Partial-optimal piecewise decoding of linear codes
P. Delsarte · IEEE Transactions on Information Theory · 1978
LetAandBbe matrices over a finite fieldGF(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 conditionuA^{T} = 0, for a transmissionu \rightarrow vofn-tuples on aq-ary totally symmetric memoryless channel. The best estimate has the formvB^{T}-f(vA^{T}), wheref(x)is the value ofymaximizing 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.