Multipermutation Codes in the Ulam Metric for Nonvolatile Memories

TL;DR

This paper explores the design and analysis of multipermutation codes in the Ulam metric for nonvolatile memory storage, providing bounds, constructions, and decoders to improve error correction in flash memory devices.

Contribution

It introduces new bounds, capacity analysis, and decoding methods for multipermutation codes in the Ulam metric, addressing a novel application in memory storage.

Findings

Derived bounds on code size and capacity in the Ulam and Hamming metrics.

Presented constructions for multipermutation codes in the Ulam metric.

Developed decoding algorithms for these codes.

Abstract

We address the problem of multipermutation code design in the Ulam metric for novel storage applications. Multipermutation codes are suitable for flash memory where cell charges may share the same rank. Changes in the charges of cells manifest themselves as errors whose effects on the retrieved signal may be measured via the Ulam distance. As part of our analysis, we study multipermutation codes in the Hamming metric, known as constant composition codes. We then present bounds on the size of multipermutation codes and their capacity, for both the Ulam and the Hamming metrics. Finally, we present constructions and accompanying decoders for multipermutation codes in the Ulam metric.