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IEEE/ACIS International Conference on Computer and Information Science (ICIS)

An improved normalized min-sum algorithm for LDPC codes

Jinlei Chen, Yan Zhang, Ruiyi Sun

Published Jun 1, 2013• 9 citations
Publisher

Abstract

An improved normalized min-sum (IN-MS) algorithm is proposed for decoding low-density parity-check (LDPC) codes. In this algorithm, two normalized factors are used in check node computing, one for the minimum data and another for the second minimum data, and this algorithm achieves a better approximation to the BP algorithm. Simulation results show that the decoding performance of IN-MS algorithm is better than that of the normalized min-sum (NMS) algorithm.

DOI
10.1109/icis.2013.6607890

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An improved normalized min-sum (IN-MS) algorithm is proposed for decoding low-density parity-check (LDPC) codes. In this algorithm, two normalized factors are used in check node computing, one for the minimum data and another for the second minimum data, and this algorithm achieves a better approximation to the BP algorithm. Simulation results show that the decoding performance of IN-MS algorithm is better than that of the normalized min-sum (NMS) algorithm.
In this paper, we present an improvement on the normalized min-sum (NMS) decoding algorithm for low density parity check codes. The modified NMS (M-NMS) algorithm introduces a more efficient adjustment for check node update computation. Taking the sub-minimum value among extrinsic information from the variable nodes into consideration, we make the correction factor varies with different iterations. Results show that, compared with standard min-sum (MS) and NMS decoding algorithms, the proposed method not only offers a better performance but also achieves a lower error floor in the high SNR region.
The NMS algorithm is most commonly used in the design of LDPC code decoders. The result of the smallest-sub-smallest operation in the minimum sum algorithm is actually only two values. According to this feature, this paper proposes an algorithm that uses two correction factors to normalize and correct the minimum value and the second minimum value. The normalized minimum sum algorithm have two correction factors λ1 and λ2, where λ1 normalizes the second smallest value, and λ2 normalizes the minimum value. Both the DN-MS algorithm and the NMS algorithm are approximate forms of the logarithmic domain BP algorithm, and have exactly the same amount of calculation. But the calculation result of the check node in the DN-MS algorithm is closer to the check node in the log domain BP algorithm, so it has better decoding performance.
To improve the decoding performance of Low Density Parity Check(LDPC) code,an efficient decoding algorithm based on min-sum algorithm is proposed. The proposed algorithm analyzes the check node update equation and at the view of probability to form an approximation min-sum equation. It adopts a dynamic normalization factor to improve the decoding performance. Detailed simulation results and comparisons with Belief Propagation(BP) algorithm show that,with little decoding performance loss,the proposed algorithm not only decreases computational load,but also improves decoding efficiency.
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.