Your translation isn't wrong – it's good English and it has the correct meaning. However, the usual information-theoretic English translation of une source would be a source.
This is Shannon's Source Coding Theorem.
I don't know whether, by de k symboles, you mean an alphabet of k different symbols, or k symbols in total. Assuming the second,
I'd translate the whole thing as
k symbols from a source with probability distribution P can asymptotically be encoded using an average of H(P) bits per symbol.
I don't know why you don't say bits par symbole in French, but I can find a statement of the theorem online as
Une source ayant une distribution P peut être asymptotiquement encodée avec H(P) bits en moyenne et pas mieux.
so it appears that in French, one doesn't always specify bits par symbole.