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 symbol is a -tuple of elements in . It is assumed that only one element error to a nearest neighbor element in a transmitted symbol 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 a 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.
Keywords
Cite
@article{arxiv.1701.08492,
title = {On Zero Error Capacity of Nearest Neighbor Error Channels with Multilevel Alphabet},
author = {Takafumi Nakano and Tadashi Wadayama},
journal= {arXiv preprint arXiv:1701.08492},
year = {2018}
}