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International Conference on Mobile Technology, Applications, and Systems

Comparison of LDPC decoding algorithms with and without estimation of noise variance

Changzheng Ma, Boon Poh Ng

Published Jan 1, 2006• 1 citation
Publisher

Abstract

The original sum product algorithms (SPA) of LDPC decoding in AWGN channel require the knowledge of noise variance. Mini-sum algorithm need not the variance estimation but has performance degradation. If the assumed noise variance of SPA algorithm deviates largely from the true value, the performance also degrade seriously. In this paper, an iterative noise variance estimation algorithm using the decoded data is presented. The true noise variance is then substituted by the estimated one. The computational load is analyzed. Performance difference between SPA, Mini-sum algorithm and our algorithm are compared by simulations.

DOI
10.1145/1292331.1292335

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The original sum product algorithms (SPA) of LDPC decoding in AWGN channel require the knowledge of noise variance. Mini-sum algorithm need not the variance estimation but has performance degradation. If the assumed noise variance of SPA algorithm deviates largely from the true value, the performance also degrade seriously. In this paper, an iterative noise variance estimation algorithm using the decoded data is presented. The true noise variance is then substituted by the estimated one. The computational load is analyzed. Performance difference between SPA, Mini-sum algorithm and our algorithm are compared by simulations.
As the code length approaches infinite, LDPC codes have the potential of approaching Shannon limits. The original message passing (sum-product) algorithms for AWGN channel require the knowledge of noise variance. If the assumed noise variance deviates from the true value, the performance tumbled. In this paper, an iterative noise variance estimation algorithm using the decoded data is presented. The true noise variance is substituted by the estimated one. The computational load is analyzed. Simulation results demonstrate the effectiveness of this method
The min-sum algorithm as an approximation of the sum-product algorithm (SPA) for decoding of LDPC codes has much lower computational complexity, but slightly worse performance than the SPA. However, severe performance degradation might occur when it is realized in hardware due to the finite precision effect, especially in two-bit precision. In order to overcome this problem, we propose a two-bit precision decoding algorithm. The proposed algorithm employs one of several decoders adaptively, based on the syndrome weight of the estimated decoder output every iteration. Numerical results show that it has similar performance to the SPA over the binary symmetric channel.
The Sum Product Algorithm (SPA) is known to offer the best performance in decoding large block length Low Density Parity Check (LDPC) codes. However, modifications in SPA to decrease the computation complexity have resulted in performance degradation. The Min Sum Algorithm (MSA) is one such variant, where the computation of the check-to-variable message is simplified to a minimum operation, instead of a hyperbolic tan calculation. Several modifications have been proposed in order to recover the performance loss of the MSA with respect to SPA. This paper proposes a modification to the MSA, based on the Wiener and Linear Minimum Mean Square Error (LMMSE) estimators for LDPC codes. The golden section search algorithm has been used to optimize the computations of the parameter estimation. Simulation results with these estimated parameters show that for low values of SNR, the modified algorithm outperforms MSA and provides performance close to that of SPA with a gain of 0.1 dB. For higher values of SNR, it outperforms MSA with a gain of 1.75 dB while providing an acceptable performance degradation with respect to SPA.
Effect of channel mismatch on decoding performance of low density parity check (LDPC) codes over binary symmetric channel (BSC) under sum-product algorithm (SPA) is analyzed in this paper. Density evolution is employed in theoretical analysis to get optimal initial value for SPA. Based on the results, a modified SPA algorithm is proposed. When decoding using this modified SPA algorithm, no channel information is needed at the decoder side. This will be of significant value for time-varying channels. Theoretical claims from density evolution are confirmed by extensive simulations. Our simulations show that by fixing the initial value for all channel conditions, decoding performance can be improved. One channel state estimation algorithm is proposed in this paper based on the error detection ability of LDPC codes. Maximum number of iterations taken when decoding a LDPC code can be dynamically adjusted according to the estimated channel state. Further performance improvements can be achieved by using the dynamic iteration number adjusting scheme together with the modified sum-product algorithm
Among the decoding algorithms for low-density parity-check(LDPC) code,sum-product algorithm(SPA) has the optimal performance but high complexity,while min-sum algorithm has simple implementation complexity but worse performance.Considering this performance-complexity contradiction,some modified min-sum algorithms are proposed.In this paper,researches are done based on one of the modified min-sum algorithms that is close to SPA in performance but the way modifying fraction works is simplified.Simplified algorithm remains similar in performance to sum-product algorithm but has a remarkably reduced implementation complexity.