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In the framework of write-once memory (WOM) codes, it is important todistinguish between codes that can be decoded directly and those that requirethat the decoder knows the current generation to successfully decode the stateof the memory. A widely used approach to construct WOM codes is to design firstnondecodable codes that approach the boundaries of the capacity region, andthen make them decodable by appending additional cells that store the currentgeneration, at an expense of a rate loss. In this paper, we propose analternative method to make nondecodable WOM codes decodable by appending cellsthat 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 theoriginal code and of the synchronous code simultaneously. We consider both thebinary and the nonbinary case. Furthermore, we propose a construction ofsynchronous WOM codes, which are then used to make nondecodable codesdecodable. For short-to-moderate block lengths, the proposed methodsignificantly reduces the rate loss as compared to the standard method.

Using Short Synchronous WOM Codes to Make WOM Codes Decodable