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International Conference on Innovations in Information, Embedded and Communication Systems

Design of Decoder using Modified Hybrid Weighted Symbol Flipping for Nonbinary Ldpc Codes

M. K. Dharani, C. Kalamani

Published Nov 18, 2014• 0 citations
OpenAlex

Abstract

A hybrid decoding algorithm which proposed for nonbinary and binary low density parity (LDPC) codes, both the algorithm combines the weighted symbol flipping (WSF) algorithm with the fast Fourier transform q-ary sum product algorithm (FFT-QSPA).The flipped position and value are determined by the symbol flipping metric and the received bit values in the first stage WSF algorithm. If the low complexity WSF algorithm is failed, the second stage FFT-QSPA is activated as a switching strategy. They are particularly effective for decoding LDPC codes constructed based on finite geometries and finite fields. Analyzing both the techniques nonbinary LDPC codes gives the better error performance and greatly reduces the computation complexity compared to binary LDPC codes. The proposed hybrid algorithm is used for some applications in communication systems for high speed and low power consumption. Keywords Nonbinary and binary low density parity-check (LDPC) code, Weighted symbol –flipping (WSF), Hybrid weighted symbol-flipping (HWSF), iterative decoding. 1.

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A hybrid decoding algorithm which proposed for nonbinary and binary low density parity (LDPC) codes, both the algorithm combines the weighted symbol flipping (WSF) algorithm with the fast Fourier transform q-ary sum product algorithm (FFT-QSPA).The flipped position and value are determined by the symbol flipping metric and the received bit values in the first stage WSF algorithm. If the low complexity WSF algorithm is failed, the second stage FFT-QSPA is activated as a switching strategy. They are particularly effective for decoding LDPC codes constructed based on finite geometries and finite fields. Analyzing both the techniques nonbinary LDPC codes gives the better error performance and greatly reduces the computation complexity compared to binary LDPC codes. The proposed hybrid algorithm is used for some applications in communication systems for high speed and low power consumption. Keywords Nonbinary and binary low density parity-check (LDPC) code, Weighted symbol –flipping (WSF), Hybrid weighted symbol-flipping (HWSF), iterative decoding. 1.
A two-stage hybrid iterative decoding algorithm with an efficient stopping criterion for nonbinary low-density parity-check (LDPC) codes is proposed, which combines weighted symbol-flipping (WSF) algorithm and fast Fourier transform q-ary sum-product algorithm (FFT-QSPA). The first WSF decoding would be stopped in advance by analyzing the trend of the number of unsatisfied checks. If the first stage decoding is stopped or failed, the second powerful FFT-QSPA is activated. The proposed decoding with the efficient stopping achieves error performance as good as that of FFT-QSPA with a low complexity, and converges faster than hybrid WSF (HWSF) algorithm.
In this paper, a new low-complexity symbol-flipping algorithm to decode nonbinary low-density parity-check (LDPC) codes is proposed. The decoding procedure updates iteratively the hard-decision received symbol vector in search of a valid codeword in the symbol vector space. Only one symbol is changed in each iteration, and symbol flipping function combines the number of failed checks and reliability of the received bits and calculated symbols. An optional mechanism to avoid infinite loops in high Galois field search is also proposed. Our studies show that the algorithm achieves an appealing tradeoff between performance and complexity over relatively low Galois field for short to medium code length.
This paper analyzes a weighted symbol-flipping (SF) algorithm for nonbinary low density parity-check (NB-LDPC) codes over binary input AWGN (BI-AWGN) channels. The weighted SF algorithm has two main parts: the symbol-flipping function and the new candidate symbol rule. First, it is demonstrated that a rule for choosing the new candidate symbol based on absolute values of observed channel outputs is equivalent to a rule based on Euclidean distances. Then, it is verified that the weighting factor of flipping function has negligible impact on algorithm performance. Motivated by this fact, a SF decoding algorithm is proposed whose flipping function requires only syndrome values and flips symbols in parallel. It is observed that SF decoding outperforms WSF for q-ary codes with large q.
A new low-complexity symbol-flipping algorithm based on majority decision to decode nonbinary low-density parity-check (LDPC) codes is proposed. The decoding procedure updates iteratively the hard-decision received symbol vector in search of a valid codeword in the symbol vector space. Only one symbol is changed in each iteration, and symbol flipping function combines the number of failed checks and reliability of the received bits and calculated symbols. Flipped symbol position is determined by majority decision and flipped value is calculated by channel output. And an optional mechanism to avoid infinite loops in high Galois field search is also proposed. Our studies show that the algorithm achieves an appealing tradeoff between performance and complexity over relatively low Galois field for short to medium code length.
An efficient symbol-flipping based decoding algorithm designed for nonbinary generalized low-density parity-check (GLDPC) codes is proposed. By extending the concept of the weighted bit flip voting (WBFV) algorithm designed for binary Hamming-code based GLDPC codes, the symbol-flipping decoding algorithm can be beneficially employed for decoding the family of GLDPC codes constructed from nonbinary constituent codes, such as nonbinary Bose Chaudhuri Hocquenghem (BCH) codes or Reed Solomon (R-S) codes. The simulation results demonstrate that improvements of 1 dB and 2.7 dB are achieved by the proposed coding scheme in comparison to the more conventional binary GLDPC codes using the WBFV decoding algorithm, when using the Galois Field GF(32) for communicating over AWGN and uncorrelated Rayleigh fading channels, respectively
Two low-complexity symbol flipping decoding algorithms, the Improved weighted-Algorithm B algorithm (Iwtd-AlgB) and the Truncation-based Distance-Symbol-Flipping-Decoding with Prediction (TD-SFDP) algorithm, are presented for non-binary Low Density Parity Check (LDPC) codes. For the Iwtd-AlgB algorithm, the scaling factor of the flipping metric can be replaced by the simple sums of the extrinsic information and the distance-based parameter, which can avoid the multiplication operations in the iterations and thus can reduce the decoding complexity. For the presented TD-SFDP algorithm, the variable nodes and the finite field symbols are truncated and classified based on the extrinsic information frequency and the flipping function. Only those nodes/symbols that satisfy the designed conditions can be involved in the message updating process. Simulations and numeric results show that, the presented two decoding algorithms can reduce the computational complexity at each iteration with a controllable performance degradation, thus can make efficient trade-offs between performance and complexity.