Danilo Silva

Network codes resilient to jamming and eavesdropping

We consider the problem of communicating information over a network secretly and reliably in the presence of a hidden adversary who can eavesdrop and inject malicious errors. We provide polynomial-time distributed network codes that are information-theoretically rate-optimal for this scenario, improving on the rates achievable in prior work by Ngai Our main contribution shows that as long as the sum of the number of links the adversary can jam (denoted by ZO) and the number of links he can eavesdrop on (denoted by ZI) is less than the network capacity (denoted by C) (i.e., ), our codes can communicate (with vanishingly small error probability) a single bit correctly and without leaking any information to the adversary. We then use this scheme as a module to design codes that allow communication at the source rate of C- ZO when there are no security requirements, and codes that allow communication at the source rate of C- ZO- ZI while keeping the communicated message provably secret from the adversary. Interior nodes are oblivious to the presence of adversaries and perform random linear network coding; only the source and destination need to be tweaked. We also prove that the rate-region obtained is information-theoretically optimal. In proving our results, we correct an error in prior work by a subset of the authors in this paper.

Pyridinium and imidazolium 1,3,4-oxadiazole ionic liquid crystals: a thermal and photophysical systematic investigation

In this study we present the synthesis and complete structural characterization of twenty five 1,3,4-oxadiazole molecules (ionic and non-ionic) with some systematic structural variations, such as number of counterions, number of alkoxy chains, alkyl chain size, type of counterion and its position on the molecule. The thermal and photophysical properties for all compounds were investigated allowing a complete and interesting simultaneous study of the effect of structural changes on these properties. We show that every parameter studied affected both the thermal and photophysical properties. For these bent core molecules, the liquid crystalline behavior was observed only for compounds containing one counterion, SmA (monolayer or bilayer) being the predominant phase. The neutral (non-ionic) compounds and the imidazolium derivatives showed emission at around 360 nm and a high quantum yield, while most of the pyridinium derivatives showed emission at around 530 nm, a low quantum yield and a complex photophysical behavior. In all cases, the quantum yield for the different counterions follows the sequence ClO4− > BF4− > DS− > NO3− > Br−(I−).

Design criteria for lattice network coding

The compute-and-forward (C-F) relaying strategy proposed by Nazer and Gastpar is a powerful new approach to physical-layer network coding. Nazer-Gastpars construction of C-F codes relies on asymptotically-good lattice partitions that require the dimension of lattices to tend to infinity. Yet it remains unclear how such C-F codes can be constructed and analyzed under practical constraints. Motivated by this, an algebraic approach was taken to compute-and-forward, which provides a framework to study C-F codes constructed from finite-dimensional lattice partitions. Building on the algebraic framework, this paper moves one step further; it aims to derive the design criteria for the C-F codes constructed from finite-dimensional lattice partitions (also referred to as lattice network codes). It is shown that the receiver parameters {aℓ} and α should be chosen such that the quantity equation is minimized, and the lattice partition should be designed such that the minimum inter-coset distance is maximized. These design criteria imply that finding the optimal receiver parameters is equivalent to solving a shortest vector problem, and designing good lattice partitions can be reduced to the design of good linear codes for complex Construction A.

On the capacity of multiplicative finite-field matrix channels

This paper deals with the multiplicative finite-field matrix channel, a discrete memoryless channel whose input and output are matrices (over a finite field) related by a multiplicative transfer matrix. Our model allows this transfer matrix to have any rank, while assuming that all transfer matrices with the same rank are equiprobable. While in general the capacity cannot be obtained in closed form, we provide a simplification of the problem (from qnm to O(n) variables) which allows for easy numerical computation. A tight upper bound on the capacity is also derived, and for the special case of constant-rank input, we obtain an exact formula. Several existing results can be obtained as special cases of our approach. In addition, we prove that the well-known approach of treating inputs and outputs as subspaces is information-lossless even in this more general case.

Communication Over Finite-Chain-Ring Matrix Channels

Though network coding is traditionally performed over finite fields, recent work on nested-lattice-based network coding suggests that, by allowing network coding over certain finite rings, more efficient physical-layer network coding schemes can be constructed. This paper considers the problem of communication over a finite-ring matrix channel Y = AX + BE, where X is the channel input, Y is the channel output, E is random error, and A and B are random transfer matrices. Tight capacity results are obtained and simple polynomial-complexity capacity-achieving coding schemes are provided under the assumption that A is uniform over all full-rank matrices and BE is uniform over all rank-t matrices, extending the work of Silva, Kschischang, and Kötter (2010), who handled the case of finite fields. This extension is based on several new results, which may be of independent interest, that generalize concepts and methods from matrices over finite fields to matrices over finite chain rings.

On transform-domain error and erasure correction by Gabidulin codes

Gabidulin codes are the rank metric analogues of Reed–Solomon codes and have found many applications including network coding. In this paper, we propose a transform-domain algorithm correcting both errors and erasures with Gabidulin codes. Interleaving or the direct sum of Gabidulin codes allows both decreasing the redundancy and increasing the error correcting capability for network coding. We generalize the proposed decoding algorithm for interleaved Gabidulin codes. The transform-domain approach allows to simplify derivations and proofs and also simplifies finding the error vector after solving the key equation.

Blind compute-and-forward

Compute-and-forward (C&F) is a promising new approach to interference management, enjoying several advantages over other information-theoretic schemes. C&F usually requires channel state information (CSI) at the receivers so that an “optimal” scaling factor can be computed for the purposes of decoding. In this paper, a blind C&F scheme-i.e., one not requiring CSI-is developed. Rather than attempting to compute the optimal scaling factor, this new scheme seeks one or more “good” scalars, i.e., scalars that allow correct decoding despite possibly being suboptimal. The region of all such good scalars is characterized. To find a good scalar, a computationally efficient scheme is proposed which involves error-detection, a hierarchically organized list, as well as a use of the smoothing lemma from lattice theory. Simulation results show that our blind C&F scheme achieves-for a class of nested lattice codes-the same throughput as its CSI-enabled counterpart at the expense of, approximately, a two-fold increase in computational complexity in the high-throughput region. Moreover, our blind C&F scheme can be applied to multisource multirelay networks with a good performance/complexity tradeoff.

Lattice network coding over finite rings

Lattice network coding is recently proposed as a practical implementation of Nazer-Gastpars compute-and-forward relaying strategy. Previous investigation of lattice network coding is mainly over finite fields. In this paper, we extend lattice network coding from finite fields to finite rings. In addition to having its own theoretical interest, this extension provides an alternative viewpoint of Nazer-Gastpars relaying strategy and this extension expands the design space of lattice network codes. In particular, we show that this extension enables the use of complex Construction D to design lattice network codes, leading to potentially higher encoder rates.

Full-diversity network coding for two-user cooperative communications

In this work, network coding is employed to obtain maximum diversity order in a network where the users have independent information to transmit to a common base station. We elaborate on the recently proposed generalized dynamic network codes (GDNC), which can only achieve part of the maximum diversity order when the inter-user channels are subject to outages. In particular, by allowing the users to perform network decoding, in this paper we show that maximum diversity order can be achieved. Results are restricted to the 2-user case, although some discussion regarding the general case is provided.

Lattice network coding via signal codes

The construction of lattice network coding schemes through signal codes is revisited. First, it is shown that the nominal coding gain of signal codes can be carried over from AWGN channels to lattice network coding. This demonstrates the potential of using signal codes in lattice network coding. However, in order to achieve the promised performance gain, all the side information related to shaping should be transmitted to the receiver. Second, the problem of delivering the side information to the receiver is considered. In particular, a generic scheme is proposed which can be optimized by solving a lattice design problem. Finally, two solutions to the lattice design problem are presented and the simulation results suggest that—with a reasonable overhead—the promised performance gain can be achieved by using our proposed scheme.