Centralized and Cooperative Transmission of Secure Multiple Unicasts using Network Coding

We introduce a method for securely delivering a set of messages to a group of clients over a broadcast erasure channel where each client is interested in a distinct message. Each client is able to obtain its own message but not the others'. In the proposed method the messages are combined together using a special variant of random linear network coding. Each client is provided with a private set of decoding coefficients to decode its own message. Our method provides security for the transmission sessions against computational brute-force attacks and also weakly security in information theoretic sense. As the broadcast channel is assumed to be erroneous, the missing coded packets should be recovered in some way. We consider two different scenarios. In the first scenario the missing packets are retransmitted by the base station (centralized). In the second scenario the clients cooperate with each other by exchanging packets (decentralized). In both scenarios, network coding techniques are exploited to increase the total throughput. For the case of centralized retransmissions we provide an analytical approximation for the throughput performance of instantly decodable network coded (IDNC) retransmissions as well as numerical experiments. For the decentralized scenario, we propose a new IDNC based retransmission method where its performance is evaluated via simulations and analytical approximation. Application of this method is not limited to our special problem and can be generalized to a new class of problems introduced in this paper as the cooperative index coding problem

Weakly Secure MDS Codes for Simple Multiple Access Networks

We consider a simple multiple access network (SMAN), where $k$ sources of unit rates transmit their data to a common sink via $n$ relays. Each relay is connected to the sink and to certain sources. A coding scheme (for the relays) is weakly secure if a passive adversary who eavesdrops on less than $k$ relay-sink links cannot reconstruct the data from each source. We show that there exists a weakly secure maximum distance separable (MDS) coding scheme for the relays if and only if every subset of $\ell$ relays must be collectively connected to at least $\ell+1$ sources, for all $0 < \ell < k$. Moreover, we prove that this condition can be verified in polynomial time in $n$ and $k$. Finally, given a SMAN satisfying the aforementioned condition, we provide another polynomial time algorithm to trim the network until it has a sparsest set of source-relay links that still supports a weakly secure MDS coding scheme.Comment: Accepted at ISIT'1

On the Existence of MDS Codes Over Small Fields With Constrained Generator Matrices

We study the existence over small fields of Maximum Distance Separable (MDS) codes with generator matrices having specified supports (i.e. having specified locations of zero entries). This problem unifies and simplifies the problems posed in recent works of Yan and Sprintson (NetCod'13) on weakly secure cooperative data exchange, of Halbawi et al. (arxiv'13) on distributed Reed-Solomon codes for simple multiple access networks, and of Dau et al. (ISIT'13) on MDS codes with balanced and sparse generator matrices. We conjecture that there exist such $[n,k]_q$ MDS codes as long as $q \geq n + k - 1$, if the specified supports of the generator matrices satisfy the so-called MDS condition, which can be verified in polynomial time. We propose a combinatorial approach to tackle the conjecture, and prove that the conjecture holds for a special case when the sets of zero coordinates of rows of the generator matrix share with each other (pairwise) at most one common element. Based on our numerical result, the conjecture is also verified for all $k \leq 7$. Our approach is based on a novel generalization of the well-known Hall's marriage theorem, which allows (overlapping) multiple representatives instead of a single representative for each subset.Comment: 8 page

Cooperative Data Exchange with Unreliable Clients

Consider a set of clients in a broadcast network, each of which holds a subset of packets in the ground set X. In the (coded) cooperative data exchange problem, the clients need to recover all packets in X by exchanging coded packets over a lossless broadcast channel. Several previous works analyzed this problem under the assumption that each client initially holds a random subset of packets in X. In this paper we consider a generalization of this problem for settings in which an unknown (but of a certain size) subset of clients are unreliable and their packet transmissions are subject to arbitrary erasures. For the special case of one unreliable client, we derive a closed-form expression for the minimum number of transmissions required for each reliable client to obtain all packets held by other reliable clients (with probability approaching 1 as the number of packets tends to infinity). Furthermore, for the cases with more than one unreliable client, we provide an approximation solution in which the number of transmissions per packet is within an arbitrarily small additive factor from the value of the optimal solution.Comment: 8 pages; in Proc. 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton 2015

Coding with Constraints: Minimum Distance Bounds and Systematic Constructions

We examine an error-correcting coding framework in which each coded symbol is constrained to be a function of a fixed subset of the message symbols. With an eye toward distributed storage applications, we seek to design systematic codes with good minimum distance that can be decoded efficiently. On this note, we provide theoretical bounds on the minimum distance of such a code based on the coded symbol constraints. We refine these bounds in the case where we demand a systematic linear code. Finally, we provide conditions under which each of these bounds can be achieved by choosing our code to be a subcode of a Reed-Solomon code, allowing for efficient decoding. This problem has been considered in multisource multicast network error correction. The problem setup is also reminiscent of locally repairable codes.Comment: Submitted to ISIT 201

Algorithms on Wireless Network Coding

Network coding is a novel technique that has a significant potential to improve throughput, robustness and security of both wireless and wireline networks. With network coding the intermediate nodes in the network have the capability to combine multiple incoming packets and forward the resulting packets over their outgoing links. This technique has a significant advantage over traditional methods such as forwarding and duplication of packets. Recently, the network coding technique has attracted a significant interest from the research community. In this dissertation, we address a number of wireless network coding problems. In particular, our work focuses on the Cooperative Data Exchange (CDE), one of the central problems in wireless network coding. In Cooperative Data Exchange, a group of clients that have a prior side information about a set of packets use a shared broadcast channel to recover the missing packets from the set. We focus on different variations of the problem, including data exchange in the presence of passive and active adversaries, data exchange subject to deadlines, as well as serving clients of different priority classes. For each variation, we analyze the complexity of the problem and present exact or approximation algorithms for its solution. We show that this set of problem is very rich and has deep connections to different areas of coding theory, algebraic geometry, and information theory

Instantly Decodable Network Coding for Real-Time Scalable Video Broadcast over Wireless Networks

In this paper, we study a real-time scalable video broadcast over wireless networks in instantly decodable network coded (IDNC) systems. Such real-time scalable video has a hard deadline and imposes a decoding order on the video layers.We first derive the upper bound on the probability that the individual completion times of all receivers meet the deadline. Using this probability, we design two prioritized IDNC algorithms, namely the expanding window IDNC (EW-IDNC) algorithm and the non-overlapping window IDNC (NOW-IDNC) algorithm. These algorithms provide a high level of protection to the most important video layer before considering additional video layers in coding decisions. Moreover, in these algorithms, we select an appropriate packet combination over a given number of video layers so that these video layers are decoded by the maximum number of receivers before the deadline. We formulate this packet selection problem as a two-stage maximal clique selection problem over an IDNC graph. Simulation results over a real scalable video stream show that our proposed EW-IDNC and NOW-IDNC algorithms improve the received video quality compared to the existing IDNC algorithms

BAN-GZKP: Optimal Zero Knowledge Proof based Scheme for Wireless Body Area Networks

BANZKP is the best to date Zero Knowledge Proof (ZKP) based secure lightweight and energy efficient authentication scheme designed for Wireless Area Network (WBAN). It is vulnerable to several security attacks such as the replay attack, Distributed Denial-of-Service (DDoS) attacks at sink and redundancy information crack. However, BANZKP needs an end-to-end authentication which is not compliant with the human body postural mobility. We propose a new scheme BAN-GZKP. Our scheme improves both the security and postural mobility resilience of BANZKP. Moreover, BAN-GZKP uses only a three-phase authentication which is optimal in the class of ZKP protocols. To fix the security vulnerabilities of BANZKP, BAN-GZKP uses a novel random key allocation and a Hop-by-Hop authentication definition. We further prove the reliability of our scheme to various attacks including those to which BANZKP is vulnerable. Furthermore, via extensive simulations we prove that our scheme, BAN-GZKP, outperforms BANZKP in terms of reliability to human body postural mobility for various network parameters (end-to-end delay, number of packets exchanged in the network, number of transmissions). We compared both schemes using representative convergecast strategies with various transmission rates and human postural mobility. Finally, it is important to mention that BAN-GZKP has no additional cost compared to BANZKP in terms memory, computational complexity or energy consumption