A coding theorem and Rényi's entropy

Let L(t) = t−1logD(∑piDtni})where pi is the probability of the ith input symbol to a noiseless channel, and ni is the length of the code sequence for the ith symbol in some uniquely decipherable code. Limiting values of L(t) are σ nipi for t = 0 and max (ni) for t = ∞. It is shown that L(t) has some desirable properties as a measure of typical code length. A coding theorem for a noiseless channel is proved. The theorem states roughly that it is possible to encode so that L(t) is close to Hα , where Hα is R∑nyi's entropy of order α and α = (1 + t)−1