be achievable. However, by the symmetry of the binary entropy function around 0 = ~ we know
that h(1 - 0) =
h(O).
Therefore for binary memoryless sources with parameter 0 < 0 < 1 the
entropy
h(O)
is achievable.
1.5.9 Converse and Conclusion
We have shown that entropy can be achieved. However, it is possible for even better codes to exist.
Since we have chosen code sequences for only the most probable source sequences our coding
methods are optimal. Nevertheless this does not yet imply that we cannot achieve compression
rates below entropy with vanishing error probabilities.
So, consider our optimal coding scheme ...
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