Technical Report CS0081

Title: Computation Channels over Finite Groups
Authors: M.G. Karpovsky and E.A. Trachtenberg
Abstract: Detection and correction of errors of arbitrary multiplicity which may appear in the input of the computation channel (defined over an arbitrary finite group) or within the channel itself are investigated. In Sections 2 and 3 the problem of building of optimal checks for the given computation channel is solved. The main tools for the solution of this problem are methods of harmonic analysis on finite groups. Optimal checks are given for some important standard computer blocks (or standard subroutines). Theorems in the following sections solve the problem of error detecting and correcting capability for a linear checks system for memoryless and memory-aided decoding procedures. This capability is group structure independent and grows exponentially when a transition from memoryless to memory-aided decoding is made.
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