Algebraic signal processing in truncated p-adic arithmetic for linear channels with memory

Abstract

We consider bandlimited linear channels with finite memory which is formally described by a polynomial g(z) with integer coefficients in the variable z that represents the unit delay operator. We present a signal processing method that operates on blocks of finite precision samples of the channel output. This signal processing method is a "softdecision" algebraic decoder that operates in real truncated p-adic arithmetic in which computations are exact i.e. there is no no round-off error. It furthermore lends itself to an efficient digital implementation whose complexity is a linear function of the memory size.