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arXiv · 1701.08492

On Zero Error Capacity of Nearest Neighbor Error Channels with Multilevel Alphabet

Takafumi Nakano·Tadashi Wadayama
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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 $d$-tuple of elements in $\{0,1,2,\dots, n-1 \}$. 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.

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Takafumi Nakano, Tadashi Wadayama. 2017-01-30. On Zero Error Capacity of Nearest Neighbor Error Channels with Multilevel Alphabet. https://doi.org/10.1587/transfun.e100.a.2647

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