INFORMATION RATES BY OVERSAMPLING THE SIGN OF A BAND-LIMITED PROCESS

A sequence of binary (+/- 1) random variables is generated by sampling a hard-limited version of a bandlimited process at n times the Nyquis t rate. The information rate I carried by these binary samples is inve stigated. It is shown by constructing a specific nonstationary, bounde d, bandlimited process, the real zeros of which are independent and id entically distributed, isolated, and lying in different Nyquist interv als, that I = log2(n + 1) (bits per Nyquist interval) is achievable. A more complicated construction in which L distinct zeros are placed in consecutive L Nyquist intervals yields achievable rates that approach (for L --> infinity) I arbitrarily closely, where I = log2n + (n - 1) log2 (n / (n - 1)), n greater-than-or-equal-to 2 (and I = 1 for n = 1 and L = 1). By exploiting the constraints imposed on the autocorrelati on function of a stationary sign (bilevel) process with a given averag e transition rate, the latter expression is shown also to yield an upp er bound on the achievable values of I. The logarithmic behavior with n(n much-less-than 1) is due to the high correlation between the overs ampled binary samples, and it is established that this trend is also a chievable with stationary sign processes. This model may be used to ga in insight into the effect of finite resolution on the information (in Shannon's sense) conveyed by the sign of a bandlimited process, and a lso to assess the limiting performance of certain oversampling-based c ommunication systems.