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Blumer, Anselm Cyril 2014-12-16T06:18:03Z 2014-12-16T06:18:03Z 10000-01-01 1982 1982 The Renyi redundancy, R(,s)(p,w), is the difference between the exponentially weighted average codeword length, (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) is the best possible. and the Renyi entropy, (Here s > 0 is a parameter, p = (p(,1),p(,2),...,p(,m)), and w = (w(,1),w(,2),...,w(,m)), where p(,i) is the probability that the i('th) codeword, consisting of w(,i) bits, is used.) As s (--->) 0('+) this approaches the usual redundancy. Huffman's algorithm generalizes in a natural way to the s > 0 case. Let R(,s)(p) be the Renyi redundancy of the Huffman code for p and s. The main result of Chapter II is a technique for computing bounds L(,s)(p) and U(,s)(p), satisfying 0 (LESSTHEQ) L(,s)(p) (LESSTHEQ) R(,s)(p) (LESSTHEQ) U(,s)(p) < 1. In the case of block to variable-length (BV) coding of a binary memoryless source, these bounds are shown to be asymptotically equal as the block length increases, generalizing a result mentioned by Krichevskii (1966). Chapter III treats the problem of minimizing the oridinary (s = 0) redundancy when p is not entirely known. Let p be a probability vector containing the probabilities of blocks of length n from some J-state unifilar (Markov) source with aphabet size A. Let P denote the class of such probability vectors, and let W denote the class of uniquely decodable codes with A('n) codewords. The minimax redundancy is The main result of Chapter III is a technique for generating a sequence of BV codes for which the minimax redundancy is bounded above by Made available in DSpace on 2014-12-16T06:18:03Z (GMT). No. of bitstreams: 1 8302809.pdf: 1610401 bytes, checksum: e372755dd22ea4680f13c94024fcab03 (MD5) Previous issue date: 1982 Embargo set by: Seth Robbins for item 71371 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 59 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1982. http://hdl.handle.net/2142/71205 (UMI)AAI8302809 Mathematics Bounds on the Redundancy of Noiseless Source Coding text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.