Ordered Binary Decision Diagrams and Minimal Trellises
Abstract
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(x1,...,xn) be the Boolean function that takes the value 0 at x1,...,xn if and only if (x1,...,xn)epsilonC. 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(x1,...,xn). 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 30, 1998
- Accession Number
- ADA356014
Entities
People
- Alexander Vardy
- John D. Lafferty
Organizations
- Carnegie Mellon University