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Joint Iterative Decoding and Noise Variance Estimation Based on Expectation-Maximization

Wang Hang-xian

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

Effects of noise variance estimation on the LDPC decoding performance are investigated.Based on the algorithm of expectation-maximization(EM),a noise variance estimation method is obtained.The method is applied to the BP decoding algorithm.Simulations show that,with the proposed method,the observed performance degradation is less than 0.1 dB when the noise variance is unknown.

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Effects of noise variance estimation on the LDPC decoding performance are investigated.Based on the algorithm of expectation-maximization(EM),a noise variance estimation method is obtained.The method is applied to the BP decoding algorithm.Simulations show that,with the proposed method,the observed performance degradation is less than 0.1 dB when the noise variance is unknown.
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 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.
This paper proposes new algorithms for joint iterative decoding and parameter estimation in Bayesian and nonBayesian method. The low-density parity-check (LDPC) codes in the presence of phase noise is focused in this paper. The nonBayesian algorithm for an unknown phase channel is based on the application of the expectation-maximization (EM) algorithm. The proposed Bayesian algorithms are obtained as an application of the sum-product algorithm to the factor graph. Comparing the performance of the considered algorithms in the case of LDPC code, the EM-KL (EM-Karhunen-Loeve) algorithm performs better than EM-SW (sliding window) algorithm.
Belief propagation (BP) is a powerful algorithm to decode low- density parity check (LDPC) codes over additive white Gaussian noise (AWGN) channels. However, the traditional BP algorithm cannot adapt efficiently to the statistical change of SNR in an AWGN channel. This paper proposes an adaptive scheme that incorporates expectation propagation (EP) into the BP based LDPC decoding process. The proposed scheme is able to perform online estimation of both stationary and time-varying SNR at the bit-level, and enhance the BP decoding performance simultaneously. Moreover, the proposed EP estimator shows a very fast convergence speed, and the additional computational overhead of the proposed decoder is less than 10% of the standard BP decoder.
LDPC decoding algorithm on channels with memory is of great significance to high speed digital com- munications.Currently used low-density parity-check codes iterative decoding algorithms on channels with memo- ry,such as Belief-Propagation iterative decoding algorithm based on channel estimation,are commonly complex and thus requiring large amount of calculation.In this paper,a min-sum algorithm is firstly introduced into LDPC itera- tive decoding algorithm based on soft noise decisions and channel estimation on hidden Markov noisy channels.Algo- rithm and calculation complexity are effectively reduced by using the functions'characteristics.Simulation results show that the algorithm not only excels conventional Belief-Propagation iterative decoding algorithms that do not concern channel memory,but also outperforms iterative decoding algorithms based on hard noise decisions and channel esti- mation.So a good compromise is made between decoding performance and algorithm complexity with low performance loss,which is useful real time communications.
Departing from traditional communication theory where decoding algorithms are assumed to perform without error, a system where noise perturbs both computational devices and communication channels is considered here. This paper studies limits in processing noisy signals with noisy circuits by investigating the effect of noise on standard iterative decoders for low-density parity-check (LDPC) codes. Concentration of decoding performance around its average is shown to hold when noise is introduced into message-passing and local computation. Density evolution equations for simple faulty iterative decoders are derived. In one model, computing nonlinear estimation thresholds shows that performance degrades smoothly as decoder noise increases, but arbitrarily small probability of error is not achievable. Probability of error may be driven to zero in another system model; the decoding threshold again decreases smoothly with decoder noise. As an application of the methods developed, an achievability result for reliable memory systems constructed from unreliable components is provided.