Coding gain: Difference between revisions

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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> (b/2D or b/s/Hz) and the nominal coding gain is ''kd''/''n''.
 
==Example==
The table below lists the nominal spectral efficiency, nominal coding gain and effective coding gain for [[Reed-Muller code|Reed-Muller codes]] of length <math>n \le 64</math>:
 
{| class="wikitable"
! Code !! <math>\rho</math> !! <math>\gamma_c</math> !! <math>\gamma_c</math> (dB) !! <math>\gamma_{eff}</math> (dB)
|-
| [8,7,2] || 1.75 || 7/4 || 2.43 || 2.0
|-
| [8,4,4] || 1.0 || 2 || 3.01 || 2.6
|-
| [16,15,2] || 1.88 || 15/8 || 2.73 || 2.1
|-
| [16,11,4] || 1.38 || 11/4 || 4.39 || 3.7
|-
| [16,5,8] || 0.63 || 5/2 || 3.98 || 3.5
|-
| [32,31,2] || 1.94 || 31/16 || 2.87 || 2.1
|-
| [32,26,4] || 1.63 || 13/4 || 5.12 || 4.0
|-
| [32,16,8] || 1.00 || 4 || 6.02 || 4.9
|-
| [32,6,16] || 0.37 || 3 || 4.77 || 4.2
|-
| [64,63,2] || 1.97 || 63/32 || 2.94 || 1.9
|-
| [64,57,4] || 1.78 || 57/16 || 5.52 || 4.0
|-
| [64,42,8] || 1.31 || 21/4 || 7.20 || 5.6
|-
| [64,22,16] || 0.69 || 11/2 || 7.40 || 6.0
|-
| [64,7,32] || 0.22 || 7/2 || 5.44 || 4.6
|-
|}
 
==Bandwidth-limited regime==