# How can the Nyquist theorem for the maximum bit-rate of a noiseless channel be derived?

I've been given the formula: $$I = 2* H * log_2(L)$$ where:

$I$ = Maximum data rate in bits per second for a noiseless channel

$H$ = Bandwidth that the channel will carry (that is, the range of frequencies, not the bit rate)

$L$ = Number of discrete levels in the signal

Could you explain to me where this formula comes from? How does it model the noiseless channel, and how is the formula derived?

I understand how it takes $log_2(x)$ bits to distinguish between $x$ number of things.

(Edited to corrected formula)

• I found a proof of the related formula: Maximum Channel Capacity = 0.5 * log (1 + P/N) at Additive white Gaussian Noise on Wikipedia. – user85543 Dec 17 '15 at 1:33