Universal secure rank-metric coding schemes with optimal communication overheads

We study the problem of reducing the communication overhead from a noisy wire-tap channel or storage system where data is encoded as a matrix, when more columns (or their linear combinations) are available. We present its applications to reducing communication overheads in universal secure linear network coding and secure distributed storage with crisscross errors and erasures and in the presence of a wire-tapper. Our main contribution is a method to transform coding schemes based on linear rank-metric codes, with certain properties, to schemes with lower communication overheads. By applying this method to pairs of Gabidulin codes, we obtain coding schemes with optimal information rate with respect to their security and rank error correction capability, and with universally optimal communication overheads, when $n \leq m$, being $n$ and $m$ the number of columns and number of rows, respectively. Moreover, our method can be applied to other families of maximum rank distance codes when $n > m$. The downside of the method is generally expanding the packet length, but some practical instances come at no cost.Comment: 21 pages, LaTeX; parts of this paper have been accepted for presentation at the IEEE International Symposium on Information Theory, Aachen, Germany, June 201

Coding for the Clouds: Coding Techniques for Enabling Security, Locality, and Availability in Distributed Storage Systems

Cloud systems have become the backbone of many applications such as multimedia streaming, e-commerce, and cluster computing. At the foundation of any cloud architecture lies a large-scale, distributed, data storage system. To accommodate the massive amount of data being stored on the cloud, these distributed storage systems (DSS) have been scaled to contain hundreds to thousands of nodes that are connected through a networking infrastructure. Such data-centers are usually built out of commodity components, which make failures the norm rather than the exception. In order to combat node failures, data is typically stored in a redundant fashion. Due to the exponential data growth rate, many DSS are beginning to resort to error control coding over conventional replication methods, as coding offers high storage space efficiency. This paradigm shift from replication to coding, along with the need to guarantee reliability, efficiency, and security in DSS, has created a new set of challenges and opportunities, opening up a new area of research. This thesis addresses several of these challenges and opportunities by broadly making the following contributions. (i) We design practically amenable, low-complexity coding schemes that guarantee security of cloud systems, ensure quick recovery from failures, and provide high availability for retrieving partial information; and (ii) We analyze fundamental performance limits and optimal trade-offs between the key performance metrics of these coding schemes. More specifically, we first consider the problem of achieving information-theoretic security in DSS against an eavesdropper that can observe a limited number of nodes. We present a framework that enables design of secure repair-efficient codes through a joint construction of inner and outer codes. Then, we consider a practically appealing notion of weakly secure coding, and construct coset codes that can weakly secure a wide class of regenerating codes that reduce the amount of data downloaded during node repair. Second, we consider the problem of meeting repair locality constraints, which specify the number of nodes participating in the repair process. We propose a notion of unequal locality, which enables different locality values for different nodes, ensuring quick recovery for nodes storing important data. We establish tight upper bounds on the minimum distance of linear codes with unequal locality, and present optimal code constructions. Next, we extend the notion of locality from the Hamming metric to the rank and subspace metrics, with the goal of designing codes for efficient data recovery from special types of correlated failures in DSS.We construct a family of locally recoverable rank-metric codes with optimal data recovery properties. Finally, we consider the problem of providing high availability, which is ensured by enabling node repair from multiple disjoint subsets of nodes of small size. We study codes with availability from a queuing-theoretical perspective by analyzing the average time necessary to download a block of data under the Poisson request arrival model when each node takes a random amount of time to fetch its contents. We compare the delay performance of the availability codes with several alternatives such as conventional erasure codes and replication schemes

Differentially Private Secure Multiplication: Hiding Information in the Rubble of Noise

We consider the problem of private distributed multi-party multiplication. It is well-established that Shamir secret-sharing coding strategies can enable perfect information-theoretic privacy in distributed computation via the celebrated algorithm of Ben Or, Goldwasser and Wigderson (the "BGW algorithm"). However, perfect privacy and accuracy require an honest majority, that is, $N \geq 2t+1$ compute nodes are required to ensure privacy against any $t$ colluding adversarial nodes. By allowing for some controlled amount of information leakage and approximate multiplication instead of exact multiplication, we study coding schemes for the setting where the number of honest nodes can be a minority, that is $N< 2t+1.$ We develop a tight characterization privacy-accuracy trade-off for cases where $N < 2t+1$ by measuring information leakage using {differential} privacy instead of perfect privacy, and using the mean squared error metric for accuracy. A novel technical aspect is an intricately layered noise distribution that merges ideas from differential privacy and Shamir secret-sharing at different layers.Comment: Extended version of papers presented in IEEE ISIT 2022, IEEE ISIT 2023 and TPDP 202

Zero-padding Network Coding and Compressed Sensing for Optimized Packets Transmission

Ubiquitous Internet of Things (IoT) is destined to connect everybody and everything on a never-before-seen scale. Such networks, however, have to tackle the inherent issues created by the presence of very heterogeneous data transmissions over the same shared network. This very diverse communication, in turn, produces network packets of various sizes ranging from very small sensory readings to comparatively humongous video frames. Such a massive amount of data itself, as in the case of sensory networks, is also continuously captured at varying rates and contributes to increasing the load on the network itself, which could hinder transmission efficiency. However, they also open up possibilities to exploit various correlations in the transmitted data due to their sheer number. Reductions based on this also enable the networks to keep up with the new wave of big data-driven communications by simply investing in the promotion of select techniques that efficiently utilize the resources of the communication systems. One of the solutions to tackle the erroneous transmission of data employs linear coding techniques, which are ill-equipped to handle the processing of packets with differing sizes. Random Linear Network Coding (RLNC), for instance, generates unreasonable amounts of padding overhead to compensate for the different message lengths, thereby suppressing the pervasive benefits of the coding itself. We propose a set of approaches that overcome such issues, while also reducing the decoding delays at the same time. Specifically, we introduce and elaborate on the concept of macro-symbols and the design of different coding schemes. Due to the heterogeneity of the packet sizes, our progressive shortening scheme is the first RLNC-based approach that generates and recodes unequal-sized coded packets. Another of our solutions is deterministic shifting that reduces the overall number of transmitted packets. Moreover, the RaSOR scheme employs coding using XORing operations on shifted packets, without the need for coding coefficients, thus favoring linear encoding and decoding complexities. Another facet of IoT applications can be found in sensory data known to be highly correlated, where compressed sensing is a potential approach to reduce the overall transmissions. In such scenarios, network coding can also help. Our proposed joint compressed sensing and real network coding design fully exploit the correlations in cluster-based wireless sensor networks, such as the ones advocated by Industry 4.0. This design focused on performing one-step decoding to reduce the computational complexities and delays of the reconstruction process at the receiver and investigates the effectiveness of combined compressed sensing and network coding

Coding for the Clouds: Coding Techniques for Enabling Security, Locality, and Availability in Distributed Storage Systems

Cloud systems have become the backbone of many applications such as multimedia streaming, e-commerce, and cluster computing. At the foundation of any cloud architecture lies a large-scale, distributed, data storage system. To accommodate the massive amount of data being stored on the cloud, these distributed storage systems (DSS) have been scaled to contain hundreds to thousands of nodes that are connected through a networking infrastructure. Such data-centers are usually built out of commodity components, which make failures the norm rather than the exception. In order to combat node failures, data is typically stored in a redundant fashion. Due to the exponential data growth rate, many DSS are beginning to resort to error control coding over conventional replication methods, as coding offers high storage space efficiency. This paradigm shift from replication to coding, along with the need to guarantee reliability, efficiency, and security in DSS, has created a new set of challenges and opportunities, opening up a new area of research. This thesis addresses several of these challenges and opportunities by broadly making the following contributions. (i) We design practically amenable, low-complexity coding schemes that guarantee security of cloud systems, ensure quick recovery from failures, and provide high availability for retrieving partial information; and (ii) We analyze fundamental performance limits and optimal trade-offs between the key performance metrics of these coding schemes. More specifically, we first consider the problem of achieving information-theoretic security in DSS against an eavesdropper that can observe a limited number of nodes. We present a framework that enables design of secure repair-efficient codes through a joint construction of inner and outer codes. Then, we consider a practically appealing notion of weakly secure coding, and construct coset codes that can weakly secure a wide class of regenerating codes that reduce the amount of data downloaded during node repair. Second, we consider the problem of meeting repair locality constraints, which specify the number of nodes participating in the repair process. We propose a notion of unequal locality, which enables different locality values for different nodes, ensuring quick recovery for nodes storing important data. We establish tight upper bounds on the minimum distance of linear codes with unequal locality, and present optimal code constructions. Next, we extend the notion of locality from the Hamming metric to the rank and subspace metrics, with the goal of designing codes for efficient data recovery from special types of correlated failures in DSS.We construct a family of locally recoverable rank-metric codes with optimal data recovery properties. Finally, we consider the problem of providing high availability, which is ensured by enabling node repair from multiple disjoint subsets of nodes of small size. We study codes with availability from a queuing-theoretical perspective by analyzing the average time necessary to download a block of data under the Poisson request arrival model when each node takes a random amount of time to fetch its contents. We compare the delay performance of the availability codes with several alternatives such as conventional erasure codes and replication schemes

Efficient radio resource management in next generation wireless networks

The current decade has witnessed a phenomenal growth in mobile wireless communication networks and subscribers. In 2015, mobile wireless devices and connections were reported to have grown to about 7.9 billion, exceeding human population. The explosive growth in mobile wireless communication network subscribers has created a huge demand for wireless network capacity, ubiquitous wireless network coverage, and enhanced Quality of Service (QoS). These demands have led to several challenging problems for wireless communication networks operators and designers. The Next Generation Wireless Networks (NGWNs) will support high mobility communications, such as communication in high-speed rails. Mobile users in such high mobility environment demand reliable QoS, however, such users are plagued with a poor signal-tonoise ratio, due to the high vehicular penetration loss, increased transmission outage and handover information overhead, leading to poor QoS provisioning for the networks' mobile users. Providing a reliable QoS for high mobility users remains one of the unique challenges for NGWNs. The increased wireless network capacity and coverage of NGWNs means that mobile communication users at the cell-edge should have enhanced network performance. However, due to path loss (path attenuation), interference, and radio background noise, mobile communication users at the cell-edge can experience relatively poor transmission channel qualities and subsequently forced to transmit at a low bit transmission rate, even when the wireless communication networks can support high bit transmission rate. Furthermore, the NGWNs are envisioned to be Heterogeneous Wireless Networks (HWNs). The NGWNs are going to be the integration platform of diverse homogeneous wireless communication networks for a convergent wireless communication network. The HWNs support single and multiple calls (group calls), simultaneously. Decision making is an integral core of radio resource management. One crucial decision making in HWNs is network selection. Network selection addresses the problem of how to select the best available access network for a given network user connection. For the integrated platform of HWNs to be truly seamless and efficient, a robust and stable wireless access network selection algorithm is needed. To meet these challenges for the different mobile wireless communication network users, the NGWNs will have to provide a great leap in wireless network capacity, coverage, QoS, and radio resource utilization. Moving wireless communication networks (mobile hotspots) have been proposed as a solution to providing reliable QoS to high mobility users. In this thesis, an Adaptive Thinning Mobility Aware (ATMA) Call Admission Control (CAC) algorithm for improving the QoS and radio resource utilization of the mobile hotspot networks, which are of critical importance for communicating nodes in moving wireless networks is proposed. The performance of proposed ATMA CAC scheme is investigated and compare it with the traditional CAC scheme. The ATMA scheme exploits the mobility events in the highspeed mobility communication environment and the calls (new and handoff calls) generation pattern to enhance the QoS (new call blocking and handoff call dropping probabilities) of the mobile users. The numbers of new and handoff calls in wireless communication networks are dynamic random processes that can be effectively modeled by the Continuous Furthermore, the NGWNs are envisioned to be Heterogeneous Wireless Networks (HWNs). The NGWNs are going to be the integration platform of diverse homogeneous wireless communication networks for a convergent wireless communication network. The HWNs support single and multiple calls (group calls), simultaneously. Decision making is an integral core of radio resource management. One crucial decision making in HWNs is network selection. Network selection addresses the problem of how to select the best available access network for a given network user connection. For the integrated platform of HWNs to be truly seamless and efficient, a robust and stable wireless access network selection algorithm is needed. To meet these challenges for the different mobile wireless communication network users, the NGWNs will have to provide a great leap in wireless network capacity, coverage, QoS, and radio resource utilization. Moving wireless communication networks (mobile hotspots) have been proposed as a solution to providing reliable QoS to high mobility users. In this thesis, an Adaptive Thinning Mobility Aware (ATMA) Call Admission Control (CAC) algorithm for improving the QoS and radio resource utilization of the mobile hotspot networks, which are of critical importance for communicating nodes in moving wireless networks is proposed