{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/71205"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/71205","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Bounds on the Redundancy of Noiseless Source Coding","abstract":"The Renyi redundancy, R(,s)(p,w), is the difference between the exponentially weighted average codeword length,","abstract_html":"The Renyi redundancy, R(,s)(p,w), is the difference between the exponentially weighted average codeword length,","abstract_has_math":false,"creators":["Blumer, Anselm Cyril"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-16T06:18:03Z","date_published":"2014-12-16T06:18:03Z","updated_at":"2026-07-22T22:26:04Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8302809"],"render_values":[{"text":"(UMI)AAI8302809","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/71205","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Blumer, Anselm Cyril"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-16T06:18:03Z","10000-01-01","1982"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/71205","(UMI)AAI8302809"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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."]},{"key":"dc:title","label":"Title","values":["Bounds on the Redundancy of Noiseless Source Coding"]}]}],"canonical_facts":{"dc:creator":["Blumer, Anselm Cyril"],"dc:date":["2014-12-16T06:18:03Z","10000-01-01","1982"],"dc:description":["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."],"dc:identifier":["http://hdl.handle.net/2142/71205","(UMI)AAI8302809"],"dc:subject":["Mathematics"],"dc:title":["Bounds on the Redundancy of Noiseless Source Coding"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:04Z"}