Multicluster interleaving on paths and cycles

Interleaving codewords is an important method not only for combatting burst errors, but also for distributed data retrieval. This paper introduces the concept of multicluster interleaving (MCI), a generalization of traditional interleaving problems. MCI problems for paths and cycles are studied. The following problem is solved: how to interleave integers on a path or cycle such that any m (m/spl ges/2) nonoverlapping clusters of order 2 in the path or cycle have at least three distinct integers. We then present a scheme using a "hierarchical-chain structure" to solve the following more general problem for paths: how to interleave integers on a path such that any m (m/spl ges/2) nonoverlapping clusters of order L (L/spl ges/2) in the path have at least L+1 distinct integers. It is shown that the scheme solves the second interleaving problem for paths that are asymptotically as long as the longest path on which an MCI exists, and clearly, for shorter paths as well.

[1]  M. Blaum,et al.  Correcting two-dimensional clusters by interleaving of symbols , 1994, Proceedings of 1994 IEEE International Symposium on Information Theory.

[2]  R. Collins,et al.  Age-specific relevance of usual blood pressure to vascular mortality: a meta-analysis of individual data for one million adults in 61 prospective studies , 2002, The Lancet.

[3]  Moni Naor,et al.  Optimal File Sharing in Distributed Networks , 1995, SIAM J. Comput..

[4]  Anxiao Jiang,et al.  Diversity coloring for information storage in networks , 2002, Proceedings IEEE International Symposium on Information Theory,.

[5]  C. de Almeida,et al.  Two-dimensional interleaving using the set partitioning technique , 1994, Proceedings of 1994 IEEE International Symposium on Information Theory.

[6]  D. Levy,et al.  Prognostic implications of echocardiographically determined left ventricular mass in the Framingham Heart Study. , 1990, The New England journal of medicine.

[7]  Solomon W. Golomb,et al.  Optimal interleaving schemes for correcting 2-D cluster errors , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[8]  K.A.S. Abdel-Ghaffar,et al.  Achieving the Reiger bound for burst errors using two-dimensional interleaving schemes , 1997, Proceedings of IEEE International Symposium on Information Theory.

[9]  Randy H. Katz,et al.  A case for redundant arrays of inexpensive disks (RAID) , 1988, SIGMOD '88.

[10]  Anxiao Jiang,et al.  Optimal t-interleaving on tori , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[11]  Jehoshua Bruck,et al.  Scheduling for efficient data broadcast over two channels , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[12]  H KatzRandy,et al.  A case for redundant arrays of inexpensive disks (RAID) , 1988 .

[13]  Tuvi Etzion,et al.  On the optimality of coloring with a lattice , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[14]  Alexander Vardy,et al.  Two-dimensional interleaving schemes with repetitions: Constructions and bounds , 2002, IEEE Trans. Inf. Theory.

[15]  M. Blaum,et al.  Two-dimensional interleaving schemes with repetitions , 1997, Proceedings of IEEE International Symposium on Information Theory.

[16]  Alexander Vardy,et al.  Interleaving Schemes for Multidimensional Cluster Errors , 1998, IEEE Trans. Inf. Theory.

[17]  Michael Luby,et al.  A digital fountain approach to reliable distribution of bulk data , 1998, SIGCOMM '98.

[18]  Mary K. Vernon,et al.  Scalable on-demand media streaming with packet loss recovery , 2001, SIGCOMM.

[19]  Moshe Schwartz,et al.  Optimal 2-Dimensional 3-Dispersion Lattices , 2003, AAECC.

[20]  Anxiao Jiang,et al.  Optimal Interleaving on Tori , 2006, SIAM J. Discret. Math..