  For vector Gaussian channels, a precise differential connection between
channel capacity and a quantity termed normalized optimal detection error
(NODE) is presented. Then, this C-NODE relationship is extended to
continuous-time Gaussian channels drawing on a waterfilling characterization
recently found for the capacity of continuous-time linear time-varying
channels. In the latter case, the C-NODE relationship becomes asymptotic in
nature. In either case, the C-NODE relationship is compared with the I-MMSE
relationship due to Guo et al. connecting mutual information in Gaussian
channels with the minimum mean-square error (MMSE) of estimation theory.
