{"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":"","footnotes":""},"msr-content-type":[3],"msr-research-highlight":[],"research-area":[],"msr-publication-type":[193716],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-154433","msr-research-item","type-msr-research-item","status-publish","hentry","msr-locale-en_us"],"msr_publishername":"IEEE Communications Society","msr_edition":"IEEE Transactions on Information 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