Summary: 1666 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 44, NO. 4, JULY 1998
A Rate-Distortion Theorem for Arbitrary Discrete Sources
Po-Ning Chen and Fady Alajaji
Abstract-- A rate-distortion theorem for arbitrary (not necessarily
stationary or ergodic) discrete-time finite-alphabet sources is given. This
result, which provides the expression of the minimum -achievable fixed-
length coding rate subject to a fidelity criterion, extends a recent data
compression theorem by Steinberg and VerdŽu.
Index Terms--Arbitrary discrete sources, data compression, rate-dis-
tortion theory, Shannon theory.
We consider the problem of source coding with a fidelity criterion
for arbitrary (not necessarily stationary or ergodic) discrete-time
finite-alphabet sources. We prove a general rate-distortion theorem
by establishing the expression of the minimum -achievable block
coding rate subject to a fidelity criterion.
In [3, Theorem 10, part a)], Steinberg and VerdŽu demonstrate a
data compression theorem for arbitrary sources under the restriction
that the probability of excessive distortion due to the achievable data
compression codes is asymptotically equal to zero (cf. [3, Definitions