During the COVID-19 pandemic the health authorities at airports and train stations try to screen and identify the travellers possibly exposed to the virus. However, many individuals avoid getting tested and hence may misreport their travel history. This is a challenge for the health authorities who wish to ascertain the truly susceptible cases in spite of this strategic misreporting. We investigate the problem of questioning travellers to classify them for further testing when the travellers are strategic or are unwilling to reveal their travel histories. We show there are fundamental limits to how many travel histories the health authorities can recover.

We introduce the problem of strategic communication and find achievable rates for this problem. The problem consists of a sender that observes a source and a receiver that would like to recover the source. The sender can send messages to the receiver over a noiseless medium whose input space is as large as the space of source signals. However, unlike standard communication, the sender is strategic. Depending on the source signal it receives, the sender may have an incentive, measured by a utility function, to misreport the signal, whereby, not all signals are necessarily recoverable at the receiver. The dilemma for the receiver lies in selecting the right signals to recover so that recovery happens with high probability. We establish achievable rates associated with these settings.

We study the setting of channel coding over a family of channels whose state is controlled by an adversarial jammer by viewing it as a zero-sum game between a finite blocklength encoder-decoder team, and the jammer. The encoder-decoder team choose stochastic encoding and decoding strategies to minimize the average probability of error in transmission, while the jammer chooses a distribution on the state-space to maximize this probability. The min-max value of the game is equivalent to channel coding for a compound channel - we call this the Shannon solution of the problem. The max-min value corresponds to finding a mixed channel with the largest value of the minimum achievable probability of error. When the min-max and max-min values are equal, the problem is said to admit a saddle-point or von Neumann solution. While a Shannon solution always exists, the communicating team's problem is nonconvex for finite blocklengths, whereby a von Neumann solution may not exist. Despite this, we show that the min-max and max-min values become equal asymptotically in the large blocklength limit, for all but finitely many rates. We explicitly characterize this limiting value as a function of the rate and obtain tight finite blocklength bounds on the min-max and max-min value. As a corollary we get an explicit expression for the ε -capacity of a compound channel under stochastic codes - the first such result, to the best of our knowledge. Our results demonstrate a deeper relation between the compound channel and mixed channel than was previously known. They also show that the conventional information-theoretic viewpoint, articulated via the Shannon solution, coincides asymptotically with the game-theoretic one articulated via the von Neumann solution. Key to our results is the derivation of new finite blocklength upper bounds on the min-max value of the game via a novel achievability scheme, and lower bounds on the max-min value obtained via the linear programming relaxation based approach we introduced in [2].

To address the demand of exponentially increasing end users, efficient use of limited spectrum is a necessity. For this, spectrum allocation among co-existing operators in licensed and unlicensed spectrum band is required to cater to the temporal and spatial traffic variations in the wireless network. In this paper, we consider multiple operator spectrum allocation problem via auctions. The classical Vickrey-Clarke-Groves (VCG) approach provides a strategy-proof and social welfare maximizing auction at the cost of high computational complexity which makes it intractable for practical implementation. We propose a sealed bid auction for spectrum allocation, which is computationally tractable and can hence be applied as per the dynamic load variations of the network. We show that the proposed algorithm is strategy-proof. Simulation results are presented to exhibit the performance comparison of the proposed algorithm and the VCG mechanism.

A new finite blocklength converse for the Slepian-Wolf coding problem, which significantly improves on the best-known converse due to Miyake and Kanaya, is presented. To obtain this converse, an extension of the linear programming (LP)-based framework for finite blocklength point-to-point coding problems is employed. However, a direct application of this framework demands a complicated analysis for the Slepian-Wolf problem. An analytically simpler approach is presented, wherein LP-based finite blocklength converses for this problem are synthesized from point-to-point lossless source coding problems with perfect side-information at the decoder. New finite blocklength converses for these point-to-point problems are derived by employing the LP-based framework, and the new converse for Slepian-Wolf coding is obtained by an appropriate combination of these converses.

We consider the problem of mean-square estimation of the state of a discrete time dynamical system having additive non-Gaussian noise. We assume that the noise has the structure that at each time instant, it is a projection of a fixed high-dimensional noise vector with a log-concave density. We derive conditions which guarantee that, as the dimension of this noise vector grows large, the optimal estimator of the problem with Gaussian noise becomes near-optimal for the problem with nonGaussian noise. The results are derived by first showing an asymptotic Gaussian lower bound on the minimum error which holds even for nonlinear systems. The bound is asymptotically tight for linear systems. For nonlinear systems, this bound is tight provided and the noise has a strongly log-concave density with some additional structure. These results imply that the estimate obtained by employing the Gaussian estimator on the non-Gaussian problem satisfies an approximate orthogonality principle, and the difference between this estimate and the optimal estimate vanishes strongly in L2. For linear systems with high-dimensional log-concave noise of this structure, we get that the Kalman filter serves as a near-optimal estimator. A key ingredient in the proofs is a recent central limit theorem of Eldan and Klartag. The minimum mean-square error is in general neither weakly upper semicontinuous nor weakly lower semicontinuous. Our results show that in the setting we consider, it is weakly continuous. We then consider mean-square estimation over a noisy network, where the problem is to jointly design strategies for sensing and estimation to minimize a composite quadratic cost. These problems do not have a static information structure, whereby the previously derived results do not apply. We consider two different cases-when the estimation part of the problem corresponds to estimating the original source sensed by the sensor, and when this part corresponds to the estimation of the action of the sensor. In the former case, we show that results analogous to the above continue to hold. The latter case corresponds to a variant of Witsenhausen's problem, wherein we show only partial results.

The linear programming (LP) based approach we introduced in [1] for finding finite blocklength converses for joint source-channel coding is extended to some network-like settings. Finite blocklength channel coding of compound and averaged channels under the maximum probability error criterion is considered. Through the LP approach new converses are obtained which imply a weak converse for both channels and a strong converse for the compound channel. The LP approach is also extended to the networked setting and a new finite blocklength converse for Slepian-Wolf coding which improves on the converse in Han [2, Lemma 7.2.2] is derived.

A linear programming (LP)-based framework is presented for obtaining converses for finite blocklength lossy joint source-channel coding problems. The framework applies for any loss criterion, generalizes certain previously known converses, and also extends to multi-terminal settings. The finite blocklength problem is posed equivalently as a nonconvex optimization problem and using a lift-and-project-like method, a close but tractable LP relaxation of this problem is derived. Lower bounds on the original problem are obtained by the construction of feasible points for the dual of the LP relaxation. A particular application of this approach leads to new converses, which recover and improve on the converses of Kostina and Verdú for finite blocklength lossy joint source-channel coding and lossy source coding. For finite blocklength channel coding, the LP relaxation recovers the converse of Polyanskiy, Poor and Verdú and leads to a new improvement on the converse of Wolfowitz, showing thereby that our LP relaxation is asymptotically tight with increasing blocklengths for channel coding, lossless source coding, and joint source-channel coding with the excess distortion probability as the loss criterion. Using a duality-based argument, a new converse is derived for finite blocklength joint source-channel coding for a class of source-channel pairs. Employing this converse, the LP relaxation is also shown to be tight for all blocklengths for the minimization of the expected average symbolwise Hamming distortion of a q-ary uniform source over a q-ary symmetric memoryless channel for any q ∈ N. The optimization formulation and the lift-and-project method are extended to networked settings and demonstrated by obtaining an improvement on a converse of Zhou et al. for the successive refinement problem for successively refinable source-distortion measure triplets.

We investigate deletion correcting codes and restricted composition codes in particular. Restricted composition codes generalize codes on permutations and multipermutations. We use graph theoretic methods to characterize codes, establish bounds on code size, and describe constructions. The substring partial order has a well-known property. For any string, the number of superstrings of a particular length depends only on the length of the original string. We generalize this property to take compositions into account. For any string, the number of superstrings of a particular composition depends only on the composition of the original string. We present a bijective proof of this fact. We apply this result to obtain a lower bound on the size of restricted composition codes. We obtain an upper bound by analyzing deletion errors when the composition of deleted symbols is restricted to a particular worst case composition. We construct binary restricted composition single-deletion correcting codes and show that they are asymptotically optimal and form an optimal coloring. There is a natural distance on compositions that provides a lower bound on deletion distance. Unrestricted deletion correcting codes can be constructed from the union of restricted composition codes as long as the set of compositions used themselves form a code. The nonbinary single-deletion correcting codes constructed by Tenengolts are a special case of our method.

We study asymmetric insertion and deletion errors in q-ary strings where a fixed symbol, say 0, is forbidden for deletion and insertion. This error generalizes the classical insertion/deletion error and models of restricted deletions, such as deletion of only 0's in run-length limited strings. We show that the size of an asymmetric insertion set is a constant for strings with fixed number of 0's, sizes of asymmetric deletion sets obey a monotonicity, and exponentially large codes exist. We show the latter by finding bounds and expressions for sizes of asymmetric insertion and deletion sets and nonasymptotic upper and lower bounds on code sizes.

Explicit nonasymptotic upper bounds on the sizes of multiple-deletion correcting codes are presented. In particular, the largest single-deletion correcting code for q-ary alphabet and string length is shown to be of size at most (qn-q)/{(q-1)(n-1)}. An improved bound on the asymptotic rate function is obtained as a corollary. Upper bounds are also derived on sizes of codes for a constrained source that does not necessarily comprise of all strings of a particular length, and this idea is demonstrated by application to sets of run-length limited strings. The problem of finding the largest deletion correcting code is modeled as a matching problem on a hypergraph. This problem is formulated as an integer linear program. The upper bound is obtained by the construction of a feasible point for the dual of the linear programming relaxation of this integer linear program. The nonasymptotic bounds derived imply the known asymptotic bounds of Levenshtein and Tenengolts and improve on known nonasymptotic bounds. Numerical results support the conjecture that in the binary case, the Varshamov-Tenengolts codes are the largest single-deletion correcting codes.

We take a graph theoretic view of deletion correcting codes. The problem of finding an n-bit s-deletion correcting code is equivalent to finding an independent set in a particular graph. We discuss the relationship between codes and colorings and demonstrate that the VT codes are optimal in a coloring sense. We describe a method of partitioning the set of bit strings by Hamming weight and finding codes within each partition. In the single deletion case, we find an optimal coloring of the constant Hamming weight induced subgraphs. We show that the resulting code is asymptotically optimal. We also prove a lower bound on size of codes constructed using these partitions for any number of deletions.