Few-Shot Channel-Agnostic Analog Coding: A Near-Optimal Scheme

In this paper, we investigate the problem of transmitting an analog source to a destination over $N$ uses of an additive-white-Gaussian-noise (AWGN) channel, where $N$ is very small (in the order of 10 or even less). The proposed coding scheme is based on representing the source symbol using a novel progressive expansion technique, partitioning the digits of expansion into $N$ ordered sets, and finally mapping the symbols in each set to a real number by applying the reverse progressive expansion. In the last step, we introduce some gaps between the signal levels to prevent the carry-over of the additive noise from propagation to other levels. This shields the most significant levels of the signal from an additive noise, hitting the signal at a less significant level. The parameters of the progressive expansion and the shielding procedure are opportunistically independent of the \SNR so that the proposed scheme achieves a distortion $D$, where $-\log(D)$ is within O(\log\log(\SNR)) of the optimal performance for all values of \SNR, leading to a channel-agnostic scheme

Lattice-Based Precoding And Decoding in MIMO Fading Systems

In this thesis, different aspects of lattice-based precoding and decoding for the transmission of digital and analog data over MIMO fading channels are investigated: 1) Lattice-based precoding in MIMO broadcast systems: A new viewpoint for adopting the lattice reduction in communication over MIMO broadcast channels is introduced. Lattice basis reduction helps us to reduce the average transmitted energy by modifying the region which includes the constellation points. The new viewpoint helps us to generalize the idea of lattice-reduction-aided precoding for the case of unequal-rate transmission, and obtain analytic results for the asymptotic behavior of the symbol-error-rate for the lattice-reduction-aided precoding and the perturbation technique. Also, the outage probability for both cases of fixed-rate users and fixed sum-rate is analyzed. It is shown that the lattice-reduction-aided method, using LLL algorithm, achieves the optimum asymptotic slope of symbol-error-rate (called the precoding diversity). 2) Lattice-based decoding in MIMO multiaccess systems and MIMO point-to-point systems: Diversity order and diversity-multiplexing tradeoff are two important measures for the performance of communication systems over MIMO fading channels. For the case of MIMO multiaccess systems (with single-antenna transmitters) or MIMO point-to-point systems with V-BLAST transmission scheme, it is proved that lattice-reduction-aided decoding achieves the maximum receive diversity (which is equal to the number of receive antennas). Also, it is proved that the naive lattice decoding (which discards the out-of-region decoded points) achieves the maximum diversity in V-BLAST systems. On the other hand, the inherent drawbacks of the naive lattice decoding for general MIMO fading systems is investigated. It is shown that using the naive lattice decoding for MIMO systems has considerable deficiencies in terms of the diversity-multiplexing tradeoff. Unlike the case of maximum-likelihood decoding, in this case, even the perfect lattice space-time codes which have the non-vanishing determinant property can not achieve the optimal diversity-multiplexing tradeoff. 3) Lattice-based analog transmission over MIMO fading channels: The problem of finding a delay-limited schemes for sending an analog source over MIMO fading channels is investigated in this part. First, the problem of robust joint source-channel coding over an additive white Gaussian noise channel is investigated. A new scheme is proposed which achieves the optimal slope for the signal-to-distortion-ratio (SDR) curve (unlike the previous known coding schemes). Then, this idea is extended to MIMO channels to construct lattice-based codes for joint source-channel coding over MIMO channels. Also, similar to the diversity-multiplexing tradeoff, the asymptotic performance of MIMO joint source-channel coding schemes is characterized, and a concept called diversity-fidelity tradeoff is introduced in this thesis

Joint source channel coding for non-ergodic channels: the distortion signal-to-noise ratio (SNR) exponent perspective

We study the problem of communicating a discrete time analog source over a channel such that the resulting distortion is minimized. For ergodic channels, Shannon showed that separate source and channel coding is optimal. In this work we study this problem for non-ergodic channels. Although not much can be said about the general problem of transmitting any analog sources over any non-ergodic channels with any distortion metric, for many practical problems like video broadcast and voice transmission, we can gain insights by studying the transmission of a Gaussian source over a wireless channel with mean square error as the distortion measure. Motivated by different applications, we consider three different non-ergodic channel models - (1) Additive white Gaussian noise (AWGN) channel whose signal-to-noise ratio (SNR) is unknown at the transmitter; (2) Rayleigh fading multiple-input multiple-output MIMO channel whose SNR is known at the transmitter; and (3) Rayleigh fading MIMO channel whose SNR is unknown at the transmitter. The traditional approach to study these problems has been to fix certain SNRs of interest and study the corresponding achievable distortion regions. However, the problems formulated this way have not been solved even for simple setups like 2 SNRs for the AWGN channel. We are interested in performance over a wide range of SNR and hence we use the distortion SNR exponent metric to study this problem. Distortion SNR exponent is defined as the rate of decay of distortion with SNR in the high SNR limit. We study several layered transmissions schemes where the source is first compressed in layers and then the layers are transmitted using channel codes that provide variable error protection. Results show that in several cases such layered transmission schemes are optimal in terms of the distortion SNR exponent. Specifically, if the band- width expansion (number of channel uses per source sample) is b, we show that the optimal distortion SNR exponent for the AWGN channel is b and it is achievable using a superposition based layered scheme. For the L-block Rayleigh fading M x N MIMO channel the optimal exponent is characterized for b < (|N - M|+1)= min(M;N) and b > MNL2. This corresponds to the entire range of b when min(M;N) = 1 and L = 1. The results also show that the exponents obtained using layered schemes which are a small subclass of joint source channel coding (JSCC) schemes are, surprisingly, as good as and better in some cases than achievable exponent of all other JSCC schemes reported so far

Markovian Processes for Quantitative Information Leakage

Quantification of information leakage is a successful approach for evaluating the security of a system. It models the system to be analyzed as a channel with the secret as the input and an output as observable by the attacker as the output, and applies information theory to quantify the amount of information transmitted through such channel, thus effectively quantifying how many bits of the secret can be inferred by the attacker by analyzing the system’s output.Channels are usually encoded as matrices of conditional probabilities, known as channel matrices. Such matrices grow exponentially in the size of the secret and observables, are cumbersome to compute and store, encode both the behavior of the system and assumptions about the attacker, and assume an input-output behavior of the system. For these reasons we propose to model the system-attacker scenario with Markovian models.We show that such models are more compact and treatable than channel matrices. Also, they clearly separate the behavior of the system from the assumptions about the attacker, and can represent even non-terminating behavior in a finite model. We provide techniques and algorithms to model and analyze both deterministic and randomized processes with Markovian models and to compute their informationleakage for a very general model of attacker. We present the QUAIL tool that automates such analysis and is able to compute the information leakage of an imperative WHILE language. Finally, we show how to use QUAIL to analyze some interesting cases of secret-dependent protocols