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We consider communication over a time-invariant discrete memoryless channel (DMC) with noiseless and instantaneous feedback. We assume that the transmitter and the receiver are not aware of the underlying channel, however, they know that it belongs to some ...
We investigate the average erasure probability of the belief propagation algorithm over the binary erasure channel (BEC) for various finite-length low- density parity-check (LDPC) ensembles. In particular, we give tight upper bounds on the "error floor", i ...
We consider the problem of compressing a binary symmetric i.i.d. source stream for two decoders, one of which has access to side-information. Kaspi found the rate-distortion tradeoff for this problem for general discrete memoryless sources for the two case ...
This paper extends the construction and analysis of Raptor codes originally designed in A. Shokrollahi (2004) for the erasure channel to general symmetric channels. We explicitly calculate the asymptotic fraction of output nodes of degree one and two for c ...
We give a short survey of several techniques to construct codes on GF(q) that approach the capacity of the q-ary symmetric channel. The q-ary symmetric channel represents the next level of difficulty after the binary erasure channel (BEC). Since the channe ...
This thesis addresses the topic of Low-Density Parity-Check (LDPC) code analysis, both asymptotically and for finite block lengths. Since in general it is a difficult problem to analyze individual code instances, ensemble averages are studied by following ...
We prove that for any given R between 0 and 1 the best threshold value for a regular LDPC code of rate R with common variable degree v and common check degree c occurs when v is at least 3 and is minimal subject to the condition R=1−v/c ...
