Extensions to the analysis of regenerative repeaters with quantized feedback

The functional iterative approach given by Zador for calculating the average bit error probability in a regenerative repeater with quantized feedback is extended to the vector case. For a channel with a rational fraction transfer function, the vector extension permits us at least formally to deal with the following practical conditions: (i) The pulse transmission plan is described by an m-ary alphabet with independent digits. (ii) Perfect and imperfect low-frequency tail cancellation cases are considered. (iii) High-frequency signal shaping and its interaction with the predominantly low-frequency tail are taken into account. Expressions for error probability on the kth digit are derived in terms of the kth vector iterate of a known function. The restriction to independent noise samples is also removed. The resulting expression for kth bit error probability is then derived from an operational iteration procedure which acts on the k + 1 dimensional joint distribution of the noise samples.