Time-Limited Codewords over Band-Limited Channels: Data Rates and the Dimension of the W-T Space.

We consider a communication system whereby -seconds time-limited codewords are transmitted over a -Hz band-limited additive white Gaussian noise channel. In the asymptotic regime as WT→∞, it is known that the maximal achievable rates with such a scheme converge to Shannon's capacity with the presence of 2WT degrees of freedom. In this work we study the degrees of freedom and the achievable information rates for finite values of WT.