Universal noiseless codes for sources of arbitrary entropy

We offer two noiseless codes for representing blocks of n integers Xⁿ generated independently by a source characterized by an unknown monotone probability function. Though assumed monotone, the source is allowed arbitrary entropy H⩾0, including zero. Our first coding procedure is illustrative, yet universal in the strong sense that the expected value of the code length L(Xⁿ) is dominated by a linear function of the source entropy, EL(Xⁿ)⩽c₀ +c₁nH. Our second procedure is asymptotically optimal in the sense that EL(Xⁿ)⩽nH+0(nH). We discuss the implications of these coding procedures for model selection using the minimum description length (MDL)