Computer Science Department
School of Computer Science, Carnegie Mellon University


Ordered Binary Decision Diagrams and Minimal Trellises

John Lafferty, Alexander Vardy*

July 1998

Keywords: Binary decision diagrams, trellises, CAD, coding theory, formal verification

Ordered binary decision diagrams (OBDDs) are graph-based data structures for representing Boolean functions. They have found widespread use in computer-aided design and in formal verification of digital circuits. Minimal trellises are graphical representations of error-correcting codes that play a prominent role in coding theory. This paper establishes a close connection between these two graphical models, as follows. Let C be a binary code of length n, and let fc(x\/1,...,,x\/n) be the Boolean function that takes the value) at x\/1,...,x\/n if and only if (x\/1,...x\/n) element C. Given this natural one-to-one correspondence between Boolean functions and binary codes, we prove that the minimal proper trellis for a code C with minimum distance d > 1 is isomorphic to the single-terminal OBDD for its Boolean indicator function fc(x\/1,...,x\/n). Prior to this result, the extensive research during the past decade on binary decision diagrams -- in computer engineering -- and on minimal trellises -- in coding theory -- has been carried out independently. As outlined in this work, the realization that binary decision diagrams and minimal trellises are essentially the same data structure opens up a range of promising possibilities for transfer of ideas between these disciplines.

35 pages

*Coordinated Science Laboratory, Univeristy of Illinois at Urbana-Champaign, 1308 W. Main Street, Urbana, IL 61801

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