Coding gain: Difference between revisions

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==Example==

If the uncoded [[BPSK]] system in [[AWGN]] environment has a [[Bit error rate]] (BER) of <math>10^{-3}</math> at the SNR level 3[[decibel|dB]], and the corresponding coded (''e.g.'', [[BCH]]) system has the same BER at an SNR level of 1.5dB, then we say the ''coding gain'' = 3dB-1.5dB = 1.5dB, due to the code (BCHused (in this case) usedBCH).

==Power-limited regime==

In the power-limited regime, 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.

==Bandwidth-limited regime==

In the bandwidth-limited regime, 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*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>.

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

==References==