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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 ...
Encoding information about continuous variables using noisy computational units is a challenge; nonetheless, asymptotic theory shows that combining multiple periodic scales for coding can be highly precise despite the corrupting influence of noise [Mathis, ...
We introduce irregular product codes, a class of codes where each codeword is represented by a matrix and the entries in each row (column) of the matrix come from a component row (column) code. As opposed to standard product codes, we do not require that a ...
Recent advances in data processing and communication systems have led to a continuous increase in the amount of data communicated over today’s networks. These large volumes of data pose new challenges on the current networking infrastructure that only offe ...
We consider communication over a noisy network under randomized linear network coding. Possible error mechanisms include node-or link-failures, Byzantine behavior of nodes, or an overestimate of the network min-cut. Building on the work of Kotter and Kschi ...
We investigate spatially coupled code ensembles. For transmission over the binary erasure channel, it was recently shown that spatial coupling increases the belief propagation threshold of the ensemble to essentially the maximum a-priori threshold of the u ...
Investigations on spatially coupled codes have lead to the conjecture that, in the infinite size limit, the average input-output conditional entropy for spatially coupled low-density parity-check ensembles, over binary memoryless symmetric channels, equals ...
Investigations on spatially coupled codes have lead to the conjecture that, in the infinite size limit, the average input-output conditional entropy for spatially coupled low-density parity-check ensembles, over binary memoryless symmetric channels, equals ...
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 ...