مرکز منطقه ای اطلاع رساني علوم و فناوري - Estimates of <img src="/images/tex/96.gif" alt="\\epsilon"> capacity for certain linear communication channels

Abstract :

The following simple abstract model for a class of communications problems is adopted: the set of possible transmitted signals $x$ is taken to be the unit ball in the $L_{2}$ space of functions defined on $[-T, T]$ (bounded energy); the transmitted signal is assumed to be operated on by a convolution operator $H$ ; and the final observed received signal $z$ is $z = Hx + n$ , where $n$ is an unknown error, caused either by additive noise, lack of complete knowledge of $H$ , or other causes, of norm less than some specified $\\epsilon$ (not necessarily small). The problem is to determine how many "distinguishable" signals can be sent, i.e., how many $x_{i}$ there are such that the $y_{i} = Hx_{i}$ are separated in norm by at least $\\epsilon$ . The chief results are asymptotic upper and lower bounds on the rate of error-free transmission possible, i.e., the ratio of the logarithm of the number of distinguishable signals to the time interval $2T$ as $T \\rightarrow \\infty$ . These estimates are in terms of the Fourier transform of the kernel of the convolution operator $H$ . The suitability of the model and the nature of the results are discussed.