On zero error capacity of Nearest Neighbor Error channels with multilevel alphabet

Abstract

This paper studies the zero error capacity of the Nearest Neighbor Error (NNE) channels with a multilevel alpha­bet. In the NNE channels, a transmitted sequence is a sequence of d-symbols belonging to the alphabet of size n. It is assumed that only one error to a nearest neighbor symbol in a transmitted sequence can occur. The NNE channels can be considered as a special type of limited magnitude error channels, and it is closely related to error models for flash memories. In this paper, we derive a lower bound of the zero error capacity of the NNE channels based on a result of the perfect Lee codes. An upper bound of the zero error capacity of the NNE channels is also derived from a feasible solution of an linear programming problem defined based on the confusion graphs of the NNE channels. As a result, a concise formula of the zero error capacity is obtained using the lower and upper bounds.