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ThinkMind // International Journal On Advances in Systems and Measurements, volume 6, numbers 3 and 4, 2013 // View article sysmea_v6_n34_2013_10


Multilevel Flash Memories: Channel Modeling, Capacities and Optimal Coding Rates

Authors:
Xiujie Huang
Aleksandar Kavcic
Xiao Ma
Guiqiang Dong
Tong Zhang

Keywords: Amplitude-modulation channel; channel capacity; input-dependent additive Gaussian noise; multilevel flash memory; optimal coding rate.

Abstract:
This paper is concerned with channel modeling and capacity evaluation of the multilevel flash memory with $m$ levels. The $m$-level flash memory is modeled as an $m$-amplitude-modulation channel with input-dependent additive Gaussian noise whose standard deviation depends on the channel input. The capacity as well as the optimal coding rate of an $m$-level flash memory channel~($m$-LFMC) is given. If the channel output is observed after a (finite) quantizer, then the channel is further transformed into a discrete memoryless channel, which yields an approximation of the capacity for the $m$-LFMC. Actually, the determination of the capacity for the $m$-LFMC can be transformed into a two-step optimization problem, which can be numerically solved by an alternating iterative algorithm. This algorithm delivers not only the optimal input/level distribution but also the optimal values of levels. This algorithm also delivers the optimized number of levels at any given voltage-to-deviation ratio. Numerical results are presented to show the consistency with well-known Smith's results for the amplitude-limited AWGN channel and the applicability of the modeling method, and to reveal that a finite level quantization of the channel output for the $m$-LFMC suffers from a negligible loss of information rate compared to the capacity.

Pages: 364 to 373

Copyright: Copyright (c) to authors, 2013. Used with permission.

Publication date: December 31, 2013

Published in: journal

ISSN: 1942-261x

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