Coding for the binary asymmetric channel

Motivated by the recent emergence of storage technologies characterized by the intrinsic asymmetries in data recording, this work presents a preliminary look of two simple but practical high-rate code constructions for the Z-channel. The constructions are based on transforming LDPC codes designed for the binary symmetric channel to bias the number of ones that are sent through the channel. Using simulation results, the performance of this new class of codes is compared against some existing codes, and under certain conditions, new codes are shown to be superior existing asymmetric error correcting codes.

[1]  Jay M. Berger A Note on Error Detection Codes for Asymmetric Channels , 1961, Inf. Control..

[2]  T. R. N. Rao,et al.  On the theory of Binary Asymmetric Error Correcting Codes , 1979, Inf. Control..

[3]  Haruhiko Kaneko,et al.  Error Control Coding for Multilevel Cell Flash Memories Using Nonbinary Low-Density Parity-Check Codes , 2009, 2009 24th IEEE International Symposium on Defect and Fault Tolerance in VLSI Systems.

[4]  David J. C. MacKay,et al.  Low-density parity check codes over GF(q) , 1998, IEEE Communications Letters.

[5]  Ninoslav Marina LDPC codes for binary asymmetric channels , 2008, 2008 International Conference on Telecommunications.

[6]  J. H. Weber,et al.  Bounds and constructions for binary block codes correcting asymmetric or unidirectional errors , 1989 .

[7]  David J. C. MacKay,et al.  Encyclopedia of Sparse Graph Codes , 1999 .

[8]  Paul H. Siegel,et al.  On codes that correct asymmetric errors with graded magnitude distribution , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.

[9]  Lara Dolecek Towards longer lifetime of emerging memory technologies using number theory , 2010, 2010 IEEE Globecom Workshops.

[10]  F. Lemmermeyer Error-correcting Codes , 2005 .

[11]  Robert G. Gallager,et al.  Low-density parity-check codes , 1962, IRE Trans. Inf. Theory.

[12]  Jehoshua Bruck,et al.  Codes for Asymmetric Limited-Magnitude Errors With Application to Multilevel Flash Memories , 2010, IEEE Transactions on Information Theory.

[13]  Torleiv Kløve,et al.  Systematic single limited magnitude asymmetric error correcting codes , 2010, 2010 IEEE Information Theory Workshop on Information Theory (ITW 2010, Cairo).

[14]  Philippe Piret,et al.  Bounds and constructions for binary asymmetric error-correcting codes , 1981, IEEE Trans. Inf. Theory.

[15]  W. W. Peterson,et al.  Error-Correcting Codes. , 1962 .

[16]  R. R. Varshamov A General Method of Constructing Asymmetric Coding Systems, Related to the Solution of a Combinatorial Problem Proposed by Dixon , 1971 .