Compressed Encoding for Rank Modulation

Rank modulation has been recently proposed as a scheme for storing information in flash memories. While rank modulation has advantages in improving write speed and endurance, the current encoding approach is based on the "push to the top" operation that is not efficient in the general case. We propose a new encoding procedure where a cell level is raised to be higher than the minimal necessary subset -instead of all - of the other cell levels. This new procedure leads to a significantly more compressed (lower charge levels) encoding. We derive an upper bound for a family of codes that utilize the proposed encoding procedure, and consider code constructions that achieve that bound for several special cases

Trade-offs between Instantaneous and Total Capacity in Multi-Cell Flash Memories

The limited endurance of flash memories is a major design concern for enterprise storage systems. We propose a method to increase it by using relative (as opposed to fixed) cell levels and by representing the information with Write Asymmetric Memory (WAM) codes. Overall, our new method enables faster writes, improved reliability as well as improved endurance by allowing multiple writes between block erasures. We study the capacity of the new WAM codes with relative levels, where the information is represented by multiset permutations induced by the charge levels, and show that it achieves the capacity of any other WAM codes with the same number of writes. Specifically, we prove that it has the potential to double the total capacity of the memory. Since capacity can be achieved only with cells that have a large number of levels, we propose a new architecture that consists of multi-cells - each an aggregation of a number of floating gate transistors

Rewriting Flash Memories by Message Passing

This paper constructs WOM codes that combine rewriting and error correction for mitigating the reliability and the endurance problems in flash memory. We consider a rewriting model that is of practical interest to flash applications where only the second write uses WOM codes. Our WOM code construction is based on binary erasure quantization with LDGM codes, where the rewriting uses message passing and has potential to share the efficient hardware implementations with LDPC codes in practice. We show that the coding scheme achieves the capacity of the rewriting model. Extensive simulations show that the rewriting performance of our scheme compares favorably with that of polar WOM code in the rate region where high rewriting success probability is desired. We further augment our coding schemes with error correction capability. By drawing a connection to the conjugate code pairs studied in the context of quantum error correction, we develop a general framework for constructing error-correction WOM codes. Under this framework, we give an explicit construction of WOM codes whose codewords are contained in BCH codes.Comment: Submitted to ISIT 201

Repair-Optimal MDS Array Codes over GF(2)

Maximum-distance separable (MDS) array codes with high rate and an optimal repair property were introduced recently. These codes could be applied in distributed storage systems, where they minimize the communication and disk access required for the recovery of failed nodes. However, the encoding and decoding algorithms of the proposed codes use arithmetic over finite fields of order greater than 2, which could result in a complex implementation. In this work, we present a construction of 2-parity MDS array codes, that allow for optimal repair of a failed information node using XOR operations only. The reduction of the field order is achieved by allowing more parity bits to be updated when a single information bit is being changed by the user.Comment: 5 pages, submitted to ISIT 201

Generalized Gray Codes for Local Rank Modulation

We consider the local rank-modulation scheme in which a sliding window going over a sequence of real-valued variables induces a sequence of permutations. Local rank-modulation is a generalization of the rank-modulation scheme, which has been recently suggested as a way of storing information in flash memory. We study Gray codes for the local rank-modulation scheme in order to simulate conventional multi-level flash cells while retaining the benefits of rank modulation. Unlike the limited scope of previous works, we consider code constructions for the entire range of parameters including the code length, sliding window size, and overlap between adjacent windows. We show our constructed codes have asymptotically-optimal rate. We also provide efficient encoding, decoding, and next-state algorithms.Comment: 7 pages, 1 figure, shorter version was submitted to ISIT 201

Constant-Weight Gray Codes for Local Rank Modulation

We consider the local rank-modulation scheme in which a sliding window going over a sequence of real-valued variables induces a sequence of permutations. Local rank- modulation is a generalization of the rank-modulation scheme, which has been recently suggested as a way of storing information in flash memory. We study constant-weight Gray codes for the local rank- modulation scheme in order to simulate conventional multi-level flash cells while retaining the benefits of rank modulation. We provide necessary conditions for the existence of cyclic and cyclic optimal Gray codes. We then specifically study codes of weight 2 and upper bound their efficiency, thus proving that there are no such asymptotically-optimal cyclic codes. In contrast, we study codes of weight 3 and efficiently construct codes which are asymptotically-optimal. We conclude with a construction of codes with asymptotically-optimal rate and weight asymptotically half the length, thus having an asymptotically-optimal charge difference between adjacent cells