Fault tolerant computing and reliable communication: A unified approach

Abstract

We define and study varying-structure linear systems (VLS) over finite Abelian groups. All the VLS computational procedures are very fast with upper bounds on the number of computer operations similar to that of fast Fourier transform algorithms over groups. Specially designed VLS process n -vectors in linear (in n ) number of computer operations. These systems are used in problems related to information channels (optimal estimation of noise-corrupted signals) and computation channels (error detection). We consider problems of optimal synthesis procedures of such systems relative to two easily computed criteria. The best approximation problem of classical systems by VLS also is studied. It is shown that the VLS constitute a class of suboptimal systems from which approximations can be found to a given information and/or computation channel. The approach chosen for these two channel types is unified. Information channel problems are usually solved in Euclidean type norms, whereas computation channel problems are dealt with via the generalized Hamming distance.