Using Short Synchronous WOM Codes to Make WOM Codes Decodable

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.