Abstract

Product codes are a class of codes which have generator matrices as the tensor product of the component codes and the codeword itself can be represented as an (m × n) array, where the component codes themselves are referred to as the row and column codes. Maximally recoverable product codes (MRPCs) are a class of codes which can recover from all information theoretically recoverable erasure patterns, given the a column and b row constraints imposed by the code. In this work, we derive puncturing and shortening properties of maximally recoverable product codes. We give a sufficient condition to characterize a certain subclass of erasure patterns as correctable and another necessary condition to characterize another subclass of erasure patterns as not correctable. In an earlier work, higher order MDS codes denoted by MDS(l) have been defined in terms of generic matrices and these codes have been shown to be constituent row codes for maximally recoverable product codes for the case of a = 1. We derive a certain inclusion-exclusion type principle for characterizing the dimension of intersection spaces of generic matrices. Applying this, we formally derive a relation between MDS(3) codes and points/lines of the associated projective space.

Abstract

In distributed storage systems, cooperative regener- ating codes tradeoff storage for repair bandwidth in the case of multiple node failures. In rack-aware distributed storage systems, there is no cost associated with transferring symbols within a rack. Hence, the repair bandwidth will only take into account cross-rack transfer. Rack-aware regenerating codes for the case of single node failures have been studied and their repair bandwidth tradeoff characterized. In this paper, we consider the frame- work of rack-aware cooperative regenerating codes for the case of multiple node failures where the node failures are uniformly distributed among a certain number of racks. We characterize the storage repair-bandwidth tradeoff as well as derive the minimum storage and minimum repair bandwidth points of the tradeoff. We also provide explicit constructions of minimum bandwidth rack-aware cooperative regenerating codes and minimum storage rack-aware cooperative regenerating codes for a large range of parameters. We also consider another extension of minimum stor- age cooperative regenerating codes, in which we design slightly sub-optimal cooperative regenerating codes with much lower sub- packetization. -MSR codes are a class of codes introduced to tradeoff sub-packetization level for a slight increase in the repair bandwidth for the case of single node failures. We introduce the framework of -MSCR codes which allow for a similar tradeoff for the case of multiple node failures. We present a construction of -MSCR codes, which can recover from two node failures, by concatenating a class of MSCR codes and scalar linear codes. We give a repair procedure to repair the -MSCR codes in the event of two node failures and calculate the repair bandwidth for the same. We characterize the increase in repair bandwidth incurred by the method in comparison with the optimal repair bandwidth. Finally, we show the subpacketization level of -MSCR codes scales logarithmically in the number of nodes.

Abstract

Reed-Solomon codes are polynomial evaluation codes and it has been shown that these can be efficiently repaired in the case of single node failures by considering the code symbols as vectors over a subfield and the helper nodes transfer multiple symbols over the subfield for repair. Tamo-Barg codes are a class of optimal LRCs which are also polynomial evaluation codes. These codes have Reed-Solomon codes as their local codes. In the case of single node failures, the repair takes place only within the local groups. In this paper, we address the question of whether the repair bandwidth within the local group can be further reduced by using the technique of Reed-Solomon repair. We give a construction based on cosets where the scheme requires lesser repair bandwidth than naive Reed-Solomon repair. We also give another construction based on optimal Reed-Solomon codes which achieve the cutset bound, where the Tamo-Barg codes are designed such that the local Reed-Solomon codes can be optimally repaired. We make the connection between these class of codes and the codes with local regeneration.

Abstract

The unmanned aerial vehicle (UAV) based communication is expected to play an important role in enabling a variety of applications in future cellular networks. However, because of the mobility of the UAVs, the communications links involving UAVs undergo large-scale temporal variations in the received signal quality, which may affect the quality-of-service of the underlying application. Therefore, it is crucial to characterize the time-varying process of signal quality observed by the UAVs. In this paper, we consider a scenario in which a cellular-connected UAV acts as a user equipment (UAV-UE), where the locations of base stations (BSs) follow a Poisson point process (PPP) and the UAV-UE is moving along a 3GPP-inspired straight-line trajectory. For this setting, we study the properties of the time-varying successful transmission process that is defined in terms of the time-varying signal-to-noise ratio (SNR) observed at the UAV. In particular, we show that this process is a wide sense stationary (WSS) process and derive its first- and second-order statistics. Finally, we establish an equivalence between the successful transmission processes observed by a UAV-UE served by terrestrial BSs and a terrestrial user served by UAV mounted BSs (UAV-BSs) each moving along an independent straight-line trajectory.

Abstract

This article proposes Convolutional Neural Network based Auto Encoder (CNN-AE) to predict location dependent rate and coverage probability of a network from its topology. We train the CNN utilising BS location data of India, Brazil, Germany and the USA and compare its performance with stochastic geometry (SG) based analytical models. In comparison to the best-fitted SGbased model, CNN-AE improves the coverage and rate prediction errors by a margin of as large as 40% and 25% respectively. As an application, we propose a low complexity, provably convergent algorithm that, using trained CNN-AE, can compute locations of new BSs that need to be deployed in a network in order to satisfy pre-defined spatially heterogeneous performance goals. Index Terms—Network Performance Prediction, Convolutional Neural Network, Stochastic Geometry, Network Design

Abstract

This paper considers beamforming for a reconfigurable intelligent surface (RIS)-aided multiple input single output (MISO) communication system in the presence of Rician multipath fading. Our aim is to jointly optimize the transmit beamformer and RIS phase shift matrix for maximizing the mean signal-to-noise (SNR) of the combined signal received over direct and indirect links. While numerical solutions are known for such optimization problems, this is the first paper to derive closedform expressions for the optimal beamformer and the phase shifter for a closely related problem. In particular, we maximize a carefully constructed lower bound of the mean SNR, which is more conducive to analytical treatment. Further, we show that effective channel gain under optimal beamforming follows Rice distribution. Next, we use these results to characterize a closedform expression for the outage probability under the proposed beamforming scheme, which is subsequently employed to derive an analytical expression for the ergodic capacity. Finally, we numerically demonstrate the efficacy of the proposed beamformer solution in comparison with the existing algorithmically obtained optimal solution for the exact mean SNR maximization. Index Terms—RIS, Optimal Beamforming, Rician Channel, Outage Analysis, Ergodic Capacity, and Maximum Mean SNR.

Abstract

This paper proposes a buffer-assisted amplify- and-forward (AF) unmanned aerial vehicle (UAV) relay for communication between two ground nodes without a direct link. These communications are essential in disaster rescue areas where fairness plays a significant role. To achieve fairness, we aim to maximize the minimum information rate. The traditional way of prefixed scheduling the time slots to transfer and receive at the UAV does not guarantee that the communication system uses high signal-to-noise ratio (SNR) communication links instead of low SNR links. Therefore, we choose to employ a buffer at the UAV to store the information and transfer it to the destination nodes in the high SNR links. The pairing of time slots is necessary here since we are using a buffer, and we do not know in which time slot data is transmitted to the destination node after it is received at the UAV. Consequently, we formulate a fairness maximization problem by jointly optimizing the trajectory and power control. Unfortunately, this formula- tion results in a non-convex problem. We propose a solution based on the principles of the minorize-maximize (MM) algorithm and linear programming relaxation techniques to solve the fairness problem and pairing of time slots. Numerical results demonstrate that the trajectory, power control, and paired slots favor the UAV and ground nodes to communicate in the high SNR channel links, thus maintaining fairness.

Abstract

State estimation in non-linear models is performed by tracking the posterior distribution recursively. A plethora of algorithms have been proposed for this task. Among them, the Gaussian particle filter uses a weighted set of particles to construct a Gaussian approximation to the posterior. In this paper, we propose to use invertible particle flow methods, derived under the Gaussian boundary conditions for a flow equation, to generate a proposal distribution close to the posterior. The resultant particle flow Gaussian particle filter (PFGPF) algorithm retains the asymptotic properties of Gaussian particle filters, with the potential for improved state estimation performance in highdimensional spaces. We compare the performance of PFGPF with the particle flow filters and particle flow particle filters in two challenging numerical simulation examples. Index Terms—Particle filters, particle flow filters, Gaussian particle filters, particle flow particle filters.

Abstract

Sparse Bayesian learning (SBL) has been successful in direction of arrival (DOA) estimation due to its robustness and high resolution using a few snapshots. Most wideband SBL algorithms make the simplifying assumption that distinct sources have the same power spectrum across frequency bands. However, this assumption may not be true in practice (for example speech signals). We analyze three wideband signal models and compare variants of wideband SBL (called SBL1, SBL2, and SBL3) with different assumptions on source signal power spectrum. The localization performance of SBL algorithms is compared with wideband processing of conventional beamforming (CBF) and multiple signal classification (MUSIC). The experimental validation is presented using simulated data and experimental LOCATA data. This comparative study shows that SBL3 which simultaneously enforces sparsity and models frequency-dependent signal spectrum shows superior performance in most scenarios. Index Terms—Compressive sensing, Sparse Bayesian learning, DOA estimation, MUSIC, CBF.

Abstract

Sound source localization is crucial in acoustic sensing and monitoring-related applications. In this paper, we do a comprehensive analysis of improvement in sound source localization by combining the direction of arrivals (DOAs) with their derivatives which quantify the changes in the positions of sources over time. This study uses the SALSA-Lite feature with a convolutional recurrent neural network (CRNN) model for predicting DOAs and their first-order derivatives. An update rule is introduced to combine the predicted DOAs with the estimated derivatives to obtain the final DOAs. The experimental validation is done using TAU-NIGENS Spatial Sound Events (TNSSE) 2021 dataset. We compare the performance of the networks predicting DOAs with derivative vs. the one predicting only the DOAs at low SNR levels. The results show that combining the derivatives with the DOAs improves the localization accuracy of moving sources. Index Terms— Deep learning, Microphone array, SALSALite, Sound event localization and detection (SELD).