Using Short Synchronous WOM Codes to Make WOM Codes Decodable

TL;DR

This paper introduces a novel approach to making nondecodable WOM codes decodable by appending short synchronous WOM codes, reducing rate loss and enabling simultaneous writing of original and synchronous code generations.

Contribution

It proposes a new method using short synchronous WOM codes to convert nondecodable codes into decodable ones, improving efficiency over traditional methods.

Findings

Significantly reduces rate loss for short-to-moderate block lengths.

Applicable to both binary and nonbinary WOM codes.

Enhances decoding capability without substantial rate compromise.

Abstract

In the framework of write-once memory (WOM) codes, it is important to distinguish between codes that can be decoded directly and those that require that the decoder knows the current generation to successfully decode the state of the memory. A widely used approach to construct WOM codes is to design first nondecodable codes that approach the boundaries of the capacity region, and then make them decodable by appending additional cells that store the current generation, at an expense of a rate loss. In this paper, we propose an alternative method to make nondecodable WOM codes decodable by appending cells that also store some additional data. The key idea is to append to the original (nondecodable) code a short synchronous WOM code and write generations of the original code and of the synchronous code simultaneously. We consider both the binary and the nonbinary case. Furthermore, we propose a construction of synchronous WOM codes, which are then used to make nondecodable codes decodable. For short-to-moderate block lengths, the proposed method significantly reduces the rate loss as compared to the standard method.