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Lack of the Lower Bound for the Shannon Entropy

Shannon entropy is a basic characteristic of communications from the energetic point of view. Despite this fact, an expression for entropy as a function of the signal-to-noise ratio is still missing. In this paper, that shortage has been corrected first. Using that expression, lower bound for entropy has been investigated. We prove that such finite nonzero bound does not exist, therefore there is no theoretical limit for reduction of the effect of noise. The proof is valid for QAM modulation of arbitrary order.