The rate-distortion function of a source is the least asymptotic coding rate permitting an expected distortion at most 
. For a memoryless source 
with a specified single-letter distortion 
, it is characterized by
![R(D)=inf_(P_(Y|X):E[d(X,Y)]<=D)I(X;Y),](/images/equations/Rate-DistortionFunction/NumberedEquation1.svg) |
where 
is mutual information and the logarithm base
determines the information unit. For bits, logarithms have base 2. The infimum ranges
over conditional distributions of a reconstruction
,
rather than over a prescribed class of linear encoders.
For a Bernoulli source of parameter 
with Hamming distortion, 
for 
and 
for 
. Here 
is binary information entropy. The restriction to a linear
encoder in linear source coding changes this
tradeoff.
