Clarification of “xMax vs. Shannon”

I have recently received several comments about my earlier postings “xMax meets Shannon” and “xMax meets Shannon once again”. These comments pointed to statements apparently made by people related to the xMax development, saying that xMax does not violate the Shannon capacity theorem, and the commentators concluded that this contradicts what I said in these posts. This is of course not the case.

Neither xMax nor any other modulation technique is capable of violating Shannon’s capacity limit. This goes without saying. In these posts I did not say that they are violating Shannon’s limit, but rather the exact opposite. The point I was making is that if their claims were true, then they would be violating Shannon’s limit, and therefore their claims are false. This is what is called in logic “proof by contradiction”. You start with the premise that the xMax claims are true, i.e. that “xMax can use 1,000 to 100,000 times less power than comparable transmission technologies.” Given that “comparable transmission technologies” are already operating at power levels close to the minimum possible according to Shannon, this implies that xMax would be capable of operating at power levels which are far below the Shannon limit. Since this is clearly false, you have a contradiction of your original premise. You then conclude that the xMax claims are false.

I am glad to hear that apparently the developers of xMax acknowledge the limits defined by the Shannon’s capacity theorem. Since this immediately falsifies their claims, I can only hope that they will publish a retraction of these claims at their earliest convenience.

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