Death penalty

I don't have anything against execution of a murderer, partially because I think that the death is not the worst thing that can happen in human life. (If you are old enough this should be obvious for you. Think about soldiers who died for their country or about ordinary people around you who died without commiting any crime. Alas, all of us are sentenced to death.) However, we know that many innocent people were convicted to death and I am convinced that execution of an innocent person is a horrible crime . EVEN ONE UNFAIR EXECUTION IS TOO MUCH! I understand that the people advocating capital punushment have a point: one should have an exceptional punishment for the most heinous crimes. I think, however, that instead of death penalty this punishment should be solitary confinement in a small cell. The prisoner should stay in this cell until his death without possibility to leave it even for one minute, without seeing anybody (even prison guards), without the right to get any information from outside. However, if he believes that he is innocent he should be able to try to overturn his conviction; therefore he should be able to write letters (but he should not have any right to receive letters).
Solitary confinement is not an unusual punishment. It is a cruel punishment, in my opinion more cruel than death penalty. If a prisoner shares this opinion he can ask for execution; I am sure that many people will do this. However, an innocent person will continue to fight for his freedom; he will have a good chance to prevail.
The last but not least: solitary confinement is not more expensive than the standard prison; in fact, it is much cheaper. A prisoner costs $25000-$30000 per year; in solitary confinement he will cost a fraction of this amount. In the early days of mathematical economics
economists solved a problem how to provide all essential nutrients for minimal cost. They found that this can be done very cheaply, but the cheapest diet uses only a small number of products and nobody will use it if he has a choice. They decided that such a diet can be appropriate only for prisoners. I would say that it is too harsh for regular prisoners, however, we are talking now about a capital punishment, about people that are kept alive only because we are afraid to make a mistake.