Analysis of sum-product decoding of low-density parity-check codes using a Gaussian approximation

@article{citeulike:474669, abstract = {Density evolution is an algorithm for computing the capacity of low-density parity-check (LDPC) codes under message-passing decoding. For memoryless binary-input continuous-output additive white Gaussian noise (AWGN) channels and sum-product decoders, we use a Gaussian approximation for message densities under density evolution to simplify the analysis of the decoding algorithm. We convert the infinite-dimensional problem of iteratively calculating message densities, which is needed to find the exact threshold, to a one-dimensional problem of updating the means of the Gaussian densities. This simplification not only allows us to calculate the threshold quickly and to understand the behavior of the decoder better, but also makes it easier to design good irregular LDPC codes for AWGN channels. For various regular LDPC codes we have examined, thresholds can be estimated within 0.1 dB of the exact value. For rates between 0.5 and 0.9, codes designed using the Gaussian approximation perform within 0.02 dB of the best performing codes found so far by using density evolution when the maximum variable degree is 10. We show that by using the Gaussian approximation, we can visualize the sum-product decoding algorithm. We also show that the optimization of degree distributions can be understood and done graphically using the visualization}, author = {Chung, Sae-Young and Richardson, T. J. and Urbanke, R. L. }, citeulike-article-id = {474669}, journal = {Information Theory, IEEE Transactions on}, number = {2}, pages = {657--670}, posted-at = {2006-01-21 23:38:38}, priority = {2}, title = {Analysis of sum-product decoding of low-density parity-check codes using a Gaussian approximation}, url = {http://ieeexplore.ieee.org/xpls/abs\_all.jsp?arnumber=910580}, volume = {47}, year = {2001} }

TY - JOUR ID - citeulike:474669 L3 - citeulike-article-id:474669 N2 - Density evolution is an algorithm for computing the capacity of low-density parity-check (LDPC) codes under message-passing decoding. For memoryless binary-input continuous-output additive white Gaussian noise (AWGN) channels and sum-product decoders, we use a Gaussian approximation for message densities under density evolution to simplify the analysis of the decoding algorithm. We convert the infinite-dimensional problem of iteratively calculating message densities, which is needed to find the exact threshold, to a one-dimensional problem of updating the means of the Gaussian densities. This simplification not only allows us to calculate the threshold quickly and to understand the behavior of the decoder better, but also makes it easier to design good irregular LDPC codes for AWGN channels. For various regular LDPC codes we have examined, thresholds can be estimated within 0.1 dB of the exact value. For rates between 0.5 and 0.9, codes designed using the Gaussian approximation perform within 0.02 dB of the best performing codes found so far by using density evolution when the maximum variable degree is 10. We show that by using the Gaussian approximation, we can visualize the sum-product decoding algorithm. We also show that the optimization of degree distributions can be understood and done graphically using the visualization IS - 2 JF - Information Theory, IEEE Transactions on EP - 670 TI - Analysis of sum-product decoding of low-density parity-check codes using a Gaussian approximation VL - 47 SP - 657 AU - Chung, Sae-Young AU - Richardson, TJ AU - Urbanke, RL PY - 2001/// UR - http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=910580 ER -