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International Conference on Computational Intelligence and Software Engineering (CiSE)

Gaussian Approximation for LDPC Codes under Group Shuffled Belief Propagation Decoding

Zhenzhen Song, Runbo Yu, Piming Ma

Published Sep 1, 2010• 1 citation
Publisher

Abstract

Group shuffled belief propagation (GSBP) algorithm is a modified algorithm to decode LDPC codes. Compared with belief propagation decoding, this algorithm converges faster. In this paper, we analyze the performance of GSBP decoding by means of Gaussian approximation. Under the assumption of Gaussian density, the updating message means during GSBP decoding are derived. The results show that the proposed algorithm can verify the fast convergence property of GSBP decoding effectively.

DOI
10.1109/wicom.2010.5600988

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Group shuffled belief propagation (GSBP) algorithm is a modified algorithm to decode LDPC codes. Compared with belief propagation decoding, this algorithm converges faster. In this paper, we analyze the performance of GSBP decoding by means of Gaussian approximation. Under the assumption of Gaussian density, the updating message means during GSBP decoding are derived. The results show that the proposed algorithm can verify the fast convergence property of GSBP decoding effectively.
A group shuffled belief propagation (GSBP) decoding for punctured low-density parity-check (LDPC) codes is proposed in the paper. The proposed GSBP decoding schedules the updating order of each bit node according to its recovery order in the standard BP decoding. This enables the proposed decoding to recover all punctured nodes in the first iteration with the minimum required number of groups. Calculation of the number of effective updates, which indicates the number of nonzero check-to-bit messages, shows that the proposed decoding can achieve faster decoding convergence than the layered BP (LBP) decoding for rate-compatible punctured LDPC (RCP-LDPC) codes. In the simulation results, the maximum SNR gain of the proposed decoding over the LBP decoding is about 0.9dB at the FER of 10-4.
To reduce the implementation complexity of a belief propagation (BP) based low-density parity-check (LDPC) decoder, shuffled BP decoding schedules, which serialize the decoding process by dividing a complete parallel message-passing iteration into a sequence of sub-iterations, have been proposed. The so-called group horizontal shuffled BP algorithm partitions the check nodes of the code graph into groups to perform group-by-group message-passing decoding. This paper proposes a new grouping technique to accelerate the message-passing rate. Performance of the proposed algorithm is analyzed by a Gaussian approximation approach. Both analysis and numerical experiments verify that the new algorithm does yield a convergence rate faster than that of existing conventional or group shuffled BP decoder with the same computing complexity constraint.
Implementing a belief propagation (BP) based LDPC decoder requires high degrees of parallelism using many component soft-in soft-output (SISO) decoding units to perform message passing from variable nodes to check nodes or vice versa. An obvious complexity-reduction solution is to serialize the decoding process, i.e., dividing a decoding iteration into several serial sub-iterations in which a sub-iteration performs only part of the complete parallel message-passing operation. The group horizontal shuffled BP (GHSBP) and vertical shuffled BP (GVSBP) algorithms respectively partition the check and variable nodes of the code graph into groups to perform group-by-group message-passing decoding. This paper proposes new techniques to improve three key elements of a GHSBP decoding algorithm, namely, the grouping method, the decoding schedule and the log-likelihood updating formulae. The (check nodes) grouping method and decoding schedule optimize certain design criterion. The new normalized min-sum updating formula with a self-adjustable correction (scaling) factor offers better nonlinear approximation. Numerical performance of new GHSBP algorithms that include part or all three new techniques indicate that the combination of the proposed grouping and decoding schedule yields a faster convergence rate and our modified min-sum algorithm gives performance superior to that of the conventional min-sum and normalized min-sum algorithm and is very close to that of the sum-product algorithm.
In this paper, we have developed several concepts such as the tree concept, the short cycle concept and the group shuffling concept of a propagation cycle to decrypt low-density parity-check (LDPC) codes. Thus, we proposed an algorithm based on group shuffling propagation where the probability of occurrence takes exponential form exponential factor appearance probability belief propagation-group shuffled belief propagation (EFAP-GSBP). This algorithm is used for wireless communication applications by providing improved decryption performance with low latency. To demonstrate the effectiveness of our suggested technique EFAP-GSBP, we ran numerous simulations that demonstrated that our algorithm is superior to the traditional BP/GSBP algorithm for decrypting LPDC codes in both regular and non-regular forms