Abstract-Shannon's celebrated source coding theorem can be viewed as a "one-sided law of large numbers." We formulate second-order noiseless source coding theorems for the deviation of the codeword lengths from the entropy. For a class of sources that includes Markov chains we prove a "one-sided central limit theorem" and a law of the iterated logarithm.
Kontoyiannis studied the second order variable length source coding for the Markov chain REF .
Second-order noiseless source coding theorems
IEEE TRANS. INFORM. THEORY
Computer Science Mathematics