When all you have is a hammer, problems look like nails.
What is the “message” of DNA if not a functioning protein? What else does DNA actually do functionally other than regulate and allow for the production of proteins?
Your wording IS sloppy as well as in error.
“Prions are protein molecules that have neither DNA nor RNA.”
Indeed ALL protein molecules have neither DNA nor RNA. You made a distinction that wasn't distinct and confuses the subject.
“Currently, prions are the suspected cause of bovine spongiform encephalopathy — Mad Cow Disease. In the Shannon model, prions would be incoherent in the channel because they have no discernible message; that is, neither DNA nor RNA.”
Proteins are perfectly capable of having a discernible message. The process of protein signal transduction shows that proteins can both contain, alter, and convey information.
“Thus the prion would lead to channel or decoding malfunctions.”
It is not the lack of DNA or RNA or the lack of a message that leads to prions causing malfunction. It is a 3-D conformation that conveys the ‘information’ to other prion proteins to ‘fold THIS way, not THAT way’.
The way you wrote the paragraph ALL proteins would lead to channel or decoding malfunctions because ALL proteins “have no discernible message; that is, neither DNA nor RNA”, if one erroneously limits “discernible message” to only DNA or RNA.
*****projection irony alert!*****