The compression performance of grammar-based codes revisited

A grammar-based code (GC) refers to a new type of universal lossless source code. The authors consider the following two questions: (1) Based on run-length encoding (RLE) can one propose a class of interesting algorithms which is superior to arithmetic coding (AC) algorithms with finite contexts and can also be used as a benchmark to evaluate GCs? (2) For each sequence x, is there a better quantity than r_k*(x) such that it can be used to derive a stronger redundancy bound for GCs? They show that the answer to both questions is yes and summarize the main results.