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Journal of Xidian University

Simplified decoding algorithm for LDPC over GF(q)

Xinmei Wang

Published Jan 1, 2011• 1 citation
OpenAlex

Abstract

A simple,yet effective decoding algorithm for LDPC(low-density parity-check) codes over GF(q) is presented.By taking advantages of the first-term Taylor's series expansion to approximate the correction term of the Jacobian logarithm used in LLR-SPA(log-likelihood ratio sum-product algorithm),we propose an algorithm which significantly simplifies the check node update computation of the optimal LLR-SPA.Compared to the offset min-sum algorithm,the proposed algorithm achieves a gain of about 0.2dB at the BER of 10-4.Moreover,unlike the offset min-sum algorithm,parameters of this algorithm are independent of the order of the Galois Filed.

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A simple,yet effective decoding algorithm for LDPC(low-density parity-check) codes over GF(q) is presented.By taking advantages of the first-term Taylor's series expansion to approximate the correction term of the Jacobian logarithm used in LLR-SPA(log-likelihood ratio sum-product algorithm),we propose an algorithm which significantly simplifies the check node update computation of the optimal LLR-SPA.Compared to the offset min-sum algorithm,the proposed algorithm achieves a gain of about 0.2dB at the BER of 10-4.Moreover,unlike the offset min-sum algorithm,parameters of this algorithm are independent of the order of the Galois Filed.
An improved decoding algorithm for low-density parity-check (LDPC) codes is presented. By taking advantages of the first-term Taylor’s series multiple expansion to approximate the correction term of the Jacobian logarithm used in LLR-SPA (log-likelihood ratio sum-product algorithm), we propose an algorithm which significantly simplifies the check node update computation of the optimal LLR-SPA. Besides, the parameter δ is introduced to determine suitable expansion points. The simulation result shows that the proposed method with ten expansion points when δ is set to 0.01 has almost identical performance compared with ideal SPA algorithm and outperforms both the min-sum algorithm (MS), the offset min-sum algorithm (OMS) and the normalised min-sum algorithm (NMS). The architecture of proposed method is also presented for implementation, which has reduced computational complexity and is feasible for hardware implementation.
Various log-likelihood-ratio-based belief-propagation (LLR-BP) decoding algorithms and their reduced-complexity derivatives for low-density parity-check (LDPC) codes are presented. Numerically accurate representations of the check-node update computation used in LLR-BP decoding are described. Furthermore, approximate representations of the decoding computations are shown to achieve a reduction in complexity by simplifying the check-node update, or symbol-node update, or both. In particular, two main approaches for simplified check-node updates are presented that are based on the so-called min-sum approximation coupled with either a normalization term or an additive offset term. Density evolution is used to analyze the performance of these decoding algorithms, to determine the optimum values of the key parameters, and to evaluate finite quantization effects. Simulation results show that these reduced-complexity decoding algorithms for LDPC codes achieve a performance very close to that of the BP algorithm. The unified treatment of decoding techniques for LDPC codes presented here provides flexibility in selecting the appropriate scheme from performance, latency, computational-complexity, and memory-requirement perspectives.
Reduced-Complexity Decoding of LDPC Codes Various log-likelihood-ratio-based belief-propagation (LLR- BP) decoding algorithms and their reduced-complexity derivatives for low-density parity-check (LDPC) codes are presented. Numerically accurate representations of the check-node update computation used in LLR-BP decoding are described. Furthermore, approximate representation of the decoding computations are shown to achieve a reduction in complexity, by simplifying the check-node update or symbol-node update, or both. In particular, two main approaches for simplified check-node updates are presented that are based on the so-called min-sum approximation coupled with either a normalization term or an additive offset term. Density evolution is used to analyze the performance of these decoding algorithms, to determine the optimum values of the key parameters, and to evaluate finite quantization effects. Simulation results show that these reduced-complexity decoding algorithms for LDPC codes achieve a performance very close to that of the BP algorithm. The unified treatment of decoding techniques for LDPC codes presented here provides flexibility in selecting the appropriate scheme from a performance, latency, computational complexity, and memory-requirement perspective.
A novel effective decoding algorithm for LDPC codes is proposed, which significantly simplifies the check node update computation of the Sum-Product Algorithm (SPA). Through simplified Taylor Series algorithm, It made index operation for multiplication and addition operations in the check node update. Compared with the existing approximations, the proposed method is less computational complexity than SPA algorithm, simulation results show that the proposed algorithm can achieve an error performance better than the Min-sum (MS) algorithm with small increase computational complexity.
Efficient implementations of the sum-product algorithm (SPA) are presented for decoding low-density parity-check (LDPC) codes using log-likelihood ratios (LLR) as messages between symbol and parity-check nodes. Various reduced-complexity derivatives of the LLR-SPA are proposed. Both serial and parallel implementations are investigated, leading to trellis and tree topologies, respectively. Furthermore, by exploiting the inherent robustness of LLRs, it is shown, via simulations, that coarse quantization tables are sufficient to implement complex core operations with negligible or no loss in performance. The unified treatment of decoding techniques for LDPC codes presented here provides flexibility in selecting the appropriate design point in high-speed applications from a performance, latency and computational complexity perspective.