|Ph.D Thesis||Department of Electrical Engineering|
|Supervisors:||Distinguished Prof. Ziv Jacob|
|Distinguished Prof. Shamai )Shitz( Shlomo|
This work investigates the performance of the iterative sum-product algorithm for decoding of LDPC codes with respect to families of memoryless channels.
In the first part of this work we consider a practical solution for decoding with respect to memoryless compound channels. We propose a message-passing algorithm operating on a graph representing both the code and the estimation mechanism. In the factor graph, the single node representing the channel realization is artificially being split to multiple nodes, so that rigorous analysis is enabled; in fact, similar approach differentiates maximum likelihood decoding from iterative decoding when parity constraints are considered. Density evolution is then used to design the modus operandi of the channel estimation nodes such that state-of-the-art performance is achieved, as indeed is verified by simulations.
In the second part of this work we address the ability of fixed LDPC ensembles to perform over a variety of channels, when full channel knowledge is provided to the decoder. We propose and analyze a new tool, information combining, followed by an extension (constrained information combining). Information combining deals with the effect of one among many parallel channels on the mutual information between a source symbol and the observations at the output of those parallel channels. For example, when multiple observations correspond to a single bit feeding the parallel channels it is shown that the binary symmetric channel is the least information conveying among all channels of the same individual mutual information, while the binary erasure channel is the most information conveying. We then use these tools to derive upper and lower bounds on the threshold of LDPC codes under iterative decoding.