Research

• Quantum error control codes: Block and Subsystem codes, Quantum convolutional codes
• Network security and protection against link failures and attacks using network coding.
• Network coding, capacity of network coding for wireless networks.
• Algorithms and applications of coding for distributed networked storage in wireless sensor networks
• Cryptography, network security, and quantum cryptography

Quantum Error Control Codes

• Title: On Quantum and Classical BCH Codes
  Abstract: Classical BCH codes that contain their (Euclidean or Hermitian) dual codes can be used to construct quantum stabilizer codes; this correspondence studies the properties of such codes. It is shown that a BCH code of length $n$ can contain its dual code only if its designed distance $\delta=O(\sqrt{n})$, and the converse is proved in the case of narrow-sense codes. Furthermore, the dimension of narrow-sense BCH codes with small design distance is completely determined, and -- consequently -- the bounds on their minimum distance are improved. These results make it possible to determine the parameters of quantum BCH codes in terms of their design parameters,
  Slides and PDF, PS, TEX.


• Title: Remarkable Degenerate Quantum Stabilizer Codes Derived from Duadic Codes
  Abstract: Good quantum codes, such as quantum MDS codes, are typically nondegenerate, meaning that errors of small weight require active error-correction, which is---paradoxically---itself prone to errors. Decoherence free subspaces, on the other hand, do not require active error correction, but perform poorly in terms of minimum distance. In this paper, examples of degenerate quantum codes are constructed that have better minimum distance than decoherence free subspaces and allow some errors of small weight that do not require active error correction. In particular, two new families of $[[n,1,\geq \sqrt{n}]]_q$ degenerate quantum codes are derived from classical duadic codes.
  Slides and PDF, PS, TEX.

Subsystem Codes

• Title: Subsystem Codes
  Abstract: We investigate various aspects of operator quantum error-correcting codes or, as we prefer to call them, subsystem codes. We give various methods to derive subsystem codes from classical codes. We give a proof for the existence of subsystem codes using a counting argument similar to the quantum Gilbert-Varshamov bound. We derive linear programming bounds and other upper bounds. We answer the question whether or not there exist $[[n,n-2d+2,r>0,d]]_q$ subsystem codes. Finally, we compare stabilizer and subsystem codes with respect to the required number of syndrome qudits,
  PDF, PS, TEX
• 
  Title: Subsystem Code Constructions
  Abstract: Subsystem codes are the most versatile class of quantum error-correcting codes known to date that combine the best features of all known passive and active error-control schemes. The subsystem code is a subspace of the quantum state space that is decomposed into a tensor product of two vector spaces: the subsystem and the co-subsystem. A generic method to derive subsystem codes from existing subsystem codes is given that allows one to trade the dimensions of subsystem and co-subsystem while maintaining or improving the minimum distance. As a consequence, it is shown that all pure MDS subsystem codes are derived from MDS stabilizer codes. The existence of numerous families of MDS subsystem codes is established. Propagation rules are derived that allow one to obtain longer and shorter subsystem codes from given subsystem codes. Furthermore, propagation rules are derived that allow one to construct a new subsystem code by combining two given subsystem codes [PDF, PS, TEX].

Quantum Convolutional Codes

• Title: Quantum Convolutional Codes Derived from Reed-Solomon and Reed-Muller Codes
  Abstract: Convolutional stabilizer codes promise to make quantum communication more reliable with attractive online encoding and decoding algorithms. This paper introduces a new approach to convolutional stabilizer codes based on direct limit constructions. Two families of quantum convolutional codes are derived from generalized Reed-Solomon codes and from Reed-Muller codes. A Singleton bound for pure convolutional stabilizer codes is given,
  PDF, PS, TEX

• Title: Quantum Convolutional BCH Codes
  Abstract: Quantum convolutional codes can be used to protect a sequence of qubits of arbitrary length against decoherence. We introduce two new families of quantum convolutional codes. Our construction is based on an algebraic method which allows to construct classical convolutional codes from block codes, in particular convolutional BCH codes. These codes have the property that they contain their Euclidean, respectively Hermitian, dual codes. Hence, they can be used to define quantum convolutional codes by the stabilizer code construction. We compute BCH-like bounds on the free distances which can be controlled as in the case of block codes, and establish that they have non-catastrophic encoders
  [PDF, PS, TEX].

Network security and protection against link failures and attacks using network coding

• Title: Network Coding-Based Protection Strategies Against Link and Node Failures Over Finite Fields
  Abstract: In this paper we develop network protection strategies against single and multiple link failures. In the proposed protection strategies, the source nodes apply network coding for their transmitted data to provide backup copy of the source data. Such techniques can be applied to optical, IP, and mesh networks.
  The capacity of the connection paths is reduced to carry the encoded data. The normalized capacity of the communication network is given by $(n-t)/n$ in case of online stream failure recovery, where t is the number of failures. We provide implementation aspects and study performance of the proposed strategies. We demonstrate an integer linear program to find disjoint paths from the sources to receivers and minimize the total cost of data protection. Finally, a comparison between these strategies and 1:N protection using extra path is demonstrated, PDF, PS, TEX.
  







• Title: Network Coding-based Protection Strategies Against a Single Link Failure in Optical Networks
  Abstract: In this paper we develop network protection strategies against a single link failure in optical networks. The motivation behind this work is the fact that %70 of all available links in an optical network suffers from a single link failure. In the proposed protection strategies, denoted NPS-I and NPS-II, we deploy network coding and reduced capacity on the working paths to provide a backup protection path that will carry encoded data from all sources. In addition, we provide implementation aspects and how to deploy the proposed strategies in case of an optical network with n disjoint working paths, PDF, PS, TEX.

Quantum Communication and Networks, Network Coding

• Title: Bounds on the Network Coding Capacity for Wireless Random Networks
  Abstract: Recently, it has been shown that the max flow capacity can be achieved in a multicast network using network coding. In this paper, we propose and analyze a more realistic model for wireless random networks. We prove that the capacity of network coding for this model is concentrated around the expected value of its minimum cut. Furthermore, we establish an upper bound for dependent wireless nodes using martingales. Our experiments show that our theoretical predications are well matched by simulation results, (PDF, PS, TEX).

• Title: Network Coding Capacity of Random Wireless Networks under a Signal-to-Interference-and-Noise Model
  Abstract: In this paper, we study network coding capacity for random wireless networks. Previous work on network coding capacity for wired and wireless networks have focused on the case where the capacities of links in the network are independent. In this paper, we consider a more realistic model, where wireless networks are modeled by random geometric graphs with interference and noise. In this model, the capacities of links are not independent. We consider two scenarios, single source multiple destinations and multiple sources multiple destinations. In the first scenario, employing coupling and martingale methods, we show that the network coding capacity for random wireless networks still exhibits a concentration behavior around the mean value of the minimum cut under some mild conditions. Furthermore, we establish upper and lower bounds on the network coding capacity for dependent and independent nodes. In the second one, we also show that the network coding capacity still follows a concentration behavior. Our simulation results confirm our theoretical predictions [PDF, PS, TEX].

Title: Algorithms and Applications of coding for distributed networked storage in wireless sensor networks

• Title: Fountain Codes Based Distributed Storage Algorithms for Large-scale Wireless Sensor Networks
  Abstract: We consider large-scale sensor networks with n nodes, out of which k are in possession, (e.g., have sensed or collected in some other way) k information packets. In the scenarios in which network nodes are vulnerable because of, for example, limited energy or a hostile environment, it is desirable to disseminate the acquired information throughout the network so that each of the n nodes stores one (possibly coded) packet and the original k source packets can be recovered later in a computationally simple way from any (1 + \epsilon)k nodes for some small \epsilon > 0. We developed two distributed algorithms for solving this problem based on simple random walks and Fountain codes. Unlike all previously developed schemes, our solution is truly distributed, that is, nodes do not know n, k or connectivity in the network, except in their own neighborhoods, and they do not maintain any routing tables. In the first algorithm, all the sensors have the knowledge of n and k. In the second algorithm, each sensor estimates these parameters through the random walk dissemination. We present analysis of the communication/transmission and encoding/decoding complexity of these two algorithms, and provide extensive simulation results as well [PDF, PS, TEX].



• Title:Decentralized Coding Algorithms for Distributed Storage in Wireless Sensor Networks
  Abstract:We study distributed storage problems for large-scale wireless sensor networks. We consider a wireless sensor network with $n$ sensors where $k$ sensors has acquired (sensed) independent information. Due to limited energy and hostile environment, sensors are vulnerable, and it is therefore desirable to disseminate the acquired information throughout the network so that each of the $n$ sensors stores one (possibly coded) packet and the original source information can be recovered later in a computationally simple way from any $k(1+\epsilon)$ of nodes for some small $\epsilon>0$. To accomplish this, we propose two distributed algorithms--LTCDS and RCDS--based on random walks and Fountain codes. Both algorithms employ simple random walks to disseminate source information, but use different coding schemes. The LTCDS and RCDS algorithms are based on LT codes and Raptor codes, respectively. Unlike all previously developed schemes, both algorithms are truly distributed. That is, except for their own neighborhoods, sensors do not need to know any global information, e.g., the number of sensors $n$, the number of sources $k$, or routing tables. We also present the analysis of the communication/transmission and encoding/decoding complexities of the proposed algorithms, as well as extensive simulation results [PDF, PS, TEX].

Cryptography and Network Security

• Title: A Multicast Security of Simple Network Management Protocol
  Abstract: SNMPv3, a simple network management protocol, is proved to be secure in unicasting communications (i.e., point-to-point or end-to-end transmission). Furthermore, a manager and an agent can authenticate and exchange secure messages between each other with no time delay or replay. In this paper, we extend the SNMPv3 unicasting security solution to be realiable for multicasting applications. In addition, we present a mutlicasting security framework for joining and leaving agents in a multicasting group.
  
  
• Title: A Light-Weight Encrypting For Real Time Video Transmission
  Abstract: In-network data aggregation is an essential technique in mission critical wireless sensor networks (WSNs) for achieving effective transmission and hence better power conservation. Common security protocols for aggregated WSNs are either hop-by-hop or end-to-end, each of which has its own encryption schemes considering different security primitives. End-to-end encrypted data aggregation protocols introduce maximum data secrecy with in-efficient data aggregation and more vulnerability to active attacks, while hop-by-hop data aggregation protocols introduce maximum data integrity with efficient data aggregation and more vulnerability to passive attacks.
  
  In this paper, we propose a secure aggregation protocol for aggregated WSNs deployed in hostile environments in which dual attack modes are present. Our proposed protocol is a blend of flexible data aggregation as in hop-by-hop protocols and optimal data confidentiality as in end-to-end protocols. Our protocol introduces an efficient $O(1)$ heuristic for checking data integrity along with cost-effective heuristic-based divide and conquer attestation process which is $O(\ln{n})$ in average -$O(n)$ in the worst scenario- for further verification of aggregated results.(PDF, PS, TEX)