Gaussian Channel

In communication theory, it is often assumed that the transmitted signals are distorted by some noise. The most common noise to assume is additive Gaussian noise, the so-called additive white Gaussian noise channel (AWGN). This chapter studies the AWGN channel in more detail. A fundamental limit is derived for the signal-to-noise ratio (SNR) specifying when it is not possible to achieve reliable communication. Often in communication systems, the signaling is allowed to occupy a certain bandwidth. Therefore, it is interesting to consider signals with a limited bandwidth. In some cases, there can be several independent parallel Gaussian channels used by the same communication system. One of the most famous results from information theory is the fundamental Shannon limit that sets requirements on the SNR for reliable communication. When deriving the limit, the capacity formula for the band-limited case is considered as the band width grows to infinity.