Efficient coefficient partitioning for decomposed DA-based inner-product computation

The Look-Up-Table (LUT) size grows exponentially with increasing number of coefficients in a straight forward implementation of memory based Distributed Arithmetic (DA) computation. To avoid exponential blow-up, the common practice breaks the entire set of coefficients into multiple groups, each represented by a much smaller LUT, and forms the result by summing up the outputs from these LUTs. A detailed inspection shows that the overall word-size of the LUTs could be minimized by proper reordering and grouping of the coefficients, thus reduces the total memory usage of the LUTs. A fast heuristic partitioning algorithm for this purpose is devised and analyzed in this paper, showing up to 16% resource reduction compared to in-order grouping. The proposed technique can be applied orthogonally to offset binary coded (OBC) LUTs for resource efficient DA implementation as well.