  Whenever inspected by humans, reconstructed signals should not be
distinguished from real ones. Typically, such a high perceptual quality comes
at the price of high reconstruction error, and vice versa. We study this
distortion-perception (DP) tradeoff over finite-alphabet channels, for the
Wasserstein-$1$ distance induced by a general metric as the perception index,
and an arbitrary distortion matrix. Under this setting, we show that computing
the DP function and the optimal reconstructions is equivalent to solving a set
of linear programming problems. We provide a structural characterization of the
DP tradeoff, where the DP function is piecewise linear in the perception index.
We further derive a closed-form expression for the case of binary sources.
