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What you have here is a binary erasure channel. Its capacity is $1-b$. By Shannon's channel coding theorem, so long as $(h+d)< c(1-b)$, we can send the file with error as small as we wish. That is, $d< c(1-b)-h$.
For the first part, it is should be $(1-b)^{h+d}$.1-(1-b)^{h+d}$. 3 added 34 characters in body Though it could be elementary for people who know information theory, its worth nontrivial question for others. So I would like to provide an answer. What you have here is a binary erasure channel. Its capacity is$1-b$. By Shannon's channel coding theorem, so long as$(h+d)(1-b) (h+d)< c$c(1-b)$, we can send the file with error as small as we wish. That is, $d< \frac{c}{1-b} -h$.c(1-b)-h$. For the first part it is$(1-b)^{h+d}$. 2 added 168 characters in body; deleted 15 characters in body; edited body Though it could be elementary for people who know information theory, its worth nontrivial question for others. So I would like to provide an answer. What you have here is a binary erasure channel. Its capacity is$1-b$. By Shannan's Shannon's channel coding theorem, so long as$(h+d)(1-b) < c$, we can send the file with error as small as we wish. That is,$d< \frac{c}{1-b} -h\$.