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Shannon in his seminal work \cite{paper:shannon} formalized the framework on the problem of digital communication of information and storage. He quantified the fundamental limits of compression and transmission rates. The quantity \textit{channel capacity} ...
This monograph describes the theory behind Raptor codes, and elucidates elements of the processes behind the design of two of the most prominent members of this class of codes: R10 and RaptorQ (RQ). R10 has already been adopted by a number of standards' bo ...
Shannon, in his seminal work, formalized the transmission of data over a communication channel and determined its fundamental limits. He characterized the relation between communication rate and error probability and showed that as long as the communicatio ...
The loop series provides a formal way to write down corrections to the Bethe entropy (and/or free energy) of graphical models. We provide methods to rigorously control such expansions for low-density parity-check codes used over a highly noisy binary symme ...
An encoding/decoding apparatus and method using a low-density parity-check code (LDPC code) is disclosed. Basic column group information, serving as a set of information regarding positions of rows with weight 1, is extracted from a reference column in eac ...
The two central topics of information theory are the compression and the transmission of data. Shannon, in his seminal work, formalized both these problems and determined their fundamental limits. Since then the main goal of coding theory has been to find ...
An efficient decoding of vector signaling codes is obtained using a circuit that ranks received signal levels, designates ranked values as representing particular code elements, and translates those particular code elements into a decoded result. An optimi ...
It is shown that given two copies of a q-ary input channel W, where q is prime, it is possible to create two channels W- and W+ whose symmetric capacities satisfy I(W-)
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For the recently proposed model of symbol-pair channels, we advance the pair-error coding theory with algebraic cyclic-code constructions and asymptotic bounds on code rates. Cyclic codes for pair-errors are constructed by a careful use of duals of known t ...
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We consider ensembles of binary linear error correcting codes, obtained by sampling each column of the generator matrix G or parity check matrix H independently from the set of all binary vectors of weight d (of appropriate dimension). We investigate the c ...
