Distribution theory and transform analysis: an introduction to generalized functions, with applications
Elements of information theory
Elements of information theory
Modern Coding Theory
Iterative decoding of binary block and convolutional codes
IEEE Transactions on Information Theory
Efficient erasure correcting codes
IEEE Transactions on Information Theory
Improved low-density parity-check codes using irregular graphs
IEEE Transactions on Information Theory
The capacity of low-density parity-check codes under message-passing decoding
IEEE Transactions on Information Theory
Design of capacity-approaching irregular low-density parity-check codes
IEEE Transactions on Information Theory
Upper bounds on the rate of LDPC codes
IEEE Transactions on Information Theory
Extrinsic information transfer functions: model and erasure channel properties
IEEE Transactions on Information Theory
Bounds on information combining
IEEE Transactions on Information Theory
Mutual information and minimum mean-square error in Gaussian channels
IEEE Transactions on Information Theory
On mutual information, likelihood ratios, and estimation error for the additive Gaussian channel
IEEE Transactions on Information Theory
Tight bounds for LDPC and LDGM codes under MAP decoding
IEEE Transactions on Information Theory
Constrained Information Combining: Theory and Applications for LDPC Coded Systems
IEEE Transactions on Information Theory
Maxwell Construction: The Hidden Bridge Between Iterative and Maximum a Posteriori Decoding
IEEE Transactions on Information Theory
Capacity-achieving codes for finite-state channels with maximum-likelihood decoding
IEEE Journal on Selected Areas in Communications - Special issue on capaciyy approaching codes
Bounds on the number of iterations for turbo-like ensembles over the binary erasure channel
IEEE Transactions on Information Theory
On universal properties of capacity-approaching LDPC code ensembles
IEEE Transactions on Information Theory
Capacity-achieving codes for channels with memory with maximum-likelihood decoding
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
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There is a fundamental relationship between belief propagation (BP) and maximum a posteriori decoding. The case of transmission over the binary erasure channel was investigated in detail in a companion paper (C. Méasson, A. Montanari, and R. Urbanke, "Maxwell's construction: The hidden bridge between iterative and maximum a posteriori decoding," IEEE Transactions on Information Theory, submitted for publication). This paper investigates the extension to general memoryless channels (paying special attention to the binary case). An area theorem for transmission over general memoryless channels is introduced and some of its many consequences are discussed. We show that this area theorem gives rise to an upper bound on the maximum a posteriori threshold for sparse graph codes. In situations where this bound is tight, the extrinsic soft bit estimates delivered by the BP decoder coincide with the correct a posteriori probabilities above the maximum a posteriori threshold. More generally, it is conjectured that the fundamental relationship between the maximum a posteriori probability (MAP) and the BP decoder which was observed for transmission over the binary erasure channel carries over to the general case. We finally demonstrate that in order for the design rate of an ensemble to approach the capacity under BP decoding the component codes have to be perfectly matched, a statement which is well known for the special case of transmission over the binary erasure channel.