Multidimensional stochastic matrices and error-correcting codes

Stochastic Integration via Error-Correcting Codes

We consider the task of summing a non-negative function f over a discrete set Ω, e.g., to compute the partition function of a graphical model. Ermon et al. have shown that in a probabilistic approximate sense summation can be reduced to maximizing f over random subsets of Ω defined by parity (XOR) constraints. Unfortunately, XORs with many variables are computationally intractable, while XORs w...

Good Error{correcting Codes Based on Very Sparse Matrices

We study two families of error-correcting codes deened in terms of very sparse matrices. `MN' (MacKay{Neal) codes are recently invented, and`Gallager codes' were rst investigated in 1962, but appear to have been largely forgotten, in spite of their excellent properties. The decoding of both codes can be tackled with a practical sum{product algorithm. We prove that these codes arèvery good', in ...

Synchronizable Error-Correcting Codes

A new technique for correcting synchronization errors in the transmission of discrete-symbol information is developed. The technique can be applied to any t-additive-error-correcting Bose-Chaudhuri-Hocquenghem code, to provide protection against synchronization errors. The synchronization error is corrected at the first complete received word after the word containing the synchronization error,...

Parallel error correcting codes

Error-Correcting Codes

Transmission of information takes place over “noisy” signals. This is the case in satellite transmissions and storing data. For this reason, it is useful to encode information so that errors can be detected and corrected. For our purposes, we will assume all information to be encoded constists of words of fixed length k using symbols from a fixed alphabet, and all encoded messages are divided i...