arXiv subjects

Emanuele Viterbo

Publications and source records attributed to Emanuele Viterbo.

At least 73 records · Page 4Linked to original sources

arXiv2017

Golden-Coded Index Coding

We study the problem of constructing good space-time codes for broadcasting $K$ independent messages over a MIMO network to $L$ users, where each user demands all the messages and already has a subset of messages as side information. As a first attempt, we consider the $2\times 2$ case and propose golden-coded index coding by partitioning the golden codes into $K$ subcodes, one for each message. The proposed scheme is shown to have the property that for any side information configuration, the minimum determinant of the code increases exponentially with the amount of information contained in the side information.

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arXiv2017

Integer-Forcing Linear Receivers: A Design Criterion for Full-Diversity STBCs

In multiple-input multiple-output (MIMO) fading channels, the design criterion for full-diversity space-time block codes (STBCs) is primarily determined by the decoding method at the receiver. Although constructions of STBCs have predominantly matched the maximum-likelihood (ML) decoder, design criteria and constructions of full-diversity STBCs have also been reported for low-complexity linear receivers. A new receiver architecture called Integer-Forcing (IF) linear receiver has been proposed to MIMO channels by Zhan et al. which showed promising results for the high-rate V-BLAST encoding scheme. In this work we address the design of full-diversity STBCs for IF linear receivers. We derive an upper bound on the probability of decoding error, and show that STBCs that satisfy the non-vanishing singular value (NVS) property provide full-diversity for the IF receiver. We also present simulation results to demonstrate that linear designs with NVS property provide full diversity for IF receiver. As a special case of our analysis on STBCs, we present an upper bound on the error probability for the V-BLAST architecture presented by Zhan \emph{et al.}, and demonstrate that the IF linear receivers provide full receive diversity. Our results supplement the existing outage probability based results for the IF receiver.

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arXiv2016

Line of Sight 2 x nr MIMO with Random Antenna Orientations

Line-of-sight (LoS) multiple-input multiple-output (MIMO) gives full spatial-multiplexing gain when the antenna array geometry and orientation are designed based on the inter-terminal distance. These known design methodologies, that hold for antenna arrays with fixed orientation, do not provide full MIMO gains for arbitrary array orientations. In this paper, we study LoS MIMO channels with random array orientations when the number of transmit antennas used for signalling is 2. We study the impact of common array geometries on error probability, and identify the code design parameter that describes the high signal-to-noise ratio (SNR) error performance of an arbitrary coding scheme. For planar receive arrays, the error rate is shown to decay only as fast as that of a rank 1 channel, and no better than 1/SNR^3 for a class of coding schemes that includes spatial multiplexing. We then show that for the tetrahedral receive array, which uses the smallest number of antennas among non-planar arrays, the error rate decays faster than that of rank 1 channels and is exponential in SNR for every coding scheme. Finally, we design a LoS MIMO system that guarantees a good error performance for all transmit/receive array orientations and over a range of inter-terminal distances.

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arXiv2016

New Error Correcting Codes for Informed Receivers

We construct error correcting codes for jointly transmitting a finite set of independent messages to an 'informed receiver' which has prior knowledge of the values of some subset of the messages as side information. The transmitter is oblivious to the message subset already known to the receiver and performs encoding in such a way that any possible side information can be used efficiently at the decoder. We construct and identify several families of algebraic error correcting codes for this problem using cyclic and maximum distance separable (MDS) codes. The proposed codes are of short block length, many of them provide optimum or near-optimum error correction capabilities and guarantee larger minimum distances than known codes of similar parameters for informed receivers. The constructed codes are also useful as error correcting codes for index coding when the transmitter does not know the side information available at the receivers.

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arXiv2016

The Two-Modular Fourier Transform of Binary Functions

In this paper, we provide a solution to the open problem of computing the Fourier transform of a binary function defined over $n$-bit vectors taking $m$-bit vector values. In particular, we introduce the two-modular Fourier transform (TMFT) of a binary function $f:G\rightarrow {\cal R}$, where $G = (\mathbb{F}_2^n,+)$ is the group of $n$ bit vectors with bitwise modulo two addition $+$, and ${\cal R}$ is a finite commutative ring of characteristic $2$. Using the specific group structure of $G$ and a sequence of nested subgroups of $G$, we define the fast TMFT and its inverse. Since the image ${\cal R}$ of the binary functions is a ring, we can define the convolution between two functions $f:G\rightarrow {\cal R}$. We then provide the TMFT properties, including the convolution theorem, which can be used to efficiently compute convolutions. Finally, we derive the complexity of the fast TMFT and the inverse fast TMFT.

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arXiv2015

Lattice Index Coding

The index coding problem involves a sender with K messages to be transmitted across a broadcast channel, and a set of receivers each of which demands a subset of the K messages while having prior knowledge of a different subset as side information. We consider the specific case of noisy index coding where the broadcast channel is Gaussian and every receiver demands all the messages from the source. Instances of this communication problem arise in wireless relay networks, sensor networks, and retransmissions in broadcast channels. We construct 'lattice index codes' for this channel by encoding the K messages individually using K modulo lattice constellations and transmitting their sum modulo a coarse lattice. We introduce a design metric called 'side information gain' that measures the advantage of a code in utilizing the side information at the receivers, and hence its goodness as an index code. Based on the Chinese remainder theorem, we then construct lattice index codes with large side information gains using lattices over the following principal ideal domains: rational integers, Gaussian integers, Eisenstein integers, and the Hurwitz quaternions. Among all lattice index codes constructed using any densest lattice of a given dimension, our codes achieve the maximum side information gain. Finally, using an example, we illustrate how the proposed lattice index codes can benefit Gaussian broadcast channels with more general message demands.

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arXiv2015

Oblivious Transfer over Wireless Channels

We consider the problem of oblivious transfer (OT) over OFDM and MIMO wireless communication systems where only the receiver knows the channel state information. The sender and receiver also have unlimited access to a noise-free real channel. Using a physical layer approach, based on the properties of the noisy fading channel, we propose a scheme that enables the transmitter to send obliviously one-of-two files, i.e., without knowing which one has been actually requested by the receiver, while also ensuring that the receiver does not get any information about the other file.

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arXiv2015

Capacity of Coded Index Modulation

We consider the special case of index coding over the Gaussian broadcast channel where each receiver has prior knowledge of a subset of messages at the transmitter and demands all the messages from the source. We propose a concatenated coding scheme for this problem, using an index code for the Gaussian channel as an inner code/modulation to exploit side information at the receivers, and an outer code to attain coding gain against the channel noise. We derive the capacity region of this scheme by viewing the resulting channel as a multiple-access channel with many receivers, and relate it to the 'side information gain' -- which is a measure of the advantage of a code in utilizing receiver side information -- of the inner index code/modulation. We demonstrate the utility of the proposed architecture by simulating the performance of an index code/modulation concatenated with an off-the-shelf convolutional code through bit-interleaved coded-modulation.

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arXiv2015

Index Codes for the Gaussian Broadcast Channel using Quadrature Amplitude Modulation

We propose index codes, based on multidimensional QAM constellations, for the Gaussian broadcast channel, where every receiver demands all the messages from the source. The efficiency with which an index code exploits receiver side information in this broadcast channel is characterised by a code design metric called "side information gain". The known index codes for this broadcast channel enjoy large side information gains, but do not encode all the source messages at the same rate, and do not admit message sizes that are powers of two. The index codes proposed in this letter, which are based on linear codes over integer rings, overcome both these drawbacks and yet provide large values of side information gain. With the aid of a computer search, we obtain QAM index codes for encoding up to 5 messages with message sizes 2^m, m <= 6. We also present the simulated performance of a new 16-QAM index code, concatenated with an off-the-shelf LDPC code, which is observed to operate within 4.3 dB of the broadcast channel capacity.

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arXiv2015

Full Diversity Unitary Precoded Integer-Forcing

We consider a point-to-point flat-fading MIMO channel with channel state information known both at transmitter and receiver. At the transmitter side, a lattice coding scheme is employed at each antenna to map information symbols to independent lattice codewords drawn from the same codebook. Each lattice codeword is then multiplied by a unitary precoding matrix ${\bf P}$ and sent through the channel. At the receiver side, an integer-forcing (IF) linear receiver is employed. We denote this scheme as unitary precoded integer-forcing (UPIF). We show that UPIF can achieve full-diversity under a constraint based on the shortest vector of a lattice generated by the precoding matrix ${\bf P}$. This constraint and a simpler version of that provide design criteria for two types of full-diversity UPIF. Type I uses a unitary precoder that adapts at each channel realization. Type II uses a unitary precoder, which remains fixed for all channel realizations. We then verify our results by computer simulations in $2\times2$, and $4\times 4$ MIMO using different QAM constellations. We finally show that the proposed Type II UPIF outperform the MIMO precoding X-codes at high data rates.

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arXiv2015

A Comparative Study of Polar Code Constructions for the AWGN Channel

We present a comparative study of the performance of various polar code constructions in an additive white Gaussian noise (AWGN) channel. A polar code construction is any algorithm that selects $K$ best among $N$ possible polar bit-channels at the design signal-to-noise-ratio (design-SNR) in terms of bit error rate (BER). Optimal polar code construction is hard and therefore many suboptimal polar code constructions have been proposed at different computational complexities. Polar codes are also non-universal meaning the code changes significantly with the design-SNR. However, it is not known which construction algorithm at what design-SNR constructs the best polar codes. We first present a comprehensive survey of all the well-known polar code constructions along with their full implementations. We then propose a heuristic algorithm to find the best design-SNR for constructing best possible polar codes from a given construction algorithm. The proposed algorithm involves a search among several possible design-SNRs. We finally use our algorithm to perform a comparison of different construction algorithms using extensive simulations. We find that all polar code construction algorithms generate equally good polar codes in an AWGN channel, if the design-SNR is optimized.

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arXiv2014

Probability Estimates for Fading and Wiretap Channels from Ideal Class Zeta Functions

In this paper, new probability estimates are derived for ideal lattice codes from totally real number fields using ideal class Dedekind zeta functions. In contrast to previous work on the subject, it is not assumed that the ideal in question is principal. In particular, it is shown that the corresponding inverse norm sum depends not only on the regulator and discriminant of the number field, but also on the values of the ideal class Dedekind zeta functions. Along the way, we derive an estimate of the number of elements in a given ideal with a certain algebraic norm within a finite hypercube. We provide several examples which measure the accuracy and predictive ability of our theorems.

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arXiv2014

Unshared Secret Key Cryptography: Finite Constellation Inputs and Ideal Secrecy Outage

The Unshared Secret Key Cryptography (USK), recently proposed by the authors, guarantees Shannon's ideal secrecy and perfect secrecy for MIMO wiretap channels, without requiring secret key exchange. However, the requirement of infinite constellation inputs limits its applicability to practical systems. In this paper, we propose a practical USK scheme using finite constellation inputs. The new scheme is based on a cooperative jamming technique, and is valid for the case where the eavesdropper has more antennas than the transmitter. We show that Shannon's ideal secrecy can be achieved with an arbitrarily small outage probability.

cs.CR↗

arXiv2014

Guaranteeing Positive Secrecy Capacity with Finite-Rate Feedback using Artificial Noise

While the impact of finite-rate feedback on the capacity of fading channels has been extensively studied in the literature, not much attention has been paid to this problem under secrecy constraint. In this work, we study the ergodic secret capacity of a multiple-input multiple-output multiple-antenna-eavesdropper (MIMOME) wiretap channel with quantized channel state information (CSI) at the transmitter and perfect CSI at the legitimate receiver, under the assumption that only the statistics of eavesdropper CSI is known at the transmitter. We refine the analysis of the random vector quantization (RVQ) based artificial noise (AN) scheme in [1], where a heuristic upper bound on the secrecy rate loss, when compared to the perfect CSI case, was given. We propose a lower bound on the ergodic secrecy capacity. We show that the lower bound and the secrecy capacity with perfect CSI coincide asymptotically as the number of feedback bits and the AN power go to infinity. For practical applications, we propose a very efficient quantization codebook construction method for the two transmit antennas case.

cs.IT↗

arXiv2014

Unshared Secret Key Cryptography

Current security techniques can be implemented with either secret key exchange or physical layer wiretap codes. In this work, we investigate an alternative solution for MIMO wiretap channels. Inspired by the artificial noise (AN) technique, we propose the unshared secret key (USK) cryptosystem, where the AN is redesigned as a one-time pad secret key aligned within the null space between transmitter and legitimate receiver. The proposed USK cryptosystem is a new physical layer cryptographic scheme, obtained by combining traditional network layer cryptography and physical layer security. Unlike previously studied artificial noise techniques, rather than ensuring non-zero secrecy capacity, the USK is valid for an infinite lattice input alphabet and guarantees Shannon's ideal secrecy and perfect secrecy, without the need of secret key exchange. We then show how ideal secrecy can be obtained for finite lattice constellations with an arbitrarily small outage.

cs.CR↗

arXiv2014

Cross-Error Correcting Integer Codes over $\mathbb{Z}_{2^m}$

In this work we investigate codes in $\mathbb{Z}_{2^m}^n$ that can correct errors that occur in just one coordinate of the codeword, with a magnitude of up to a given parameter $t$. We will show upper bounds on these cross codes, derive constructions for linear codes and respective decoding algorithm. The constructions (and decoding algorithms) are given for length $n = 2$ and $n = 3$, but for general $m$ and $t$.

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arXiv2014

Phase Precoding for the Compute-and-Forward Protocol

The compute-and-forward (CoF) is a relaying protocol, which uses algebraic structured codes to harness the interference and remove the noise in wireless networks. We propose the use of phase precoders at the transmitters of a network, where relays apply CoF strategy. We define the {\em phase precoded computation rate} and show that it is greater than the original computation rate of CoF protocol. We further give a new low-complexity method for finding network equations. We finally show that the proposed precoding scheme increases the degrees-of-freedom (DoF) of CoF protocol. This overcomes the limitations on the DoF of the CoF protocol, recently presented by Niesen and Whiting. Using tools from Diophantine approximation and algebraic geometry, we prove the existence of a phase precoder that approaches the maximum DoF when the number of transmitters tends to infinity.

cs.IT↗

arXiv2014

Artificial Noise Revisited

The artificial noise (AN) scheme, proposed by Goel and Negi, is being considered as one of the key enabling technology for secure communications over multiple-input multiple-output (MIMO) wiretap channels. However, the decrease in secrecy rate due to the increase in the number of Eve's antennas is not well understood. In this paper, we develop an analytical framework to characterize the secrecy rate of the AN scheme as a function of Eve's signal-to-noise ratio (SNR), Bob's SNR, the number of antennas in each terminal, and the power allocation scheme. We first derive a closed-form expression for the average secrecy rate. We then derive a closed-form expression for the asymptotic instantaneous secrecy rate with large number of antennas at all terminals. Finally, we derive simple lower and upper bounds on the average and instantaneous secrecy rate that provide a tool for the system design.

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