A new upper bound on ε-capacity

Summary form only given. Suppose that two outputs of a linear, time-invariant channel are distinguishable at the receiver if and only if they are separated in L₂ norm by ε. The inputs to the channel are assumed to be power limited and are nonzero only on the finite time interval [0, T]. Let N_max(T, ε) be the maximum number of distinguishable outputs for given T, ε > 0. The ε-capacity of the channel, C_ε, is defined as the limit, as T → ∞, of log₂[N_max(T, ε)]/T b/s. It has been shown that the noise spectral density that minimizes Shannon capacity, C_S, is proportional to the power spectral density of the input. It has also been shown that the resulting upper bound on C_ε is less than or equal to the Shannon capacity of a channel consisting of the original channel plus an additive noise source (not necessarily Gaussian) with variance ε²/4, but otherwise having arbitrary statistics. Numerical results have been obtained for models of subscriber loop channels, showing that the new upper bound is significantly better than an upper bound derived previously by Root.