Rewriting flash memories and dirty-paper coding

This paper considers that write-once memory (WOM) codes can be seen as a type of dirty-paper code. The current state of the memory, which is known to the encoder, plays the role of the known interference of dirty-paper coding. Erez, Shamai and Zamir showed that lattice strategies can achieve the capacity of the known-interference channel. In this paper, lattices are used to design a WOM code. Encoding is performed modulo a shaping lattice with respect to a lattice fundamental region to obtain a codeword, to be added to the current state of the memory. The fundamental region is designed to accommodate the limitations of the flash memory system, particularly, that values can only increase. The criterion for evaluation is average number of writes. In order to improve the average number of writes, “coset select” bits are introduced, to maximize the average number of writes. For an eight-dimensional lattice, numerical results for practical parameter choices show a promising trend.

[1]  N. J. A. Sloane,et al.  Sphere Packings, Lattices and Groups , 1987, Grundlehren der mathematischen Wissenschaften.

[2]  Brian M. Kurkoski.  Rewriting codes for flash memories based upon lattices, and an example using the E8 lattice , 2010, 2010 IEEE Globecom Workshops.

[3]  Uri Erez,et al.  Achieving 1/2 log (1+SNR) on the AWGN channel with lattice encoding and decoding , 2004, IEEE Transactions on Information Theory.

[4]  Meir Feder,et al.  Low Density Lattice Codes , 2006, ISIT.

[5]  Stephan ten Brink,et al.  A close-to-capacity dirty paper coding scheme , 2004, ISIT.

[6]  Adi Shamir,et al.  How to Reuse a "Write-Once" Memory , 1982, Inf. Control..

[7]  Paul H. Siegel,et al.  Multilevel 2-cell t-write codes , 2012, 2012 IEEE Information Theory Workshop.

[8]  N. J. A. Sloane,et al.  A fast encoding method for lattice codes and quantizers , 1983, IEEE Trans. Inf. Theory.

[9]  Paul H. Siegel,et al.  Efficient two-write WOM-codes , 2010, 2010 IEEE Information Theory Workshop.

[10]  Brian M. Kurkoski.  The E8 Lattice and Error Correction in Multi-Level Flash Memory , 2011, 2011 IEEE International Conference on Communications (ICC).

[11]  Shlomo Shamai,et al.  Capacity and lattice strategies for canceling known interference , 2005, IEEE Transactions on Information Theory.

[12]  Max H. M. Costa,et al.  Writing on dirty paper , 1983, IEEE Trans. Inf. Theory.

[13]  Brian M. Kurkoski.  Lattice-based WOM codebooks that allow two writes , 2012, 2012 International Symposium on Information Theory and its Applications.