Inspired by group testing algorithms and the coded computation paradigm, we propose and analyze a novel multiple access scheme for detecting active users in large-scale networks. The scheme consists of a simple randomized detection algorithm that uses computation coding as intermediate steps for computing logical disjunction functions over the multiple access channel (MAC). First we show that given an efficient MAC code for disjunction computation the algorithm requires @math decision steps for detecting @math active users out of @math users. Subsequently we present a simple suboptimal code for a class of MACs with arbitrarily varying sub-gaussian noise that uniformly requires @math channel uses for solving the activity detection problem. This shows that even in the presence of noise an efficient detection of active users is possible. Our approach reveals that the true crux of the matter lies in constructing efficient codes for computing disjunctions over a MAC.
The problem of user activity detection in large-scale networks has been already addressed in the context of compressive sensing in @cite_4 @cite_5 where the authors show the existence of a non-adaptive optimal activity detection strategy. The approach in @cite_4 @cite_5 relies heavily on methods from high dimensional probability and on methods for estimating certain partial sums affected by noise.
@cite_5 @cite_4
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This paper gives a precise characterization of the fundamental limits of adaptive sensing for diverse estimation and testing problems concerning sparse signals. We consider in particular the setting introduced in (IEEE Trans. Inform. Theory 57 (2011) 6222–6235) and show necessary conditions on the minimum signal magnitude for both detection and estimation: if x ? R^n is a sparse vector with s non-zero components then it can be reliably detected in noise provided the magnitude of the non-zero components exceeds v 2 s . Furthermore, the signal support can be exactly identified provided the minimum magnitude exceedsv 2 log s . Notably there is no dependence on n , the extrinsic signal dimension. These results show that the adaptive sensing methodologies proposed previously in the literature are essentially optimal, and cannot be substantially improved. In addition, these results provide further insights on the limits of adaptive compressive sensing. A possible future application in communications is the wireless uplink transmission in sensor networks. This application is mainly characterized by sporadic transmission over a random access channel. Since each sensor has a low activity probability, the signal for Multi-User Detection (MUD) is sparse. Compressive Sensing (CS) theory introduces detectors that are able to recover sparse signals reliably. When applied to MUD, CS detectors perform a joint detection of both data and user activity. This allows for less control signaling, since information about the activity state of each user no longer need to be signaled. Additionally, CS detectors are able to reliably detect sparse signals even in under-determined systems. In the context of transmission with Code Division Multiple Access (CDMA) this property can be exploited by reducing the length of spreading sequences, which increases the symbol-rate for a given bandwidth, and making the CDMA system overloaded. In this paper we introduce the application of greedy CS detection algorithms to detect CDMA spread multi-user data. This two-part paper considers an uplink massive device communication scenario in which a large number of devices are connected to a base station (BS), but user traffic is sporadic so that in any given coherence interval, only a subset of users is active. The objective is to quantify the cost of active user detection and channel estimation and to characterize the overall achievable rate of a grant-free two-phase access scheme in which device activity detection and channel estimation are performed jointly using pilot sequences in the first phase and data is transmitted in the second phase. In order to accommodate a large number of simultaneously transmitting devices, this paper studies an asymptotic regime where the BS is equipped with a massive number of antennas. The main contributions of Part I of this paper are as follows. First, we note that as a consequence of having a large pool of potentially active devices but limited coherence time, the pilot sequences cannot all be orthogonal. However, despite the nonorthogonality, this paper shows that in the asymptotic massive multiple-input multiple-output regime, both the missed device detection and the false alarm probabilities for activity detection can always be made to go to zero by utilizing compressed sensing techniques that exploit sparsity in the user activity pattern. Part II of this paper further characterizes the achievable rates using the proposed scheme and quantifies the cost of using nonorthogonal pilot sequences for channel estimation in achievable rates. In this paper, we address the challenging problem of effi- cient temporal activity detection in untrimmed long videos. While most recent work has focused and advanced the de- tection accuracy, the inference time can take seconds to minutes in processing one video, which is computationally prohibitive for many applications with tight runtime con- straints. This motivates our proposed budget-aware frame- work, which learns to perform activity detection by intel- ligently selecting a small subset of frames according to a specified time or computational budget. We formulate this problem as a Markov decision process, and adopt a recurrent network to model a policy for the frame selec- tion. To train the network, we employ a recurrent policy gradient approach to approximate the gradient of the non- decomposable and non-differentiable objective defined in our problem. In the extensive experiments on two bench- mark datasets, we achieve competitive detection accuracy, and more importantly, our approach is able to substantially reduce computational time and detect multiple activities in only 348ms for each untrimmed long video of THUMOS14 and ActivityNet.