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Lagrangian optimization is used to find the optimal code rate allocation, from a PSNR perspective, starting from commonly available source coding outputs, such as intermediate rate-distortion traces.

Given that evolution is a stochastic process, the natural way to think about optimization is to ask what proportion of mutations increase versus decrease the score – a truly optimal code will have zero improvement mutations, and a highly optimized code will be improved by only a tiny fraction of the many possible mutations.

As evolution has no foresight, optimality of the modern genetic code suggests that it evolved from less optimal code variants.

The two examples just considered might suggest that it is always easy to find an optimal code.

It was observed that the optimal code length is the same as the symbol interval in the low rate scenario.

Figure 7 depicts the BER performance with the optimal code parameters for different p values for the 1D system.

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The optimal coding procedure optimized according to these criteria is summarized in Appendix, where also a few implementation details are discussed.

Third, it utilizes a complexity-distortion model to determine the optimal coding parameter values to achieve global optimization.

Inspection of the optimal codes readily reveals the main source of this non-optimality: in all optimal solutions Arg changes its position from the fourth to the third column of the table (Fig. 11b).

Arithmetic coding encodes strings of symbols as ranges of real numbers and achieves more nearly optimal codes.

Certain matrices of minimum rank yield optimal codes.

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