Coding gain: Difference between revisions

Revision as of 01:37, 11 May 2019

Revision as of 01:38, 11 May 2019

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==Bandwidth-limited regime==

In the ''bandwidth-limited regime'' (<math>\rho > 2 ~b/2D</math>, ''i.e.'' the ___domain of non-binary signaling), the effective coding gain <math>\gamma_\mathrm{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_\mathrm{norm}</math> required to achieve the target <math>P_s(E)</math> with <math>A</math> and the <math>SNR_\mathrm{norm}</math> required to achieve the target <math>P_s(E)</math> with M-[[Pulse-amplitude modulation|PAM]] or (M&times;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>