where kappa has (carries) the units of X. Finally, the channel rate R is defined as
| R | (⨀Xᵢ) = | Σ | H(Xᵢ) - H(X),(3) |
| I | I |
where X is the denumerable[18] cartesian product space
| X = | ⨂ | Xᵢ.(4) |
| I |
Next, we define the angle Θ
| -R(⨀Xᵢ) | |||
| I | |||
| | Θ | (⨀Xᵢ) | = | sin⁻¹e | (5) |
| I |
and the norm
|X| = κ(2πe)⁻¹ᐟ² eH(X).(6)
Now, if[19] a statistically independent basis; i.e., one for which
| κ | ||
| R(⨀Xᵢ) | ≡ | constant,(7) |
| I |