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Applied Mechanics and Materials

A Novel LLR-BP Algorithm for LDPC Codes Based on Taylor Series and Least Squares

Xing Ru Zhang, Jianping Li, Chao Shi Cai

Published Nov 1, 2013• 0 citations
Publisher

Abstract

An effective log-likelihood-ratio-based belief propagation (LLR-BP) algorithm is proposed. It can reduce computational complexity of decoding algorithm for Low Density Parity Check (LDPC) codes. By using the Taylor series and least squares, high order multiplication based on the hyperbolic tangent (tanh) rule is converted to a first-order multiplication and addition after simplification. Moreover, all the logarithmic and exponential operations disappear without significant loss of the decoding performance. The simulation results show that the performance of the proposed scheme is similar to the general LLR-BP. In particular, we show that the modified algorithm with low complexity can achieve better BER than the other decoding algorithm in high signal-to-noise ratio region.

DOI
10.4028/www.scientific.net/amm.462-463.193

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An effective log-likelihood-ratio-based belief propagation (LLR-BP) algorithm is proposed. It can reduce computational complexity of decoding algorithm for Low Density Parity Check (LDPC) codes. By using the Taylor series and least squares, high order multiplication based on the hyperbolic tangent (tanh) rule is converted to a first-order multiplication and addition after simplification. Moreover, all the logarithmic and exponential operations disappear without significant loss of the decoding performance. The simulation results show that the performance of the proposed scheme is similar to the general LLR-BP. In particular, we show that the modified algorithm with low complexity can achieve better BER than the other decoding algorithm in high signal-to-noise ratio region.
Many classes of high-performance Low-density parity check codes are based on parity check matrices composed of permutation sub matrices. The emulation-simulation framework further allows the algorithm and implementation to be iteratively redefined to improve the error floor performance of message passing decoder. Log-Like hood-Ratio (LLR) based Belief-Propagation (BP) algorithm is presented for Low Density Parity Check codes. Numerically accurate representation of check node update computation used in LLR-BP decoding is described. The implementation of Sum-Product algorithm (SPA) within Low Density Parity Check Code (LDPC) decoder is described in this paper and the correction term is used to improve the decoding performance of min-sum algorithm (MSA). Quantization and log-tanh function approximation in sum-product decoder strongly affect which absorbing set dominates in error floor region. For LDPC decoder, bit error rate (BER) decreases with increase in the signal to noise ratio.
To improve the decoding speed and reduce the complexity of low-density parity-check (LDPC) codes, this paper proposes a hybrid LDPC decoding algorithm that combined with the distribution characteristics of log-likelihood ratio (LLR) of all variable node information before each iteration. During the process of decoding, there is a judgment based on an interval value and a threshold value to select the Belief Propagation (BP) algorithm or the Minimal Sum (MS) algorithm to decode, so the proposed hybrid algorithm effectively combines the excellent performance of BP algorithm and the simple operation of MS algorithm. The simulation results show that the algorithm can greatly reduce the computational complexity and achieve similar decoding performance compared with the BP algorithm.
Several decoding algorithms based on oscillation Log-likelihood ratio (LLR) for Lowdensity parity-check (LDPC) codes are investigated in this paper, based on which, an improved decoding algorithm which uses the accumulated LLR as the final bit decision merit is proposed. This approach improves the decoding performance with only a very small increase in storage and computation. Combined with normalized belief-propagation (BP), two algorithms are given, which are named as accumulate normalized BP (ACC-Nor-BP) and compare-add normalized BP (CA-Nor-BP). The storage requirements and computational complexity of ACC-Nor-BP is lower than that of CA-Nor-BP and CA-BP, but performance is close to the CA-Nor-BP and better than CA-BP; therefore ACC-Nor-BP algorithm is an effectively improved BP algorithm which has a good balance between performance and complexity.
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.
LDPC (Low Density Parity Check Codes) is a low -density puppet test code applied to channel codes. Among the existing LDPC decoding algorithms, the LLR-BP decoding arithmetic is too complicated to calculate the calculation due to the containing a large number of bilateral positive cut functions. Therefore, this article proposes a LDPC decoding algorithm that combines the Modified Weighted Bit Flipping Decoding Algorithm (MWBF) with the Logarithmic Likelihood Ratio Based Confidence Propagation Algorithm (LLR-BP). In the process of the LLR-BP decoding iteration, the introduction of the MWBF algorithm not only does it reduce the complexity of iteration and decoding, but also avoids the traditional weighted bit-flipping decoding algorithm (WBF). Excessive effects of code performance.