Duality Bounds on the Cut-Off Rate with Applications to Ricean Fading

We propose a technique to derive upper bounds on Gallager's cost-constrained random coding exponent function. Applying this technique to the non-coherent peak-power or average-power limited discrete time memoryless Ricean fading channel, we obtain the high signal-to-noise ratio (SNR) expansion of this channel's cut-off rate. At high SNR the gap between channel capacity and the cut-off rate approaches a finite limit. This limit is approximately 0.26 nats per channel-use for zero specular component (Rayleigh) fading and approaches 0.39 nats per channel-use for very large specular components. We also compute the asymptotic cut-off rate of a Rayleigh fading channel when the receiver has access to some partial side information concerning the fading. It is demonstrated that the cut-off rate does not utilize the side information as efficiently as capacity, and that the high SNR gap between the two increases to infinity as the imperfect side information becomes more and more precise

Duality Bounds on the Cut-Off Rate with Applications to Ricean Fading

Abstract — We propose to use an expression of Csiszár & Körner’s to upper bound Gallager’s E0(, Q, r) function. We demonstrate this approach by computing the high SNR asymptotic expansion of the computational cut-off rate of the peak- or averagepower limited discrete-time memoryless Ricean fading channel with no — or with only partial — side information at the receiver. I. The Cut-Off Rate Consider a discrete-time memoryless channel over the input alphabet X and the output alphabet Y. For any input x ∈ X let w(·|x) be the density, with respect to some fixed measure µ on Y, of the output distribution that is induced by the input x ∈ X. Let g: X → [0, ∞) be some given cost function, and let the allowed cost Υ ≥ 0 be fixed. Following Gallager [1] we define for any probability measure Q on X, for any ≥ 0, and for any r ≥ 0 �� � �+1 1 r(g(x)−Υ) E0(, Q, r) = − log e w(y|x) 1+ dQ(x) dµ(y). We shall say that the cost constraint is active if sup Q:E Q[g(X)]≤