arXiv subjects

Salah A. Aly

Publications and source records attributed to Salah A. Aly.

At least 55 records · Page 3Linked to original sources

arXiv2008

Network Protection Codes Against Link Failures Using Network Coding

Protecting against link failures in communication networks is essential to increase robustness, accessibility, and reliability of data transmission. Recently, network coding has been proposed as a solution to provide agile and cost efficient network protection against link failures, which does not require data rerouting, or packet retransmission. To achieve this, separate paths have to be provisioned to carry encoded packets, hence requiring either the addition of extra links, or reserving some of the resources for this purpose. In this paper, we propose network protection codes against a single link failure using network coding, where a separate path using reserved links is not needed. In this case portions of the link capacities are used to carry the encoded packets. The scheme is extended to protect against multiple link failures and can be implemented at an overlay layer. Although this leads to reducing the network capacity, the network capacity reduction is asymptotically small in most cases of practical interest. We demonstrate that such network protection codes are equivalent to error correcting codes for erasure channels. Finally, we study the encoding and decoding operations of such codes over the binary field.

cs.IT↗

arXiv2008

Network Protection Codes: Providing Self-healing in Autonomic Networks Using Network Coding

Agile recovery from link failures in autonomic communication networks is essential to increase robustness, accessibility, and reliability of data transmission. However, this must be done with the least amount of protection resources, while using simple management plane functionality. Recently, network coding has been proposed as a solution to provide agile and cost efficient network self-healing against link failures, in a manner that does not require data rerouting, packet retransmission, or failure localization, hence leading to simple control and management planes. To achieve this, separate paths have to be provisioned to carry encoded packets, hence requiring either the addition of extra links, or reserving some of the resources for this purpose. In this paper we introduce autonomic self-healing strategies for autonomic networks in order to protect against link failures. The strategies are based on network coding and reduced capacity, which is a technique that we call network protection codes (NPC). In these strategies, an autonomic network is able to provide self-healing from various network failures affecting network operation. The techniques improve service and enhance reliability of autonomic communication. Network protection codes are extended to provide self-healing from multiple link failures in autonomic networks. We provide implementation aspects of the proposed strategies. We present bounds and network protection code constructions. Finally, we study the construction of such codes over the binary field. The paper also develops an Integer Linear Program formulation to evaluate the cost of provisioning connections using the proposed strategies.

cs.NI↗

arXiv2008

Protection Schemes for Two Link Failures in Optical Networks

In this paper we develop network protection schemes against two link failures in optical networks. The motivation behind this work is the fact that the majority of all available links in an optical network suffer from single and double link failures. In the proposed network protection schemes, NPS2-I and NPS2-II, we deploy network coding and reduced capacity on the working paths to provide backup protection paths. In addition, we demonstrate the encoding and decoding aspects of the proposed schemes.

cs.IT↗

arXiv2008

Constructions of Subsystem Codes over Finite Fields

Subsystem codes protect quantum information by encoding it in a tensor factor of a subspace of the physical state space. Subsystem codes generalize all major quantum error protection schemes, and therefore are especially versatile. This paper introduces numerous constructions of subsystem codes. It is shown how one can derive subsystem codes from classical cyclic codes. Methods to trade the dimensions of subsystem and co-subystem are introduced that maintain or improve the minimum distance. As a consequence, many optimal subsystem codes are obtained. Furthermore, it is shown how given subsystem codes can be extended, shortened, or combined to yield new subsystem codes. These subsystem code constructions are used to derive tables of upper and lower bounds on the subsystem code parameters.

quant-ph↗

arXiv2008

Network Coding-based Protection Strategies Against a Single Link Failure in Optical Networks

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.

cs.IT↗

arXiv2008

Network Coding Capacity of Random Wireless Networks under a SINR Model

Previous work on network coding capacity for random 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 modelled by random geometric graphs with interference and noise. In this model, the capacities of links are not independent. By employing coupling and martingale methods, we show that, under mild conditions, the network coding capacity for random wireless networks still exhibits a concentration behavior around the mean value of the minimum cut.

cs.IT↗

arXiv2008

Secure Hop-by-Hop Aggregation of End-to-End Concealed Data in Wireless Sensor Networks

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.

cs.CR↗

arXiv2008

Asymmetric and Symmetric Subsystem BCH Codes and Beyond

Recently, the theory of quantum error control codes has been extended to subsystem codes over symmetric and asymmetric quantum channels -- qubit-flip and phase-shift errors may have equal or different probabilities. Previous work in constructing quantum error control codes has focused on code constructions for symmetric quantum channels. In this paper, we develop a theory and establish the connection between asymmetric quantum codes and subsystem codes. We present families of subsystem and asymmetric quantum codes derived, once again, from classical BCH and RS codes over finite fields. Particularly, we derive an interesting asymmetric and symmetric subsystem codes based on classical BCH codes with parameters $[[n,k,r,d]]_q$, $[[n,k,r,d_z/d_x]]_q$ and $[[n,k',0,d_z/d_x]]_q$ for arbitrary values of code lengths and dimensions. We establish asymmetric Singleton and Hamming bounds on asymmetric quantum and subsystem code parameters; and derive optimal asymmetric MDS subsystem codes. Finally, our constructions are well explained by an illustrative example. This paper is written on the occasion of the 50th anniversary of the discovery of classical BCH codes and their quantum counterparts were derived nearly 10 years ago.

quant-ph↗

arXiv2008

Propagation Rules of Subsystem Codes

We demonstrate propagation rules of subsystem code constructions by extending, shortening and combining given subsystem codes. Given an $[[n,k,r,d]]_q$ subsystem code, we drive new subsystem codes with parameters $[[n+1,k,r,\geq d]]_q$, $[[n-1,k+1,r,\geq d-1]]_q$, $[[n,k-1,r+1,d]]_q$. The interested readers shall consult our companion papers for upper and lower bounds on subsystem codes parameters, and introduction, trading dimensions, families, and references on subsystem codes [1][2][3] and references therein.

quant-ph↗

arXiv2008

Families of LDPC Codes Derived from Nonprimitive BCH Codes and Cyclotomic Cosets

Low-density parity check (LDPC) codes are an important class of codes with many applications. Two algebraic methods for constructing regular LDPC codes are derived -- one based on nonprimitive narrow-sense BCH codes and the other directly based on cyclotomic cosets. The constructed codes have high rates and are free of cycles of length four; consequently, they can be decoded using standard iterative decoding algorithms. The exact dimension and bounds for the minimum distance and stopping distance are derived. These constructed codes can be used to derive quantum error-correcting codes.

cs.IT↗

arXiv2008

Subsystem Code Constructions

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.

quant-ph↗

arXiv2007

A Note on Quantum Hamming Bound

Proving the quantum Hamming bound for degenerate nonbinary stabilizer codes has been an open problem for a decade. In this note, I prove this bound for double error-correcting degenerate stabilizer codes. Also, I compute the maximum length of single and double error-correcting MDS stabilizer codes over finite fields.

quant-ph↗

arXiv2007

Bounds on the Network Coding Capacity for Wireless Random Networks

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 upper and lower bounds for wireless nodes using Chernoff bound. Our experiments show that our theoretical predictions are well matched by simulation results.

cs.IT↗

arXiv2007

Network Coding Capacity of Random Wireless Networks under a Signal-to-Interference-and-Noise Model

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.

cs.IT↗

arXiv2007

Quantum Convolutional BCH Codes

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 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 the codes have non-catastrophic encoders.

quant-ph↗

arXiv2007

Quantum Convolutional Codes Derived From Reed-Solomon and Reed-Muller Codes

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.

quant-ph↗

arXiv2007

Duadic Group Algebra Codes

Duadic group algebra codes are a generalization of quadratic residue codes. This paper settles an open problem raised by Zhu concerning the existence of duadic group algebra codes. These codes can be used to construct degenerate quantum stabilizer codes that have the nice feature that many errors of small weight do not need error correction; this fact is illustrated by an example.

cs.IT↗

arXiv2006

Subsystem Codes

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.

quant-ph↗