We introduce a novel mechanism, called timid/bold coding, by which feedback can be used to improve coding performance. For a certain class of DMCs, called compound-dispersion channels, we show that timid/bold coding allows for an improved second-order coding rate compared with coding without feedback. For DMCs that are not compound dispersion, we show that feedback does not improve the second-order coding rate. Thus we completely determine the class of DMCs for which feedback improves the second-order coding rate. An upper bound on the second-order coding rate is provided for compound-dispersion DMCs. We also show that feedback does not improve the second-order coding rate for very noisy DMCs. The main results are obtained by relating feedback codes to certain controlled diffusions.

The entropy of a quantum system is a measure of its randomness and is useful in quantifying entanglement. We study the problem of measuring the von Neumann and Rényi entropies of an unknown mixed quantum state given access to independent copies of the state. For Rényi entropy of integral order exceeding one, we determine the order-optimal copy complexity and show that it is strictly lower than the number of copies required to learn the underlying state. The main technical innovation is a concentration result for certain polynomials that arise in the Kerov algebra of Young diagrams, which is proven using the cycle structure of compositions of certain types of permutations. For von Neumann entropy and Rényi entropy of non-integral orders, we provide upper and lower bounds on the sample complexity of the Empirical Young Diagram (EYD) algorithm, which is the analogue of the empirical plug-in estimator in classical estimation.

We introduce a new distortion measure for point processes called functional-covering distortion. It is inspired by intensity theory and is related to both the covering of point processes and the logarithmic-loss distortion. We obtain the distortion-rate function with feedforward under this distortion measure for a large class of point processes. For Poisson processes, we characterize the rate-distortion region for a two-encoder CEO problem and show that feedforward does not improve this region.

We study two-receiver Poisson channels using tools derived from stochastic calculus. We obtain a general formula for the mutual information over the Poisson channel that allows for conditioning and the use of auxiliary random variables. We then use this formula to compute necessary and sufficient conditions under which one Poisson channel is less noisy and/or more capable than another, which turn out to be distinct from the conditions under which this ordering holds for the discretized versions of the channels. We also use a general formula to determine the capacity region of the more capable Poisson broadcast channel with independent message sets, the more capable Poisson wiretap channel, and the general two-decoder Poisson broadcast channel with degraded message sets.

It is shown that feedback does not improve the second-order coding rate for a class of discrete memoryless channels which complements the class of channels for which feedback is known to improve the second-order coding rate. A refined achievability scheme is presented for the second-order rate when feedback helps. Moreover, for such channels an upper bound is derived on the achievable rate with feedback utilizing a novel proof technique.

In-band full-duplex (FD) communication provides a promising alternative to half-duplex (HD) for wireless systems, due to increased spectral efficiency and capacity. In this paper, HD and FD radio implementations of two way, two hop, and two way two hop communication are compared in terms of degrees of freedom (DoF) under a realistic residual self-interference (SI) model. DoF analysis is carried out for each communication scenario for HD, antenna conserved (AC), and RF chain conserved (RC) FD radio implementations. The DoF analysis indicates that for the two way channel, the achievable AC FD with imperfect SI cancellation performs strictly below HD, and RC FD DoF tradeoff is superior when the SI can be sufficiently cancelled. For the two hop channel, FD is better when the relay has a large number of antennas and enough SI cancellation. For the two way two hop channel, when both nodes require similar throughput, the achievable DoF pairs for FD do not outperform HD. FD still can achieve better DoF pairs than HD, provided the relay has sufficient number of antennas and SI suppression.

We study two-receiver Poisson channels using tools derived from stochastic calculus. We compute necessary and sufficient conditions under which the continuous-time, continuous-space Poisson channel is less noisy and more capable, which turn out to be distinct from the conditions under which the “sampled” channel is less noisy and more capable. We also determine the capacity region of the more capable Poisson broadcast channel with independent message sets, the more capable Poisson wiretap channel, and the general two-decoder Poisson broadcast channel with degraded message sets.

In this paper, we analyze the coexistence of a primary and a secondary (cognitive) network when both networks use the IEEE 802.11 based distributed coordination function for medium access control. Specifically, we consider the problem of channel capture by a secondary network that uses spectrum sensing to determine the availability of the channel, and its impact on the primary throughput. We integrate the notion of transmission slots in Bianchi's Markov model with the physical time slots, to derive the transmission probability of the secondary network as a function of its scan duration. This is used to obtain analytical expressions for the throughput achievable by the primary and secondary networks. Our analysis considers both saturated and unsaturated networks. By performing a numerical search, the secondary network parameters are selected to maximize its throughput for a given level of protection of the primary network throughput. The theoretical expressions are validated using extensive simulations carried out in the Network Simulator 2. Our results provide critical insights into the performance and robustness of different schemes for medium access by the secondary network. In particular, we find that the channel captures by the secondary network does not significantly impact the primary throughput, and that simply increasing the secondary contention window size is only marginally inferior to silent-period based methods in terms of its throughput performance.