Redundancy rates for renewal and other processes

The paper addresses the theoretical issue of universal noiseless source coding, viz., the best possible redundancy bound achievable for a given class of source models by block to variable-length lossless coding. For parametric model classes such as memoryless or Markov sources, this bound grows as the log of the block-length n, [1,2,4]. The authors show that for the non-parametric class of renewal processes the growth rate is O(√n), while for the class of Markov renewal processes of order k the rate is O(n^k+1k+2/)