Capacity of General Discrete Noiseless Channels

Details Capacity of General Discrete Noiseless Channels Capacity of General Discrete Noiseless Channels

2008-02-18

arxiv.org/abs/0802.2451v2

Computer Science

Information Theory

4 pages. Essentially the paper that appeared in Proc. ISCTA '07, 2007. From v1 to v2, one error was corrected

Scientific paper

This paper concerns the capacity of the discrete noiseless channel introduced by Shannon. A sufficient condition is given for the capacity to be well-defined. For a general discrete noiseless channel allowing non-integer valued symbol weights, it is shown that the capacity--if well-defined--can be determined from the radius of convergence of its generating function, from the smallest positive pole of its generating function, or from the rightmost real singularity of its complex generating function. A generalisation is given for Pringsheim's Theorem and for the Exponential Growth Formula to generating functions of combinatorial structures with non-integer valued symbol weights.

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