# Cover and Thomas' Remark on Average Probability of Error for an $(M, n)$ code

I am confused by one remark on the average probability of error for $$(M, n)$$ code given in Cover and Thomas' book "Elements of Information Theory".

They said $$P_e^{(n)}$$ is a probability of error only if the message is chosen uniformly over the message set $$\{1, 2, ..., 2^M\}$$. Isn't the message set $$\{1, 2, ..., M\}$$? Where does this $$2^M$$ come from? Is this an errata?

Thanks to everyone who's trying to help out.

Here are the definitions of $$(M, n)$$ code and the average probability of error $$P_e^{(n)}$$ given in the book. Also the exact statement I have a problem with (highlighted):

• Agreed, this is very probably a typo. $2^M$ does not make any sense in this context. Probably the authors already had the rate in mind, which is defined next. Jan 28, 2022 at 7:55
• I’m voting to close this question because it is too local (typo induced confusion) and has no lasting value to the site. Jan 28, 2022 at 9:45
• Please delete the question now that you know it is due to a typo. Leaving it will only serve to obfuscate search results on this topic. Jan 28, 2022 at 9:49
• Please do not delete the question as there is no reason to do so. Incidentally, you might want to know your question has sparked a discussion: math.meta.stackexchange.com/questions/34519 Jan 29, 2022 at 5:12

over the message set $$\{1,2,...,M\}$$