Improved Upper Bounds on the Average Redundancy of Optimal RVLC

It is shown that efficient reversible variable length codes (RVLCs) with numerous codewords can be obtained if suboptimal RVLCs for the average distributions of monotone sources with relatively small alphabet sizes are multiplied by some fixed-length codes. Employing these RVLCs, the best known upper bounds on the average redundancy of optimal RVLC are almost halved. In particular, it is proved that the average redundancy of optimal RVLC for sources with
n
symbols is less than 11/
n
+0.11345 bits for
n
> 32. Some other upper bounds are also derived which are either suboptimal in some sense for small
n
or easily computable for large
n
or descriptive of asymptotic behavior. Moreover, we prove that the penalty of using optimal RVLC instead of Huffman code is less than 0.0848 bits for almost all sources with sufficiently large alphabet size. These results provide stronger evidence that, overall, the cost of benefiting from the desired properties of RVLC is not significant in terms of the redundancy.