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IEEE Communications Letters

Hybrid Iterative Decoding for Low-Density Parity-Check Codes Based on Finite Geometries

Li Jian, Xian‐Da Zhang

Published Jan 1, 2008• 16 citations
Publisher

Abstract

In this letter, a two-stage hybrid iterative decoding algorithm which combines two iterative decoding algorithms is proposed to reduce the computational complexity of finite geometry low-density parity-check (FG-LDPC) codes. We introduce a fast weighted bit-flipping (WBF) decoding algorithm for the first stage decoding. If the first stage decoding fails, the decoding is continued by the powerful belief propagation (BP) algorithm. The proposed hybrid decoding algorithm greatly reduces the computational complexity while maintains the same performance compared to that of using the BP algorithm only.

DOI
10.1109/lcomm.2008.071563

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In this letter, a two-stage hybrid iterative decoding algorithm which combines two iterative decoding algorithms is proposed to reduce the computational complexity of finite geometry low-density parity-check (FG-LDPC) codes. We introduce a fast weighted bit-flipping (WBF) decoding algorithm for the first stage decoding. If the first stage decoding fails, the decoding is continued by the powerful belief propagation (BP) algorithm. The proposed hybrid decoding algorithm greatly reduces the computational complexity while maintains the same performance compared to that of using the BP algorithm only.
Based on decoding performance,complexity and latency of finite-geometry low-density parity-check(FG-LDPC) codes,an efficient decoding algorithm is proposed.The new algorithm is a hybrid bit-flipping(BF)/majority-logic(MLG) decoding scheme.In BF decoding,an efficient method was explored to measure the reliability of the checks.At the completion of a small number of iterations,the output from BF decoding is decoded by MLG decoding.In the hybrid algorithm,there are no float operations.Simulation results show that the hybrid algorithm can provide 0.3?dB coding gain over weight bit-flipping(WBF) decoding.
In this paper, a new two-stage hybrid algorithm for decoding Low-Density Parity-Check (LDPC) codes is proposed that incorporates two iterative decoding. For the first stage of decoding, we offer a new decoding algorithm called Improved Variable Multi Weighted Bit-Flipping (IVMWBF) algorithm. Since the IVMWBF algorithm is based on the idea of flipping variable multi bits in each iteration, both improvement in performance and reduction in iteration number and computational complexity are observed in this algorithm. The proposed hybrid algorithm which is a combination of the IVMWBF and BP algorithms, while having a performance exactly similar to that of the BP algorithm, has less complexity compared to that algorithm.
Based on decoding performance, complexity and latency of finite-geometry low-density parity-check (LDPC) codes, an efficient decoding algorithm is proposed. The algorithm is a hybrid bit-flipping (BF)/majority-logic (MLG) algorithm. In the algorithm, there are two stages. At the first stage, a code is decoded with bit-flipping (BF) with a small fixed number of iterations. Then the output from bit-flipping (BF) decoder is decoded by majority-logic (MLG) decoding. And in bit-flipping (BF) decoding, a new method is used to find the least reliable position. In the hybrid algorithm, there aren't real operations. Simulation results show that the algorithm provides 0.3dB coding gain over weight bit-flipping (WBF) decoding, and within 1 dB away from sum-product algorithm (SPA) decoding.
This paper presents a low-complexity iterative joint detection and decoding algorithm for finite geometry-low density parity check (FG-LDPC) coded multiple-input multiple-output (MIMO) systems, in which the MIMO channel detector and the FG-LDPC decoder iteratively exchange soft information. The key to the simplicity of the algorithm is the use of a bit flipping-based decoder for FG-LDPC code. An important issue addressed here is the generation of soft information from the binary outputs of the bit-flipping decoder to be fed back to the MIMO detector. Simulation results show that the proposed joint detection and decoding algorithm achieves a substantial reduction in decoding error probability compared to a cascaded detector and a decoder. We also compare the performance with belief-propagation (BP) based detector-decoders which are significantly more complex. The new algorithm provides a practical approach to joint detection and decoding of popular FG-LDPC codes in a MIMO system, a task which is computationally unmanageable with a BP algorithm.
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.
In this paper, a hybrid decoding algorithm for finite-geometry low-density parity-check (FG-LDPC) codes is proposed. The algorithm is based on the interior point method with barrier function introduced by Wadayama. First, an efficient implementation of Wadayama's algorithm is presented. The main idea behind the modification is to approximate the barrier function for the fundamental polytope defining the code so that it contains only one linear constraint for each of the parity-check constraints. A two-stage hybrid decoding which combines the interior point decoding (IPD) and a low-complexity decoding algorithm for FG-LDPC codes is then proposed. In the first stage, the interior point decoding is used to generate a search point. If the first stage decoding fails, the decoding is continued by the low-complexity algorithm that is initialized by the result of the IPD. Compared with a conventional iterative message-passing (IMP) decoder, the proposed hybrid algorithm achieves better bit-error rate (BER) and frame-error rate (FER) for small block lengths at medium to high signal-to-noise ratio (SNR).