Calderbank, AR; Fishburn, PC; Rabinovich, A, *Covering properties of convolutional codes and associated lattices*,
IEEE Transactions on Information Theory, vol. 41 no. 3
(1995),
pp. 732-746 [doi] .
**Abstract:**

*This study proposes several Markov methods for the analysis of the expected and worst case performance of sequence-based methods of quantization. The quantization algorithm is assumed as a dynamic programming where the current step is dependent on metric functions. The main objective is to obtain a concise representation of these metric functions including the possible trajectories of the dynamic programming algorithm. To demonstrate this, the quantization of equiprobable binary data using a convolutional code is considered. In addition, these methods are also applicable to the quantization of arbitrary symmetric probability distributions using convolutional codes. For certain convolutional codes a formula that depends only on the distribution of differences for a single pair of path metrics is derived for expected use.*