.Simulations show that the algorithm achieves better performance than the BP algorithm at high signal noise ratio.The algorithm is also less complex than the BP algorithm and provides a good tradeoff between performance and complexity for any check node degree distribution in the LDPC codes.
In this paper, a modified min-sum decoding algorithm based on classified correction is proposed for low density parity check (LDPC) codes. Different from the single correction in the normalized belief propagation (BP)-based and offset BP-based algorithms [4], the proposed algorithm utilizes two corrections for both minimum and sub-minimum magnitudes of input messages in check nodes. These two correction factors can be obtained by analyzing the offset of updated messages in check nodes between the BP and the min-sum algorithms associated with check node degree. Simulation results show that the proposed algorithm can achieve performance very close to that of the BP algorithm. Furthermore, the FPGA implementation of this algorithm can reach a throughput of 200 Mbps at BER=10-6with lower complexity and fewer resources than the BP 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.
To further improve the decoding performance of the Normalized BP-Based algorithm,an improved Normalized BP-Based algorithm was proposed.The correction factor was changed dynamically according the amount of the information from the check nodes to variable nodes in order to achieve non-linear compensation of BP-Based algorithm.The simulation results show that when the bit error rate was less than 0.5×10-2,the improved algorithms could get about 0.1 dB gain,compared with Normalized BP-Based algorithm,only with slight increase in complexity,and the number of iterations did not increase.
The paper presents a novel approach to reduce the bit error rate (BER) in iterative belief propagation (BP) decoding of low density parity check (LDPC) codes. The behavior of the BP algorithm is first investigated as a function of number of decoder iterations, and it is shown that typical uncorrected error patterns can be classified into 3 categories: oscillating, nearly-constant, or random-like, with a predominance of oscillating patterns at high Signal-to-Noise (SNR) values. A proposed decoder modification is then introduced based on tracking the number of failed parity check equations in the intermediate decoding iterations, rather than relying on the final decoder output (after reaching the maximum number of iterations). Simulation results with a rate ¿ (1024,512) progressive edge-growth (PEG) LDPC code show that the proposed modification can decrease the BER by as much as 10-to-40%, particularly for high SNR values.
Many classes of high-performance Low-density parity check codes are based on parity check matrices composed of permutation sub matrices. The emulation-simulation framework further allows the algorithm and implementation to be iteratively redefined to improve the error floor performance of message passing decoder. Log-Like hood-Ratio (LLR) based Belief-Propagation (BP) algorithm is presented for Low Density Parity Check codes. Numerically accurate representation of check node update computation used in LLR-BP decoding is described. The implementation of Sum-Product algorithm (SPA) within Low Density Parity Check Code (LDPC) decoder is described in this paper and the correction term is used to improve the decoding performance of min-sum algorithm (MSA). Quantization and log-tanh function approximation in sum-product decoder strongly affect which absorbing set dominates in error floor region. For LDPC decoder, bit error rate (BER) decreases with increase in the signal to noise ratio.