There is no Theoretical Limit for Noise Reduction in Digital Communications

Shannon entropy is a basic characteristic of communications from energetic point of view. Entropy has been expressed as a function of signal to noise ratio, and lower bound for entropy has been investigated. We prove that finite nonzero bound does not exist, therefore in case of M-QAM modulation, there is no theoretical limit for reduction of the effect of noise. In our investigations, averaging is considered, exploiting the zero expected value of the Gaussian noise.

Index Terms—Shannon entropy, probability of successful communication, bit error rate, signal to noise ratio, bound for noise reduction.