On Precision-Redundancy Relation in the Design of Source Coding Algorithms

Consider an m-ary memoryless source, producing symbols alpha₁,..., alpha_m with probabilities p₁, ..., p_m. We assume that instead of true probabilities, we have to use their approximate values pcirc₁, ..., pcirc_m with maximum absolute error: delta* = max_i|p_i - pcirc_i| . By P_min = min_i {p_i} we denote the smallest source´s probability. We assume that p_min > 0, and that it is relatively large w.r.t approximation error delta*/p_min < 1.