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Partial-optimal piecewise decoding of linear codes

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Let A and B be matrices over a finite field GF(q) , with same column size n, having linearly independent rows. The problem is to find an optimal estimate of the "information" uB^{T} from the partial "syndrome" vA^{T} , with the condition uA^{T} = 0 , for a transmission u \rightarrow v of n -tuples on a q -ary totally symmetric memoryless channel. The best estimate has the form vB^{T}-f(vA^{T}) , where f(x) is the value of y maximizing a so-called decision function \Delta (x,y) . Explicit expressions are obtained for \Delta ; they allow computation of the critical probabilities of the channel. The theory is applied to multidimensional orthogonal check set decoding.

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Information Theory, IEEE Transactions on  (Volume:24 ,  Issue: 1 )