Capacity Bounds for Relay Channels with Inter-symbol Interference and Colored Gaussian Noise

The capacity of a relay channel with inter-symbol interference (ISI) and additive colored Gaussian noise is examined under an input power constraint. Prior results are used to show that the capacity of this channel can be computed by examining the circular degraded relay channel in the limit of infinite block length. The current work provides single letter expressions for the achievable rates with decodeand- forward (DF) and compress-and-forward (CF) processing employed at the relay. Additionally, the cut-set bound for the relay channel is generalized for the ISI/colored Gaussian noise scenario. All results hinge on showing the optimality of the decomposition of the relay channel with ISI/colored Gaussian noise into an equivalent collection of coupled parallel, scalar, memoryless relay channels. The region of optimality of the DF and CF achievable rates are also discussed. Optimal power allocation strategies are also discussed for the two lower bounds and the cut-set upper bound. As the maximizing power allocations for DF and CF appear to be intractable, the desired cost functions are modified and then optimized. The resulting rates are illustrated through the computation of numerical examples.Comment: 42 pages, 9 figure

Compound Multiple Access Channel with Common Message and Intersymbol Interference

In this paper, we characterize the capacity region for the two-user linear Gaussian compound Multiple Access Channel with common message (MACC) and with intersymbol interference (ISI) under an input power constraint. The region is obtained by converting the channel to its equivalent memoryless one by defining an n-block memoryless circular Gaussian compound MACC model and applying the discrete Fourier transform (DFT) to decompose the n-block channel into a set of independent parallel channels whose capacities can be found easily. Indeed, the capacity region of the original Gaussian compound MACC equals that of the n-block circular Gaussian compound MACC in the limit of infinite block length. Then by using the obtained capacity region, we derive the capacity region of the strong interference channel with common message and ISI.Comment: 5 pages, 2 figures, This paper is presented at the International Symposium on Telecommunications (IST