4 research outputs found

    Using Short Synchronous WOM Codes to Make WOM Codes Decodable

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    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.Comment: To appear in IEEE Transactions on Communications. The material in this paper was presented in part at the 2012 IEEE International Symposium on Information Theory, Cambridge, MA, July 201

    Using Short Synchronous WOM Codes to Make WOM Codes Decodable

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    Making WOM Codes Decodable using Short Synchronous WOM Codes

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    While some write once memory (WOM) codes are inherently decodable, others require the added knowledge of the current generation in order to successfully decode the state of the memory. If there is no limit on the code length, n, a binary non-decodable t-write WOM code can be made decodable at an insignificant cost in terms of code rate by adding t - 1 cells to store the current generation after replicating the code enough times for the t - 1 cells to be of negligible weight. This justifies the research on non-decodable WOM codes. However, if n is bounded, the t - 1 additional cells may introduce a significant loss in terms of code rate. In this paper, we propose a new method to make non-decodable WOM codes decodable at a lower price when n is bounded. The main idea is to add cells that do not only store the current generation, but also additional data, by using a synchronous (t - 1)-write WOM code of length t - 1 or slightly above which does not contain the all-zero codeword. A bound on the rate of a simple family of synchronous WOM codes with n = t is given, as well as very short codes from this family. Better codes are then obtained by local manipulations of these codes. Finally, a construction of synchronous WOM codes with good properties is proposed to reach higher values of t
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