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International Symposium on High-capacity Optical Networks and Enabling Technologies

Fast decoding of low density parity check codes

Nassib Laouini, Larbi Ben Hadj Slama, Ammar Bouallègue

Published Dec 1, 2012• 5 citations
Publisher

Abstract

The Layered Belief Propagation L-BP algorithm is is a modified Belief Propagation BP algorithm, where the check nodes are divided in subgroups called layers and each iteration is broken into multiple sub-iterations. In this paper, we consider layered belief propagation decoding and propose an efficient variable node layering for decoding LDPC codes that performs well. We compare the performance of the first introduced LDPC decoding algorithm BP and Layered BP using check node layering with Layered BP using variable node layering in terms of bit error rate (BER). We show that the convergence for decoding LDPC codes is increasing by using a simple and efficient layering strategy.

DOI
10.1109/honet.2012.6421434

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The Layered Belief Propagation L-BP algorithm is is a modified Belief Propagation BP algorithm, where the check nodes are divided in subgroups called layers and each iteration is broken into multiple sub-iterations. In this paper, we consider layered belief propagation decoding and propose an efficient variable node layering for decoding LDPC codes that performs well. We compare the performance of the first introduced LDPC decoding algorithm BP and Layered BP using check node layering with Layered BP using variable node layering in terms of bit error rate (BER). We show that the convergence for decoding LDPC codes is increasing by using a simple and efficient layering strategy.
Layered decoding is well appreciated in Low-Density Parity-Check (LDPC) decoder implementation since it provides efficient and high-throughput implementation of LDPC decoders. Variable-Node Layered Belief Propagation (VL-BP) algorithm and their reduced-complexity derivatives for LDPC codes are presented. The VL-BP algorithm is a modification of Belief Propagation algorithm (BP), where the variable nodes are divided in subgroups called layers and each iteration is broken into multiple sub-iterations. Some simplifications can also be made to lower the complexity of both BP and CL-BP algorithms, and particularly the complexity of the check node update rule. In this paper, we consider Variable Node Layered BP (VL-BP) algorithm and propose an optimized min-sum VL-BP (MS VL-BP) algorithm for decoding LDPC code which has better performance not only from MS VL-BP algorithm but also from BP algorithm. In this decoding method, unlike other layered algorithms, we consider for the first layer a set of variable nodes that has a low value of the intrinsic information. Simulation results show that good performance can be achieved, and which can even be improved by the addition of either a normalization term or an additive offset term.
Schedule plays an important role in layered belief propagation (BP) decoding of low-density parity-check (LDPC) codes. It affects the error-rate performance as well as convergence rate of the decoder. In this paper, an efficient scheduling scheme is proposed to arrange the updating order of check nodes for layered BP decoder of regular LDPC codes. This scheme selects check node one at a time based on the reliability of the variable nodes. Specifically each time the check node with maximum number of low-reliability neighbors is selected. For simplicity, we introduce the updating state instead of the real-time messages to represent variable-node reliability. Simulation results on regular LDPC codes prove that the proposed scheduling scheme can obtain efficient schedules with fast convergence and good error-rate performance.
An efficient dynamic schedule for layered belief-propagation (LBP) decoding of low-density parity-check (LDPC) codes is presented, in which the check nodes connecting to a variable node with maximum relative message residual are chosen in each dynamic decoding iteration, and then LBP is performed for these check nodes. In this schedule we combined the features of lazy schedule and node-wise residual belief propagation (NWRBP) together while keeping the extra computational complexity very low. Simulation results show that the new schedule speeds up the convergence rate and greatly improves error performance at medium to high signal-to-noise ratio (SNR) when compared to the standard LBP decoding algorithm.
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.
Shuffled decoding is known to provide efficient and high-throughput implementation of LDPC decoders. In this paper, a new grouping technique of variable nodes to accelerate the message-passing rate is presented. In this algorithm, unlike other group-shuffled decoding methods, we consider for the first sub-group a set of variable nodes that has a low value of the intrinsic information, where the variable nodes of the code graph are divided into sub-groups called layers to perform group-by-group message-passing decoding and each iteration is broken into multiple sub-iterations. This paper proposes a simplification of the Variable Node group-shuffled Belief Propagation (Optimized VN group-shuffled BP) to lower the complexity of the check node update rule. Simulation results, verify that the Optimized VN group-shuffled BP does yield a faster convergence rate than both Belief Propagation (BP) and Check Node group-shuffled Belief Propagation (CN group-shuffled BP) decoder.
A hybrid belief propagation (BP) decoding algorithm for low-density parity-check code is proposed to accelerate the convergence of decoding and reduce the number of decoding iterations. The hybrid scheme is presented by integrating the BP algorithm with the bit-flipping function which is used as adaptive weighted factor in the BP iteration decoding. The adaptive weighting factor is based on the average weighted reliability measure of the hard output of decoder. The proposed hybrid adaptive weighted iteration scheme can efficiently increase the convergence speed of the belief propagation decoding and therefore improve the error performance. Simulation results show that the proposed algorithm can significantly reduce the decoding complexity and achieve better error performances as compared with the sum-product algorithm.