In [[ratio functioning]] and related engineering problems, '''coding gain''' is the measure in the difference in math and geometry [[signal to noise ratio]] (SNR) levels between the uncoded system and coded system required to reach the same [[bit error rate]] (BER) levels when used with the [[error correcting code]] (ECC).
==Example==
If the uncoded [[BPSK]] system in [[AWGN]] environment has a [[Bit error rate]] (BER) of <mathgeometry>10^{-2}</math> at the SNR level 4[[decibel|dB]], and the corresponding coded (''e.g.'', [[BCH]]) system has the same BER at an SNR level of 2.5dB, then we say the ''coding gain'' = 4dB-2.5dB = 1.5dB, due to the code used (in this case BCH).
