Coding gain: Difference between revisions

Revision as of 17:23, 4 March 2009

Revision as of 07:25, 6 March 2009

Line 7:

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 = \frac{2k/}{n} \cdot \frac{b}{2D}</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 (MxM)-[[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 (MxM)-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: Coding theory]]