Exact Moderate Deviation Asymptotics in Streaming Data Transmission

In this paper, a streaming transmission setup is considered where an encoder observes a new message in the beginning of each block and a decoder sequentially decodes each message after a delay of $T$ blocks. In this streaming setup, the fundamental interplay between the coding rate, the error probability, and the blocklength in the moderate deviations regime is studied. For output symmetric channels, the moderate deviations constant is shown to improve over the block coding or non-streaming setup by exactly a factor of $T$ for a certain range of moderate deviations scalings. For the converse proof, a more powerful decoder to which some extra information is fedforward is assumed. The error probability is bounded first for an auxiliary channel and this result is translated back to the original channel by using a newly developed change-of-measure lemma, where the speed of decay of the remainder term in the exponent is carefully characterized. For the achievability proof, a known coding technique that involves a joint encoding and decoding of fresh and past messages is applied with some manipulations in the error analysis.Comment: 23 pages, 1 figure, 1 table, Submitted to IEEE Transactions on Information Theor

Cramer type moderate deviations for random fields and mutual information estimation for mixed-pair random variables

In this dissertation we first study Cramer type moderate deviation for partial sums of random fields by applying the conjugate method. In 1938 Cramer published his results on large deviations of sums of i.i.d. random variables after which a lot of research has been done on establishing Cramer type moderate and large deviation theorems for different types of random variables and for various statistics. In particular results have been obtained for independent non-identically distributed random variables for the sum of independent random to estimate the mutual information between two random variables. The estimates enjoy a central limit theorem under some regular conditions on the distributions. The theoretical results are demonstrated by simulation study. variables with p-th moment (p \u3e 2) and for different types of dependent random variables. In this work we establish Cramer type exact moderate deviation theorem for random fields. We then show that obtained results are applicable to the partial sums of linear random fields with short or long memory and to non-parametric regression with random field errors. We also show that the result for linear random fields can be applied to calculate the tail probability of partial sums of various models such as the autoregressive fractionally integrated moving average FARIMA(p;\beta; q) processes. The results can also be used to approximate the risk measures such as quantiles and tail conditional expectations of time series or spacial random fields. We also study the mutual information estimation for mixed-pair random variables. One random variable is discrete and the other one is continuous. We develop a kernel metho