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Ordered binary decision diagrams and minimal trellises
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DOI：10.1109/12.795225.png)
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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 f(c)(x(1),...,x(n)) be the Boolean function that takes the value 0 at x(1),...,x(n) if and only if (x(1),...,x(n)) is an element of 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 f(c)(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.
Keyword:
binary decision diagrams
trellises
CAD
coding theory
formal verification
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