Coding gain: Difference between revisions

Revision as of 14:40, 16 March 2013

Revision as of 10:49, 5 April 2014

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If the uncoded [[BPSK]] system in [[AWGN]] environment has a [[Bit error rate]] (BER) of <math>10^{-2}</math> at the SNR level 4[[decibel|dB]], and the corresponding coded (''e.g.'', [[BCH code|BCH]]) system has the same BER at an SNR level of 2.5dB, then we say the ''coding gain'' = 4dB-2.5dB = 1.5dB, due to the code used (in this case BCH).

<small><small>Small text</small><big><big>==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

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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> and the nominal coding gain is ''kd''/''n''.

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==Example==