C = B log₂(1 + S/N) · mutual information · water-filling power allocation
Capacity C: – bps
Mutual Info I(X;Y): – bits
Spectral Efficiency: – bps/Hz
Shannon (1948): channel capacity C = B log₂(1+S/N) is the maximum error-free data rate.
Binary Symmetric Channel with crossover p: I(X;Y) = 1 - H(p) = 1 - (-p log p - (1-p) log(1-p)).
Water-filling (parallel Gaussian channels): allocate power P_i = (μ - N_i)⁺ where μ is chosen so ΣP_i = P_total.
Total capacity = Σ B log₂(1 + P_i/N_i). More power goes to less noisy channels.