A new lower-bound for the maximin redundancy in pattern coding
IEEE - Trans. on Information Theory
We show that the maximin average redundancy in pattern coding is eventually larger than 1.84 (n/ log n)^(1/3) for messages of length n.
This completes the results obtained recently on pattern redundancy, although it does not fill the gap between known lower- and upper-bounds.
The problem of pattern coding raised much interest recently, as strongly universal codes have been proved to exist for patterns while universal message coding is impossible for memoryless sources on an infinite alphabet.
The proof uses fine combinatorial results on partitions with small summands.