Coding gain: Difference between revisions

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==Power-limited regime==

In the ''power-limited regime'' (<math>\rho \le 2b/2D</math>), 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]] (''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>.

This definition is normalized so that <math>\gamma_c(A) = 1</math> for 2-PAM.

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 and the nominal coding gain is <math>kd/n</math>.

==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 (M*MMxM)-[[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>.

This definition is normalized so that <math>\gamma_c(A) = 1</math> for M-PAM or (M*MMxM)-QAM.

==References==

MIT OpenCourseWare (http://ocw.mit.edu), 6.451 Principles of Digital Communication II, Lecture Notes sections 5.3, 5.5, 6.3

[[Category: Error detection and correction]]

[[Category: Coding theory]]

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[[Category: Error detection and correction]]

[[de:Codegewinn]]