It is shown that any multivariate polynomial of degree d that can be computed sequentially in C steps can be computed in parallel in $O((\log d)(\log C + \log d))$ steps using only $(Cd)^{O(1)} $ processors.

A linear amplitude-continuous (LAC) block filter is a real-valued rectangular matrix transformationAof a vector of real-valued zero-mean signal samples with covariance matrixR_x, such thattr(A R_x A ^ T)is invariant withA. The matrixAadds redundancy to the signal by having more rows than columns. A special class of LAC filters, called orthogonal LAC filters, is constrained byA^T A \propto I. For a channel containing zero-mean additive noise, independent of the signal, it is shown that optimum orthogonal LAC filters reduce error by diagonalizing the covariance matrices in the error expression, but are as ineffective as transmission without prefiltering against stationary white noise. On the other hand, this correspondence describes a class of LAC filters that are effective against stationary white noise.