Linear Programming Decoding of Spatially Coupled Codes
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Balanced bipolar codes consist of sequences in which the symbols ‘−1’ and ‘+1’ appear equally often. Several generalizations to larger alphabets have been considered in literature. For example, for the q-ary alphabet {−q+1,−q+3, . . . , q−1}, known concept ...
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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Polar coding is a recently invented technique for communication over binary-input memoryless channels. This technique allows one to transmit data at rates close to the symmetric-capacity of such channels with arbitrarily high reliability, using low-complex ...
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 ...
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 ...
Given a code C is an element of F-2(n) and a word c is an element of C, a witness of c is a subset W subset of {, 1 ... , n} of coordinate positions such that c differs from any other codeword c' is an element of C on the indices in W. If any codeword poss ...
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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} ...
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 ...
In multi-terminal communication systems, signals carrying messages meant for different destinations are often observed together at any given destination receiver. Han and Kobayashi (1981) proposed a receiving strategy which performs a joint unique decoding ...
Probabilistic construction of codes on two-dimensional arrays is proposed and analyzed. Instead of a pure combinatorial erasure model used in traditional array codes, we propose a mixed combinatorial-probabilistic model of limiting the number of column fai ...
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