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Abstmct-It is known that the expected codeword length L,, of the best uniquely decodable (UD) code satisfies H(X) < L,, < H(X) + 1. LetXbearandomvariablewhichcantakeonnvalues.Thenitisshown that the average codeword length L, :, for the best one-to-one (not necessBluy uniquely decodable) code for X is shorter than the average codeword length L,, for the best mdquely decodable code by no more thau (log2 log, n) + 3. Let Y be a random variable taking OII a fiite or countable number of values and having entropy H. Then it is proved that L,:,>H-log2 (H+l)-log, log2 (H+l)- ...-6. Some relations are eatahlished amoug the Kolmogorov, Cl&in, and extension complexities. Finally it is shown that, for all computable probability distributions, the universal prefix codes associated with the conditional Chaitin complexity have expected codeword length within a constant of the Shannon entropy.

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