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Decision diagram method for calculation of pruned Walsh transform

Content Provider	IEEE Xplore Digital Library
Author	Jankovic, D. Stankovic, R.S. Drechsler, R.
Copyright Year	1968
Abstract	Discrete Walsh transform is an orthogonal transform often used in spectral methods for different applications in signal processing and logic design. FFT-like algorithms make it possible to efficiently calculate the discrete Walsh spectrum. However, for their exponential complexity, these algorithms are practically unsuitable for large functions. For this reason, a Binary Decision Diagram (BDD) based recursive method for Walsh spectrum calculation has been introduced in Clarke et al. (1993). A disadvantage of this algorithm is that the resulting Multi-Terminal Binary Decision Diagram (MTBDD) representing the Walsh spectrum for f can be large for some functions. Another disadvantage turns out if particular Walsh coefficients are to be computed separately. The algorithm always calculates the entire spectrum and, therefore, it is rather inefficient for applications where a subset of Walsh spectral coefficients, i.e., the pruned Walsh spectrum, is required. In this paper, we propose another BDD-based method for Walsh spectrum calculation adapted for application where the pruned Walsh spectrum is needed. The method takes advantage of the property that for most switching functions, the size of a BDD for f is usually quite a bit smaller than the size of the MTBDD for the Walsh spectrum. In our method, a MTBDD representing the Walsh spectrum is not: constructed. Instead, two additional fields are assigned to each node in the BDD for the processed function f. These fields are used to store the results of intermediate calculations. Pairs of spectral coefficients are calculated and stored in the fields assigned to the root node. Therefore, the calculation complexity of the proposed algorithm is proportional to the size of the BDD for f whose spectrum is calculated. Experimental results demonstrate the efficiency of the approach.
Sponsorship	IEEE Computer Society Technical Committee on Distributed Process IEEE Computer Society Technical Committee on VLSI IEEE Technical Committee on Computer Architecture IEEE Computer Society
Starting Page	147
Ending Page	157
Page Count	11
File Size	337453
File Format	PDF
ISSN	00189340
Volume Number	50
Issue Number	2
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2001-02-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Discrete transforms Signal processing algorithms Data structures Boolean functions Binary decision diagrams Logic design Circuit synthesis Fault detection
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Computational Theory and Mathematics Software Hardware and Architecture

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