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oai:www.ideals.illinois.edu:2142/81972 2023-07-11 col_2142_5131 col_2142_10761 com_2142_5130 com_2142_10755 com_2142_234

Vardy, Alexander Trachtenberg, Ari 2015-09-25T20:21:15Z 2015-09-25T20:21:15Z 10000-01-01 2000 2000 We consider two graph-based techniques for correcting the errors introduced into a transmission by a noisy channel. In the first technique, which is based on decoding with a layered graph known as a trellis, we examine generalization of heuristically good codes called lexicodes. We propose and analyze a method for designing generalized lexicodes that minimize or constrain various trellis decoding parameters. The second technique is based on decoding with factor graphs, which are smaller than trellis representations and have enjoyed much attention in the recent literature. We look at a specific type of factor graphs known as Tanner graphs, for which a decoding algorithm is known. This decoding algorithm is proven to always converge to a maximum-likelihood decoding if and only if the corresponding Tanner graph is cycle-free. However, we show that cycle-free Tanner graphs cannot support good codes, because of their weak structure. This weakness has a direct affect on codes of Tanner graphs with cycles, which we analyze as well. Made available in DSpace on 2015-09-25T20:21:15Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 9955672.pdf: 4521518 bytes, checksum: 79c46f59e62e8e543ed113579c7dcd81 (MD5) Previous issue date: 2000 Embargo set by: Seth Robbins for item 83253 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 101 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2000. http://hdl.handle.net/2142/81972 (MiAaPQ)AAI9955672 eng Mathematics Error -Correcting Codes on Graphs: Lexicodes, Trellises and Factor Graphs text Computer Science Computer Science University of Illinois at Urbana-Champaign Dissertation Ph.D.