The concept of weighted entropy is not so new. However, this recent reference seems to give a good discussion.

https://arxiv.org/abs/1710.10798

If I understand your problem correctly you need to find weights that give you a weighted entropy below the channel capacity and correspond to your evaluation of the relative importance of the different symbols. This is an optimisation problem.

The concept of weighted entropy with weight function $\varphi$ defined as

$$ H_\varphi = -\sum_i \phi(A_i) p(A_i) \log p(A_i) $$

is not so new. However, this recent reference seems to give a good discussion.

https://arxiv.org/abs/1710.10798

If I understand your problem correctly you need to find weights that give you a weighted entropy below the channel capacity and correspond to your evaluation of the relative importance of the different symbols. This is an optimisation problem.