On optimality and redundancy of side information version of SWLZ

In this work, we establish the pointwise optimality of side information version of SWLZ algorithm for stationary ergodic sources. We also obtain a pointwise upper bound on the redundancy rate of this side information version of SWLZ algorithm for a subclass of φ-mixing sources, which includes Markov sources as a special case. This upper bound obtained differs only by a constant factor from the best bound that has been obtained on redundancy rate for the original SWLZ algorithm itself.