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  1. We consider a scenario wherein two parties Alice and Bob are provided X1 and X2 – samples that are IID from a PMF P_X1X2. Alice and Bob can communicate to Charles over (noiseless) communication links of rate R1 and R2 respectively. Their goal is to enable Charles generate samples Y such that the triple (X1,X2,Y) has a PMF that is close, in total variation, to P_X1X2Y. In addition, the three parties may posses shared common randomness at rate C. We address the problem of characterizing the set of rate triples (R1, R2, C) for which the above goal can be accomplished. We provide a set of sufficient conditions, i.e., an achievable rate region for this three party setup. Our work also provides a complete characterization of a point-to-point setup wherein Bob is absent and Charles is provided with side-information. 
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  2. We consider the problem of decentralized sequential active hypothesis testing (DSAHT), where two transmitting agents, each possessing a private message, are actively helping a third agent–and each other–to learn the message pair over a discrete memoryless multiple access channel (DM-MAC). The third agent (receiver) observes the noisy channel output, which is also available to the transmitting agents via noiseless feedback. We formulate this problem as a decentralized dynamic team, show that optimal transmission policies have a time-invariant domain, and characterize the solution through a dynamic program. Several alternative formulations are discussed involving time-homogenous cost functions and/or variable-length codes, resulting in solutions described through fixed-point, Bellman-type equations. Subsequently, we make connections with the problem of simplifying the multi-letter capacity expressions for the noiseless feedback capacity of the DM-MAC. We show that restricting attention to distributions induced by optimal transmission schemes for the DSAHT problem, without loss of optimality, transforms the capacity expression, so that it can be thought of as the average reward received by an appropriately defined stochastic dynamical system with time-invariant state space. 
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  3. In this paper we study codes with sparse generator matrices. More specifically, codes with a certain constraint on the weight of all the columns in the generator matrix are considered. The end result is the following. For any binary-input memoryless symmetric (BMS) channel and any e>0.085, we show an explicit sequence of capacity-achieving codes with all the column wights of the generator matrix upper bounded by (log N) to the power (1+e), where N is the code block length. The constructions are based on polar codes. Applications to crowdsourcing are also shown. 
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  4. A new class of structured codes called quasi group codes (QGCs) is introduced. A QGC is a subset of a group code. In contrast with the group codes, QGCs are not closed under group addition. The parameters of the QGC can be chosen, such that the size of C C is equal to any number between C and C 2 . We analyze the performance of a specific class of QGCs. This class of QGCs is constructed by assigning single-letter distributions to the indices of the codewords in a group code. Then, the QGC is defined as the set of codewords whose index is in the typical set corresponding to these singleletter distributions. The asymptotic performance limits of this class of QGCs are characterized using single-letter information quantities. Corresponding covering and packing bounds are derived. It is shown that the point-to-point channel capacity and optimal rate-distortion function are achievable using QGCs. Coding strategies based on QGCs are introduced for three fundamental multi-terminal problems: the Körner-Marton problem for modulo prime-power sums, computation over the multiple access channel (MAC), and MAC with distributed states. For each problem, a single-letter achievable rate-region is derived. It is shown, through examples, that the coding strategies improve upon the previous strategies based on the unstructured codes, linear codes, and group codes. Index Terms— Quasi structure 
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  5. Crowdsourcing has been widely adopted to perform large projects suitable for human participation, in which tasks are usually distributed to workers. Many such projects involve classification/labeling certain collections of items through semisupervised clustering, in which queries on small subsets of the items are assigned to workers in the crowd. The answers are collected by a taskmaster and the goal is to fully recover the labels. This problem can be modeled as a sparsely encoded source coding problem, where each query answer, regarded as a code bit, is the XOR of a small number of labels, as source information bits. While the problem of designing compression/source coding schemes achieving Shannon’s optimal compression rate is very well-studied, a few have considered sparsely encoded schemes. In this paper we leverage the connections between this problem and well-studied codes with sparse representations for the channel coding problem to provide querying schemes with almost optimal number of queries, each of which involving only a constant number of labels. We also extend this scenario to the case where some workers can be unresponsive. For this case, we propose querying schemes where each query involves only log n items, where n is the total number of items to be labeled. Furthermore, we consider classification of two correlated labeling systems and provide two-stage querying schemes with almost optimal number of queries each involving a constant number of labels. 
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  6. We investigate faithful simulation of distributed quantum measurements as an extension of Winter's measurement compression theorem. We characterize a set of communication and common randomness rates needed to provide faithful simulation of distributed measurements. To achieve this, we introduce binning and mutual packing lemma for distributed quantum measurements. These techniques can be viewed as the quantum counterpart of their classical analogues. Finally, using these results, we develop a distributed quantum-to-classical rate distortion theory and characterize a rate region analogous to Berger-Tung's in terms of single-letter quantum mutual information quantities. 
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  7. In this paper, we investigate the necessity of finite blocklength codes in distributed transmission of independent message sets over channels with feedback. We provide two examples of three user interference channels with feedback where codes with asymptotically large effective lengths are sub-optimal. As a result, we conclude that coded transmission using finite effective length codes is necessary to achieve optimality. We argue that the sub-optimal performance of large effective length codes is due to their inefficiency in preserving the correlation between the inputs to the distributed terminals in the communication system. This correlation is made available by the presence of feedback at the terminals and is used as a means for coordination between them when using finite effective length coding strategies. 
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