TY - JOUR
T1 - Universal Redundancy Rates for the Class of B-Processes Do Not Exist
AU - Shields, Paul
AU - Weiss, Benjamin
PY - 1995/3
Y1 - 1995/3
N2 - We show that for any sequence ρ(n) = o(n) and any sequence of prefix codes, there is a B-process of entropy arbitrarily close to the maximum possible entropy for which the expected redundancy is at least as large as ρ(n) for infinitely many n. This extends earlier work of the first author, whose examples had 0 entropy, [5]. The class of B-prucesses, that is, stationary codings of independent and identically distributed (i.i.d.) processes, includes the aperiodic Markov chains and functions thereof, aperiodic renewal and regenerative processes, and m-dependent processes, as well as many other processes of interest. In particular, our results show that the search for a universal redundancy rate for the class of all B-processes is doomed to failure, and redundancy rates for any given subclass must be obtained by direct analysis of that subclass.
AB - We show that for any sequence ρ(n) = o(n) and any sequence of prefix codes, there is a B-process of entropy arbitrarily close to the maximum possible entropy for which the expected redundancy is at least as large as ρ(n) for infinitely many n. This extends earlier work of the first author, whose examples had 0 entropy, [5]. The class of B-prucesses, that is, stationary codings of independent and identically distributed (i.i.d.) processes, includes the aperiodic Markov chains and functions thereof, aperiodic renewal and regenerative processes, and m-dependent processes, as well as many other processes of interest. In particular, our results show that the search for a universal redundancy rate for the class of all B-processes is doomed to failure, and redundancy rates for any given subclass must be obtained by direct analysis of that subclass.
KW - B-processes
KW - Redundancy
KW - universal redundancy-rates
UR - http://www.scopus.com/inward/record.url?scp=0029277594&partnerID=8YFLogxK
U2 - 10.1109/18.370156
DO - 10.1109/18.370156
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AN - SCOPUS:0029277594
SN - 0018-9448
VL - 41
SP - 508
EP - 512
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 2
ER -