# Code gain

The code gain , also coding gain , describes in coding theory the difference between the required bit energy in relation to the spectral noise power density between an uncoded and encoded message in order to achieve the same bit error rate . The uncoded message represents the reference with which the message encoding by means of channel coding is compared.

The coding of a message in this context is always accomplished by the channel coding , which has the task of ensuring more security against, for example, transmission or storage errors by adding redundant information. The causes of errors can be faults such as those triggered by noise .

The influence of the error size is expressed in coding theory by the bit energy-to-noise power density ratio , which represents the ratio of the energy E b expended for an information bit to the spectral noise power density N 0 . ${\ displaystyle {\ frac {E_ {b}} {N_ {0}}}}$

The code gain C (in dB) results from:

${\ displaystyle C = \ left. {\ frac {E_ {b}} {N_ {0}}} \ right | _ {\ mathrm {uncoded}} - \ left. {\ frac {E_ {b}} {N_ {0}}} \ right | _ {\ mathrm {coded}}}$.

The bit energy is standardized and takes into account that redundant bits are transmitted in the coded transmission. ${\ displaystyle E_ {b}}$

Noise and coding affect the bit error rate in information transmission.

## literature

• Kristian Kroschel: data transfer. An introduction. Springer-Verlag, Berlin / Heidelberg 1991, ISBN 3-540-53746-5 .