Coding gain: Difference between revisions

Revision as of 07:25, 6 March 2009

Revision as of 07:26, 6 March 2009

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==Bandwidth-limited regime==

In the ''bandwidth-limited regime'' (<math>\rho > 2b/2D</math>), the effective coding gain <math>\gamma_{eff}(A)</math> of a signal set <math>A</math> at a given target error rate <math>P_s(E)</math> is defined as the difference in dB between the <math>SNR_{norm}</math> required to achieve the target <math>P_s(E)</math> with <math>A</math> and the <math>SNR_{norm}</math> required to achieve the target <math>P_s(E)</math> with M-[[Pulse-amplitude modulation|PAM]] or (MxM''M''&nbsp;&times;&nbsp;''M'')-[[Quadrature amplitude modulation|QAM]] (''i.e.'' no coding). The nominal coding gain <math>\gamma_c(A)</math> is defined as

: <math>\gamma_c(A) = {(2^\rho - 1)d^2_\min (A) \over 6E_s}.</math>