Abstract
It is well-known that the redundancy of the Shannon code lies in the interval (0, 1). In order to study the overall performance of the Shannon code, we consider its redundancy as a random variable on the set of sources with n symbols, i.e., Rsh(n), and examine its statistical parameters. It is shown that the mean of Rsh(n) gets close to 0.5 for sources with large alphabet size n. Moreover, we observe that its variance tends to zero as n increases. Briefly speaking, for almost all sources with a large alphabet size, the redundancy of the Shannon code is almost 0.5 bits.
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