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

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