On viewing block codes as finite automata

Authors:
Priti Shankar;Amitava Dasgupta;Kaustubh Deshmukh;B. Sundar Rajan
Affiliations:
Department of Computer Science and Automation, Indian Institute of Science, Bangalore 560012, India;Department of Computer Science and Automation, Indian Institute of Science, Bangalore 560012, India;Department of Computer Science and Engineering, University of Washington, Seattle, WA;Department of Electrical Communication Engineering, Indian Institute of Science, Bangalore 560012, India
Venue:
Theoretical Computer Science
Year:
2003

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Abstract

Block codes are viewed from a formal language theoretic perspective. It is shown that properties of trellises for subclasses of block codes called rectangular codes follow naturally from the Myhill Nerode theorem. A technique termed subtrellis overlaying is introduced with the object of reducing decoder complexity. Necessary and sufficient conditions for trellis overlaying are derived from the representation of the block code as a group, partitioned into a subgroup and its cosets. The conditions turn out to be simple constraints on coset leaders. It is seen that overlayed trellises are tail-biting trellises for which decoding is generally more efficient than that for conventional trellises. Finally, a decoding algorithm for tail-biting trellises is described, and the results of some simulations are presented.