Asymptotic Estimates in Information Theory with Non-Vanishing Error Probabilities

This monograph presents a unified treatment of single- and multi-user problems in Shannon's information theory where we depart from the requirement that the error probability decays asymptotically in the blocklength. Instead, the error probabilities for various problems are bounded above by a non-vanishing constant and the spotlight is shone on achievable coding rates as functions of the growing blocklengths. This represents the study of asymptotic estimates with non-vanishing error probabilities. In Part I, after reviewing the fundamentals of information theory, we discuss Strassen's seminal result for binary hypothesis testing where the type-I error probability is non-vanishing and the rate of decay of the type-II error probability with growing number of independent observations is characterized. In Part II, we use this basic hypothesis testing result to develop second- and sometimes, even third-order asymptotic expansions for point-to-point communication. Finally in Part III, we consider network information theory problems for which the second-order asymptotics are known. These problems include some classes of channels with random state, the multiple-encoder distributed lossless source coding (Slepian-Wolf) problem and special cases of the Gaussian interference and multiple-access channels. Finally, we discuss avenues for further research.Comment: Further comments welcom

Writing on Dirty Paper with Resizing and its Application to Quasi-Static Fading Broadcast Channels

This paper studies a variant of the classical problem of ``writing on dirty paper'' in which the sum of the input and the interference, or dirt, is multiplied by a random variable that models resizing, known to the decoder but not to the encoder. The achievable rate of Costa's dirty paper coding (DPC) scheme is calculated and compared to the case of the decoder's also knowing the dirt. In the ergodic case, the corresponding rate loss vanishes asymptotically in the limits of both high and low signal-to-noise ratio (SNR), and is small at all finite SNR for typical distributions like Rayleigh, Rician, and Nakagami. In the quasi-static case, the DPC scheme is lossless at all SNR in terms of outage probability. Quasi-static fading broadcast channels (BC) without transmit channel state information (CSI) are investigated as an application of the robustness properties. It is shown that the DPC scheme leads to an outage achievable rate region that strictly dominates that of time division.Comment: To appear in IEEE International Symposium on Information Theory 200

Fundamental limits of many-user MAC with finite payloads and fading

Consider a (multiple-access) wireless communication system where users are connected to a unique base station over a shared-spectrum radio links. Each user has a fixed number $k$ of bits to send to the base station, and his signal gets attenuated by a random channel gain (quasi-static fading). In this paper we consider the many-user asymptotics of Chen-Chen-Guo'2017, where the number of users grows linearly with the blocklength. In addition, we adopt a per-user probability of error criterion of Polyanskiy'2017 (as opposed to classical joint-error probability criterion). Under these two settings we derive bounds on the optimal required energy-per-bit for reliable multi-access communication. We confirm the curious behaviour (previously observed for non-fading MAC) of the possibility of perfect multi-user interference cancellation for user densities below a critical threshold. Further we demonstrate the suboptimality of standard solutions such as orthogonalization (i.e., TDMA/FDMA) and treating interference as noise (i.e. pseudo-random CDMA without multi-user detection).Comment: 38 pages, conference version accepted to IEEE ISIT 201

Short-packet Transmission via Variable-Length Codes in the Presence of Noisy Stop Feedback

We present an upper bound on the error probability achievable using variable-length stop feedback codes, for a fixed size of the information payload and a given constraint on the maximum latency and the average service time. Differently from the bound proposed in Polyanskiy et al. (2011), which pertains to the scenario in which the stop signal is sent over a noiseless feedback channel, our bound applies to the practically relevant setup in which the feedback link is noisy. By numerically evaluating our bound, we illustrate that, for fixed latency and reliability constraints, noise in the feedback link can cause a significant increase in the minimum average service time, to the extent that fixed-length codes without feedback may be preferable in some scenarios.Comment: Submitted to a Transactions on Wireless Communication

Second-Order Coding Rates for Channels with State

We study the performance limits of state-dependent discrete memoryless channels with a discrete state available at both the encoder and the decoder. We establish the epsilon-capacity as well as necessary and sufficient conditions for the strong converse property for such channels when the sequence of channel states is not necessarily stationary, memoryless or ergodic. We then seek a finer characterization of these capacities in terms of second-order coding rates. The general results are supplemented by several examples including i.i.d. and Markov states and mixed channels