Covering Properties of Convolutional Codes and Associated Lattices

This paper describes methods for analyzing the expected and the worst-case performance of sequence based methods of qauntization. We suppose that the quantization algorithm is dynamic programming, where the current step depends on a vector of path metrics, which we call a metric function. Our principal objective is a concise representation of these metric functions and the possible trajectories of the dynamic programming algorithm. We shall consider quantization of equiprobable binary data using a convolutional code. Here the additive group of the code splits the set of metric functions into a finite collection of subsets. The subsets form the vertices of a directed graph, where edges are labeled by aggregate incremental increases mean square error (mse).