Argument from Shannon code before proof of coding theorem in Info theorem book.

constanc c is the description of the program to compute the probability distribution. You input that program, plus the description in the Shannon-Fano code to the Turing machine and it should be able to give you the string you want, so this constitutes a description of the string, and thus its length is an upper bound on the Kolmogorov complexity.

If c is sufficiently small, i.e. the map is simple enough, the bound on the Kolmogorov omplexity will be more stringent, and thus the coding theorem approaches an equality more.

This argument, however, only explains why if there is bias, in a simple map, one expects the bias to correlate with Kolmogorov complexity. But it doesn't explain why there should be bias in the first place.

My arguments using transducers try to explain both, but it'd be nice to see how these two arguments fit