{"id":154433,"date":"2006-10-01T00:00:00","date_gmt":"2006-10-01T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/unifying-views-of-tail-biting-constructions-for-linear-block-codes\/"},"modified":"2018-10-16T20:43:48","modified_gmt":"2018-10-17T03:43:48","slug":"unifying-views-of-tail-biting-constructions-for-linear-block-codes","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/unifying-views-of-tail-biting-constructions-for-linear-block-codes\/","title":{"rendered":"Unifying Views of Tail-Biting Constructions for Linear Block Codes"},"content":{"rendered":"<div class=\"asset-content\">\n<p>In this paper, we present new ways of describing and<br \/>\nconstructing linear tail-biting trellises for block codes. We extend<br \/>\nthe well-known Bahl\u2013Cocke\u2013Jelinek\u2013Raviv (BCJR) construction<br \/>\nfor conventional trellises to tail-biting trellises. The BCJR-like labeling<br \/>\nscheme yields a simple specification for the tail-biting trellis<br \/>\nfor the dual code, with the dual trellis having the same state-complexity<br \/>\nprofile as that of the primal code . Finally, we show that the<br \/>\nalgebraic specification of Forney for state spaces of conventional<br \/>\ntrellises has a natural extension to tail-biting trellises.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>In this paper, we present new ways of describing and constructing linear tail-biting trellises for block codes. We extend the well-known Bahl\u2013Cocke\u2013Jelinek\u2013Raviv (BCJR) construction for conventional trellises to tail-biting trellises. The BCJR-like labeling scheme yields a simple specification for the tail-biting trellis for the dual code, with the dual trellis having the same state-complexity profile [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"IEEE Communications Society","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"IEEE Transactions on Information Theory","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"Copyright \u00a9 2007 IEEE. Reprinted from IEEE Communications Society. This material is posted here with permission of the IEEE. Internal or personal use of this material is permitted. However, permission to reprint\/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. 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