Coding gain: Difference between revisions

Revision as of 11:20, 24 March 2009

Revision as of 11:21, 24 March 2009

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==Power-limited regime==

In the ''power-limited regime'' (where the nominal [[spectral efficiency]] <math>\rho \le 2</math> ([b/2D or b/s/Hz)], ''i.e.'' the ___domain of binary signaling), the effective coding gain <math>\gamma_{eff}(A)</math> of a signal set <math>A</math> at a given target error probability per bit <math>P_b(E)</math> is defined as the difference in dB between the <math>E_b/N_0</math> required to achieve the target <math>P_b(E)</math> with <math>A</math> and the <math>E_b/N_0</math> required to achieve the target <math>P_b(E)</math> with 2-[[Pulse-amplitude modulation|PAM]] or (2&times;2)-[[Quadrature amplitude modulation|QAM]] (''i.e.'' no coding). The nominal coding gain <math>\gamma_c(A)</math> is defined as

: <math>\gamma_c(A) = {d^2_\min(A) \over 4E_b}.</math>