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This paper studies the zero error capacity of the Nearest Neighbor Error(NNE) channels with a multilevel alphabet. In the NNE channels, a transmittedsymbol is a $d$-tuple of elements in $\{0,1,2,\dots, n-1 \}$. It is assumedthat only one element error to a nearest neighbor element in a transmittedsymbol can occur. The NNE channels can be considered as a special type oflimited magnitude error channels, and it is closely related to error models forflash memories. In this paper, we derive a lower bound of the zero errorcapacity of the NNE channels based on a result of the perfect Lee codes. Anupper bound of the zero error capacity of the NNE channels is also derived froma feasible solution of a linear programming problem defined based on theconfusion graphs of the NNE channels. As a result, a concise formula of thezero error capacity is obtained using the lower and upper bounds.

ieice transactions on fundamentals of electronics, communications and computer sciences/ieice transactions on fundamentals of electronics, communications and computer science

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