A variable-to-fixed length lossless source code optimizing a different criterion of average coding rate from Tunstall code

In this paper we define the average coding rate of a variable-to-fixed length (VF) lossless source code as the expectation of the pointwise coding rate, which is called average pointwise coding rate. It has been shown that the Tunstall code is asymptotically optimal under the criterion optimizing the average pointwise coding rate. In this paper, we propose a new VF code attaining optimal average pointwise coding rate for each finite number of leaves. An incremental parsing tree construction algorithm like the one that builds Tunstall codes is presented. It is proved that this code is optimal under the criterion of the average pointwise coding rate, and that the average pointwise coding rate of this code converges asymptotically to the entropy of the stationary memoryless source emitting the encoded data.