Bounds on epsilon -rate for linear, time-invariant, multiinput/multioutput channels

Upper and lower bounds on the epsilon -rate of a linear, time-invariant multiple input multiple output channel are derived by using the same volume argument previously used by W.L. Root (1968) for single input single output channels. Because these bounds are not very tight, an approximation to the epsilon -rate is presented which lies between the upper and lower bounds, and can be used to compare epsilon -rates for different channels. The extension considered uses a result due to Lerer (1978) on the eigenvalue distribution of a convolution operator with a matrix kernel (impulse response). The present results are used to assess the increase in data rate attainable by designing input signals which exploit the multidimensional nature of the channel, relative to treating each constituent channel in isolation. Numerical results based upon a simple model for two coupled twisted-pair wires are presented.<
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