Improved constructions of permutation and multi-permutation codes correcting a burst of stable deletions

TL;DR

This paper introduces improved methods for constructing permutation and multi-permutation codes that can correct bursts of stable deletions, with reduced redundancy and efficient encoding, enhancing their reliability in applications like flash memory.

Contribution

It presents new constructions for permutation and multi-permutation codes correcting burst stable deletions, with reduced redundancy and a linear-time encoder for single deletions.

Findings

Reduces redundancy to log n + 2log log n + O(1) for burst stable deletion correction.

Provides a linear-time encoder with optimal redundancy for single stable deletion correction.

Generalizes constructions to multi-permutations and variable length burst models.

Abstract

Permutation codes and multi-permutation codes have been widely considered due to their various applications, especially in flash memory. In this paper, we consider permutation codes and multi-permutation codes against a burst of stable deletions. In particular, we propose a construction of permutation codes correcting a burst stable deletion of length $s$, with redundancy $\log n+ 2\log \log n+O(1)$. Compared to the previous known results, our improvement relies on a different strategy to retrieve the missing symbol on the first row of the array representation of a permutation. We also generalize our constructions for multi-permutations and the variable length burst model. Furthermore, we propose a linear-time encoder with optimal redundancy for single stable deletion correcting permutation codes.