Optimal receiver design for convolutional codes and channels with memory via control theoretical concepts

Abstract

The optimum maximum likelihood receiver for estimating the information sequence that passes through a convolutional encoder and a channel with a known finite memory part followed by a noisy memoryless part is derived using control theoretic concepts. The problem is modeled as a regulator control problem in which the plant under consideration is a finite state machine with the information symbols as inputs. It is in a form in which dynamic programming can be applied to obtain a general solution. The case of sending pulse amplitude modulated (PAM) signals over a linear channel with additive white Gaussian noise is analyzed in detail and upper and lower bounds are derived for the performance criterion, the probability of an information sequence error. Applying the coding concept of concatenation, a suboptimum solution for overcoming the “curse of dimensionality” is discussed.