{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T22:21:53Z","timestamp":1725488513841},"publisher-location":"Berlin, Heidelberg","reference-count":21,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540671411"},{"type":"electronic","value":"9783540465416"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2000]]},"DOI":"10.1007\/3-540-46541-3_1","type":"book-chapter","created":{"date-parts":[[2007,8,2]],"date-time":"2007-08-02T16:03:24Z","timestamp":1186070604000},"page":"1-12","source":"Crossref","is-referenced-by-count":5,"title":["Codes and Graphs"],"prefix":"10.1007","author":[{"given":"M. Amin","family":"Shokrollahi","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2000,3,24]]},"reference":[{"key":"1_CR1","doi-asserted-by":"publisher","first-page":"1732","DOI":"10.1109\/18.556669","volume":"42","author":"N. Alon","year":"1996","unstructured":"N. Alon and M. Luby. A linear time erasure-resilient code with nearly optimal recovery. IEEE Trans. Inform. Theory, 42:1732\u20131736, 1996.","journal-title":"IEEE Trans. Inform. Theory"},{"key":"1_CR2","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1145\/273865.273901","volume":"45","author":"S. Arora","year":"1998","unstructured":"S. Arora and S. Safra. Probabilistic checking of proofs: a new characterization of NP. J. ACM, 45:70\u2013122, 1998.","journal-title":"J. ACM"},{"key":"1_CR3","doi-asserted-by":"publisher","first-page":"384","DOI":"10.1109\/TIT.1978.1055873","volume":"24","author":"E.R. Berlekamp","year":"1978","unstructured":"E.R. Berlekamp, R.J. McEliece, and H.C.A. vanTilborg. On the inherent intractability of certain coding problems. IEEE Trans. Inform. Theory, 24:384\u2013386, 1978.","journal-title":"IEEE Trans. Inform. Theory"},{"key":"1_CR4","unstructured":"C. Berroux, A. Glavieux, and P. Thitimajshima. Near Shannon limit error-correcting coding and decoding. In Proceedings of ICC\u201993, pages 1064\u20131070, 1993."},{"key":"1_CR5","unstructured":"P. Elias. Coding for two noisy channels. In Information Theory, Third London Symposium, pages 61\u201376, 1955."},{"key":"1_CR6","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/4347.001.0001","volume-title":"Low Density Parity-Check Codes","author":"R. G. Gallager","year":"1963","unstructured":"R. G. Gallager. Low Density Parity-Check Codes. MIT Press, Cambridge, MA, 1963."},{"key":"1_CR7","unstructured":"M. Luby, M. Mitzenmacher, and M.A. Shokrollahi. Analysis of random processes via and-or tree evaluation. In Proceedings of the 9th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 364\u2013373, 1998."},{"key":"1_CR8","doi-asserted-by":"crossref","unstructured":"M. Luby, M. Mitzenmacher, M.A. Shokrollahi, and D. Spielman. Analysis of low density codes and improved designs using irregular graphs. In Proceedings of the 30th Annual ACM Symposium on Theory of Computing, pages 249\u2013258, 1998.","DOI":"10.1145\/276698.276756"},{"key":"1_CR9","doi-asserted-by":"crossref","unstructured":"M. Luby, M. Mitzenmacher, M.A. Shokrollahi, and D. Spielman. Improved low-density parity-check codes using irregular graphs and belief propagation. In Proceedings 1998 IEEE International Symposium on Information Theory, page 117, 1998.","DOI":"10.1109\/ISIT.1998.708706"},{"key":"1_CR10","doi-asserted-by":"crossref","unstructured":"M. Luby, M. Mitzenmacher, M.A. Shokrollahi, D. Spielman, and V. Stemann. Practical loss-resilient codes. In Proceedings of the 29th annual ACM Symposium on Theory of Computing, pages 150\u2013159, 1997.","DOI":"10.1145\/258533.258573"},{"key":"1_CR11","doi-asserted-by":"publisher","first-page":"399","DOI":"10.1109\/18.748992","volume":"45","author":"D.J.C. MacKay","year":"1999","unstructured":"D.J.C. MacKay. Good error-correcting codes based on very sparse matrices. IEEE Trans. Inform. Theory, 45:399\u2013431, 1999.","journal-title":"IEEE Trans. Inform. Theory"},{"key":"1_CR12","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1007\/BF02579283","volume":"2","author":"G. A. Margulis","year":"1982","unstructured":"G. A. Margulis. Explicit constructions of graphs without short cycles and low density codes. Combinatorica, 2:71\u201378, 1982.","journal-title":"Combinatorica"},{"key":"1_CR13","unstructured":"T. Richardson, M.A. Shokrollahi, and R. Urbanke. Design of provably good low-density parity check codes. IEEE Trans. Inform. Theory (submitted), 1999."},{"key":"1_CR14","unstructured":"T. Richardson and R. Urbanke. The capacity of low-density parity check codes under message-passing decoding. IEEE Trans. Inform. Theory (submitted), 1998."},{"key":"1_CR15","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","volume":"27","author":"C. E. Shannon","year":"1948","unstructured":"C. E. Shannon. A mathematical theory of communication. Bell System Tech. J., 27:379\u2013423, 623\u2013656, 1948.","journal-title":"Bell System Tech. J."},{"key":"1_CR16","doi-asserted-by":"crossref","unstructured":"M.A. Shokrollahi. New sequences of linear time erasure codes approaching the channel capacity. To appear in the Proceedings of AAECC\u201913, 1999.","DOI":"10.1007\/3-540-46796-3_7"},{"key":"1_CR17","doi-asserted-by":"publisher","first-page":"1710","DOI":"10.1109\/18.556667","volume":"42","author":"M. Sipser","year":"1996","unstructured":"M. Sipser and D. Spielman. Expander codes. IEEE Trans. Inform. Theory, 42:1710\u20131722, 1996.","journal-title":"IEEE Trans. Inform. Theory"},{"key":"1_CR18","doi-asserted-by":"publisher","first-page":"1723","DOI":"10.1109\/18.556668","volume":"42","author":"D. Spielman","year":"1996","unstructured":"D. Spielman. Linear-time encodable and decodable error-correcting codes. IEEE Trans. Inform. Theory, 42:1723\u20131731, 1996.","journal-title":"IEEE Trans. Inform. Theory"},{"key":"1_CR19","doi-asserted-by":"publisher","first-page":"533","DOI":"10.1109\/TIT.1981.1056404","volume":"27","author":"M. R. Tanner","year":"1981","unstructured":"M. R. Tanner. A recursive approach to low complexity codes. IEEE Trans. Inform. Theory, 27:533\u2013547, 1981.","journal-title":"IEEE Trans. Inform. Theory"},{"key":"1_CR20","first-page":"3","volume":"7","author":"V. V. Zyablov","year":"1971","unstructured":"V. V. Zyablov. An estimate of the complexity of constructing binary linear cascade codes. Probl. Inform. Transm., 7:3\u201310, 1971.","journal-title":"Probl. Inform. Transm."},{"key":"1_CR21","first-page":"18","volume":"11","author":"V. V. Zyablov","year":"1976","unstructured":"V. V. Zyablov and M. S. Pinsker. Estimation of error-correction complexity of Gallager low-density codes. Probl. Inform. Transm., 11:18\u201328, 1976.","journal-title":"Probl. Inform. Transm."}],"container-title":["Lecture Notes in Computer Science","STACS 2000"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-46541-3_1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,1]],"date-time":"2019-05-01T18:09:59Z","timestamp":1556734199000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-46541-3_1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000]]},"ISBN":["9783540671411","9783540465416"],"references-count":21,"URL":"https:\/\/doi.org\/10.1007\/3-540-46541-3_1","relation":{},"ISSN":["0302-9743"],"issn-type":[{"type":"print","value":"0302-9743"}],"subject":[],"published":{"date-parts":[[2000]]}}}