TY - GEN

T1 - Further results on relative redundancy

AU - Das, Hirakendu

AU - Orlitsky, Alon

AU - Santhanam, Narayan Prasad

AU - Zhang, Junan

PY - 2008/9/29

Y1 - 2008/9/29

N2 - Standard redundancy measures the excess number of bits needed to compress a sequence as a function of the sequence's length. Since long sequences can have arbitrarily low minimum description length (MDL), even low standard redundancy can be arbitarily high compared to the sequence's MDL. By contrast, relative redundancy evaluates the excess number of bits as a function of the sequence's MDL. Hence unlike standard redundancy, low relative redundancy implies that the number of bits needed to compress any sequence is essentially the lowest possible. Results in [1] show that for iid distributions over binary alphabets, block relative redundancy essentially equals block standard redundancy while sequential relative redundancy is about twice its standard counterpart. We show that unlike binary alphabets, for larger alphabets both block and sequential relative redundancy essentially equal their standard counterparts. We also define and determine expected relative redundancy and show that it is almost same as worst-case relative redundancy.

AB - Standard redundancy measures the excess number of bits needed to compress a sequence as a function of the sequence's length. Since long sequences can have arbitrarily low minimum description length (MDL), even low standard redundancy can be arbitarily high compared to the sequence's MDL. By contrast, relative redundancy evaluates the excess number of bits as a function of the sequence's MDL. Hence unlike standard redundancy, low relative redundancy implies that the number of bits needed to compress any sequence is essentially the lowest possible. Results in [1] show that for iid distributions over binary alphabets, block relative redundancy essentially equals block standard redundancy while sequential relative redundancy is about twice its standard counterpart. We show that unlike binary alphabets, for larger alphabets both block and sequential relative redundancy essentially equal their standard counterparts. We also define and determine expected relative redundancy and show that it is almost same as worst-case relative redundancy.

UR - http://www.scopus.com/inward/record.url?scp=52349087524&partnerID=8YFLogxK

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U2 - 10.1109/ISIT.2008.4595327

DO - 10.1109/ISIT.2008.4595327

M3 - Conference contribution

AN - SCOPUS:52349087524

SN - 9781424422579

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 1940

EP - 1943

BT - Proceedings - 2008 IEEE International Symposium on Information Theory, ISIT 2008

T2 - 2008 IEEE International Symposium on Information Theory, ISIT 2008

Y2 - 6 July 2008 through 11 July 2008

ER -