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Register a new userAn Information Theoretic Point of View to Contention Resolution
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Added by
Venkatesh Ramaiyan
Publication date
2013
fields
Informatics Engineering
and research's language is
English
Authors
Venkatesh Ramaiyan
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We consider a slotted wireless network in an infrastructure setup with a base station (or an access point) and N users. The wireless channel gain between the base station and the users is assumed to be i.i.d., and the base station seeks to schedule the user with the highest channel gain in every slot (opportunistic scheduling). We assume that the identity of the user with the highest channel gain is resolved using a series of contention slots and with feedback from the base station. In this setup, we formulate the contention resolution problem for opportunistic scheduling as identifying a random threshold (channel gain) that separates the best channel from the other samples. We show that the average delay to resolve contention is related to the entropy of the random threshold. We illustrate our formulation by studying the opportunistic splitting algorithm (OSA) for i.i.d. wireless channel [9]. We note that the thresholds of OSA correspond to a maximal probability allocation scheme. We conjecture that maximal probability allocation is an entropy minimizing strategy and a delay minimizing strategy for i.i.d. wireless channel. Finally, we discuss the applicability of this framework for few other network scenarios.
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Given a probability measure $mu$ over ${mathbb R}^n$, it is often useful to approximate it by the convex combination of a small number of probability measures, such that each component is close to a product measure. Recently, Ronen Eldan used a stochastic localization argument to prove a general decomposition result of this type. In Eldans theorem, the `number of components is characterized by the entropy of the mixture, and `closeness to product is characterized by the covariance matrix of each component. We present an elementary proof of Eldans theorem which makes use of an information theory (or estimation theory) interpretation. The proof is analogous to the one of an earlier decomposition result known as the `pinning lemma.
A key practical constraint on the design of Hybrid automatic repeat request (HARQ) schemes is the size of the on-chip buffer that is available at the receiver to store previously received packets. In fact, in modern wireless standards such as LTE and LTE-A, the HARQ buffer size is one of the main drivers of the modem area and power consumption. This has recently highlighted the importance of HARQ buffer management, that is, of the use of buffer-aware transmission schemes and of advanced compression policies for the storage of received data. This work investigates HARQ buffer management by leveraging information-theoretic achievability arguments based on random coding. Specifically, standard HARQ schemes, namely Type-I, Chase Combining and Incremental Redundancy, are first studied under the assumption of a finite-capacity HARQ buffer by considering both coded modulation, via Gaussian signaling, and Bit Interleaved Coded Modulation (BICM). The analysis sheds light on the impact of different compression strategies, namely the conventional compression log-likelihood ratios and the direct digitization of baseband signals, on the throughput. Then, coding strategies based on layered modulation and optimized coding blocklength are investigated, highlighting the benefits of HARQ buffer-aware transmission schemes. The optimization of baseband compression for multiple-antenna links is also studied, demonstrating the optimality of a transform coding approach.
It is commonly believed that the hidden layers of deep neural networks (DNNs) attempt to extract informative features for learning tasks. In this paper, we formalize this intuition by showing that the features extracted by DNN coincide with the result of an optimization problem, which we call the `universal feature selection problem, in a local analysis regime. We interpret the weights training in DNN as the projection of feature functions between feature spaces, specified by the network structure. Our formulation has direct operational meaning in terms of the performance for inference tasks, and gives interpretations to the internal computation results of DNNs. Results of numerical experiments are provided to support the analysis.
We summarize recent contributions in the broad area of age of information (AoI). In particular, we describe the current state of the art in the design and optimization of low-latency cyberphysical systems and applications in which sources send time-stamped status updates to interested recipients. These applications desire status updates at the recipients to be as timely as possible; however, this is typically constrained by limited system resources. We describe AoI timeliness metrics and present general methods of AoI evaluation analysis that are applicable to a wide variety of sources and systems. Starting from elementary single-server queues, we apply these AoI methods to a range of increasingly complex systems, including energy harvesting sensors transmitting over noisy channels, parallel server systems, queueing networks, and various single-hop and multi-hop wireless networks. We also explore how update age is related to MMSE methods of sampling, estimation and control of stochastic processes. The paper concludes with a review of efforts to employ age optimization in cyberphysical applications.
We generalize a result by Carlen and Cordero-Erausquin on the equivalence between the Brascamp-Lieb inequality and the subadditivity of relative entropy by allowing for random transformations (a broadcast channel). This leads to a unified perspective on several functional inequalities that have been gaining popularity in the context of proving impossibility results. We demonstrate that the information theoretic dual of the Brascamp-Lieb inequality is a convenient setting for proving properties such as data processing, tensorization, convexity and Gaussian optimality. Consequences of the latter include an extension of the Brascamp-Lieb inequality allowing for Gaussian random transformations, the determination of the multivariate Wyner common information for Gaussian sources, and a multivariate version of Nelsons hypercontractivity theorem. Finally we present an information theoretic characterization of a reverse Brascamp-Lieb inequality involving a random transformation (a multiple access channel).
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