We study the rates of source coding a T-seconds finite duration piece from a W-Hz band-limited real white Gaussian process with the mean squared error as a distortion measure. First we derive a discrete representation by projecting the signal of interest on the set of prolate spheroidal wave functions. We derive next a lower bound and an upper bound for the smallest rate that guarantees a distortion level with a probability (1-\epsilon) and we numerically evaluate these bounds. We also show that the derived bounds are asymptotically tight where they converge to Shannon's formula.
This paper concerns the maximum coding rate at which a code of given blocklength can be transmitted with a given block-error probability over a non-coherent Rayleigh block-fading channel with multiple transmit and receive antennas (MIMO). In particular, a high-SNR normal approximation of the maximum coding rate is presented, which is proved to become accurate as the signal-to-noise ratio (SNR) and the number of coherence intervals L tend to infinity.
We study the problem of image registration in the finite-resolution regime and characterize the error probability of algorithms as a function of properties of the transformation and the image capture noise. Specifically, we define a channel- aware Feinstein decoder to obtain upper bounds on the minimum achievable error probability under finite resolution. We specifi- cally focus on the higher-order terms and use Berry-Esseen type CLTs to obtain a stronger characterization of the achievability condition for the problem. Then, we derive a strong type-counting result to characterize the performance of the MMI decoder in terms of the maximum likelihood decoder, in a simplified setting of the problem. We then describe how this analysis, when related to the results from the channel-aware context provide stronger characterization of the finite-sample performance of universal image registration.
In this work, we consider a Gaussian multiple access channel (GMAC) subject to block fading that is independent across users. We derive inner bounds on the capacity region for a given finite codeword length and non-vanishing average probability of error. We assume perfect channel state information (CSI) at the receiver (CSIR) and no CSI at the transmitters. The bounds are derived subject to a peak power constraint on the transmitted codewords. Our inner bounds are derived using Gaussian codebooks. These bounds characterize deviation from the ergodic capacity region upto second-order. Using numerical examples, we illustrate the back-off from the boundary of the ergodic capacity region.