Information transfer through disordered media by diffuse waves

We consider the information content h of a scalar multiple-scattered, diffuse wave field ψ(r) and the information capacity C of a communication channel that employs diffuse waves to transfer the information through a disordered medium. Both h and C are shown to be directly related to the mesoscopic correlations between the values of ψ(r) at different positions r in space, arising due to the coherent nature of the wave. For the particular case of a communication channel between two identical linear arrays of n1 equally spaced transmitters or receivers (receiver spacing $a),$ we show that the average capacity 〈C〉∝n and obtain explicit analytic expressions for $〈C〉/n$ in the limit of →n∞ and kl→∞, where k=2π/λ, λ is the wavelength, and l is the mean free path. Modification of the above results in the case of finite but large n and kl is discussed as well. If the signal to noise ratio $S/N$ exceeds some critical value (S/N)c, $〈C〉/n$ is a nonmonotonic function of a, exhibiting maxima at ka=mπ (m=1,2,). For smaller $S/N,$ ka=mπ correspond to local minima, while the absolute maximum of $〈C〉/n$ is reached at some ka~(S/N)1/2<π. We define the maximum average information capacity 〈C〉ₘₐₓ as $〈C〉$ maximized over the receiver spacing a and the optimal normalized receiver spacing (ka)ₒₚₜ as the spacing maximizing $〈C〉.$ Both 〈C〉ₘₐₓ/n and (ka)ₒₚₜ scale as (S/N)1/2 for S/N<(S/N)c, while (ka)ₒₚₜ=mπ and 〈C〉ₘₐₓ/n~log(S/N) for S/N>(S/N)c.