TY - GEN

T1 - A characterization of the number of subsequences obtained via the deletion channel

AU - Liron, Y.

AU - Langberg, M.

PY - 2012

Y1 - 2012

N2 - Motivated by the study of deletion channels, this work presents improved bounds on the number of subsequences obtained from a binary sting X of length n under t deletions. It is known that the number of subsequences in this setting strongly depends on the number of runs in the string X; where a run is a maximal sequence of the same character. Our improved bounds are obtained by a structural analysis of the family of r-run strings X, an analysis in which we identify the extremal strings with respect to the number of subsequences. Specifically, for every r, we present r-run strings with the minimum (respectively maximum) number of subsequences under any t deletions; and perform an exact analysis of the number of subsequences of these extremal strings.

AB - Motivated by the study of deletion channels, this work presents improved bounds on the number of subsequences obtained from a binary sting X of length n under t deletions. It is known that the number of subsequences in this setting strongly depends on the number of runs in the string X; where a run is a maximal sequence of the same character. Our improved bounds are obtained by a structural analysis of the family of r-run strings X, an analysis in which we identify the extremal strings with respect to the number of subsequences. Specifically, for every r, we present r-run strings with the minimum (respectively maximum) number of subsequences under any t deletions; and perform an exact analysis of the number of subsequences of these extremal strings.

UR - http://www.scopus.com/inward/record.url?scp=84867533197&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2012.6284240

DO - 10.1109/ISIT.2012.6284240

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AN - SCOPUS:84867533197

SN - 9781467325790

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 503

EP - 507

BT - 2012 IEEE International Symposium on Information Theory Proceedings, ISIT 2012

T2 - 2012 IEEE International Symposium on Information Theory, ISIT 2012

Y2 - 1 July 2012 through 6 July 2012

ER -