Typical digital
communication systems uses M-
quadrature amplitude modulation (QAM) to communicate through an analog channel (specifically a
communication channel with
Gaussian noise). For Higher bit rates (M) the minimum
signal-to-noise ratio (SNR) required by a QAM system with
Error Correcting Codes is about 1.53
dB higher than minimum SNR required by a Gaussian source(>30% more transmitter power) as given in the
Shannon–Hartley theorem : C = B \log_2 \left( 1+\frac{S}{N} \right) where :
C is the
channel capacity in
bits per second; :
B is the
bandwidth of the channel in
hertz; :
S is the total signal power over the bandwidth and :
N is the total noise power over the bandwidth. :
S/N is the
signal-to-noise ratio of the communication signal to the Gaussian noise interference expressed as a straight power ratio (not as
decibels). This 1.53 dB difference is called the
shaping gap. Typically, a digital system will encode bits with uniform probability to maximize the
entropy. Shaping codes act as a buffer between digital sources and the modulator. They will receive uniformly distributed data and convert it to a Gaussian-like distribution before presenting it to the modulator. Shaping codes are helpful in reducing transmit power and thus reducing the cost of the power amplifier and the interference caused to other users in the vicinity. ==Application==