TY - GEN
T1 - Quasi-cross lattice tilings with applications to flash memory
AU - Schwartz, Moshe
PY - 2011/10/26
Y1 - 2011/10/26
N2 - We consider lattice tilings of ℝn by a shape we call a (k+, k-,n)-quasi-cross. Such lattices form perfect error-correcting codes which correct a single limited-magnitude error with prescribed maximal-magnitudes of positive error and negative error (the ratio of which is called the balance ratio). These codes can be used to correct both disturb and retention errors in flash memories, which are characterized by having limited magnitudes and different signs. We construct infinite families of perfect codes for any rational balance ratio, and provide a specific construction for (2, 1, n)-quasi-cross lattice tiling. The constructions are related to group splitting and modular B1 sequences. We also study bounds on the parameters of lattice-tilings by quasi-crosses, connecting the arm lengths of the quasi-crosses and the dimension. We also prove constraints on group splitting, a specific case of which shows that the parameters of the lattice tiling by (2, 1, n)-quasi-crosses is the only ones possible.
AB - We consider lattice tilings of ℝn by a shape we call a (k+, k-,n)-quasi-cross. Such lattices form perfect error-correcting codes which correct a single limited-magnitude error with prescribed maximal-magnitudes of positive error and negative error (the ratio of which is called the balance ratio). These codes can be used to correct both disturb and retention errors in flash memories, which are characterized by having limited magnitudes and different signs. We construct infinite families of perfect codes for any rational balance ratio, and provide a specific construction for (2, 1, n)-quasi-cross lattice tiling. The constructions are related to group splitting and modular B1 sequences. We also study bounds on the parameters of lattice-tilings by quasi-crosses, connecting the arm lengths of the quasi-crosses and the dimension. We also prove constraints on group splitting, a specific case of which shows that the parameters of the lattice tiling by (2, 1, n)-quasi-crosses is the only ones possible.
UR - http://www.scopus.com/inward/record.url?scp=80054816032&partnerID=8YFLogxK
U2 - https://doi.org/10.1109/ISIT.2011.6033934
DO - https://doi.org/10.1109/ISIT.2011.6033934
M3 - Conference contribution
SN - 9781457705953
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 2133
EP - 2137
BT - 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011
T2 - 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011
Y2 - 31 July 2011 through 5 August 2011
ER -