Will the capacity of a channel becomes unbounded if i increase its signal-to-noise ratio $S/N$ without limit?
By the sampling theorem, uniform samples taken at more than twice the bandwidth of a band-limited signal can be used to reconstruct the signal perfectly by sinc interpolation. For each different set of sample values there is a different band-limited function. In absence of noise, by increasing the bit depth of the samples one can store an unlimited amount of information per sample into the band-limited signal, and get it back simply by sampling and digitizing it again.