Reconfigurable Multiple Constant Multiplication Using Minimum Adder Depth

The problem of reconfigurable multiple constant multiplication (ReMCM) is about finding an cost-effective network of shifts, additions, subtractions, and multiplexers to implement the multiplication of a single input variable with one out of several sets of coefficients. Most previous publications only focus on the problem with a single output, whereas the algorithm proposed here solves a multiple output ReMCM problem using a adder-graph based minimal logic depth approach. The use of minimal logic depth restricts the length of critical path and it was shown in previous work that minimum depth MCM is advantageous in terms of power consumption. The use of a adder-graph heuristic gives more possibilities for adder formation to reduce the total number of adders and multiplexers. For the polyphase decimation filters, the relation between filter length and decimation factor has been shown to have a influence on the implementation cost. Experimental results showed that a ReMCM can be implemented with up to 38% less area for decimation factor of 8 than a parallel implementation of the polyphase subfilters, while the single output problems can also be solved with results comparable to the known algorithms.