Coding gain: Difference between revisions

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: <math>\gamma_c(A) = {d^2_\min(A) \over 4E_b}.</math>
 
This definition is normalized so that <math>\gamma_c(A) = 1</math> for 2-PAM or (2&times;2)-QAM. If the average number of nearest neighbors per transmitted bit is equal to one, the effective coding gain <math>\gamma_{eff}(A)</math> is approximately equal to the nominal coding gain <math>\gamma_c(A)</math>. However, if the average number of nearest neighbors per transmitted bit is greater than one, the effective coding gain <math>\gamma_{eff}(A)</math> is less than the nominal coding gain <math>\gamma_c(A)</math> by an amount which depends on the steepness of the <math>P_b(E)</math> ''vs.'' <math>E_b/N_0</math> curve at the target <math>P_b(E)</math>.
This definition is normalized so that <math>\gamma_c(A) = 1</math> for 2-PAM or (2&times;2)-QAM.
 
For the special case of a binary [[linear block code]] <math>C</math> with parameters <math>[n,k,d]</math>, the nominal [[spectral efficiency]] is <math>\rho = 2k/n </math> (b/2D or b/s/Hz) and the nominal coding gain is ''kd''/''n''.