 
Summary: 1666 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 44, NO. 4, JULY 1998
A RateDistortion Theorem for Arbitrary Discrete Sources
PoNing Chen and Fady Alajaji
Abstract A ratedistortion theorem for arbitrary (not necessarily
stationary or ergodic) discretetime finitealphabet 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 TermsArbitrary discrete sources, data compression, ratedis
tortion theory, Shannon theory.
I. INTRODUCTION
We consider the problem of source coding with a fidelity criterion
for arbitrary (not necessarily stationary or ergodic) discretetime
finitealphabet sources. We prove a general ratedistortion 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
