Finite Blocklength Analysis of Gaussian Random Coding in AWGN Channels under Covert Constraint

This paper considers the achievability and converse bounds on the maximal channel coding rate at a given blocklength and error probability over AWGN channels. The problem stems from covert communication with Gaussian codewords. By re-visiting [18], we first present new and more general achievability bounds for random coding schemes under maximal or average probability of error requirements. Such general bounds are then applied to covert communication in AWGN channels where codewords are generated from Gaussian distribution while meeting the maximal power constraint. Further comparison is made between the new achievability bounds and existing one with deterministic codebooks.Comment: 18 page

The First and Second Order Asymptotics of Covert Communication over AWGN Channels

This paper investigates the asymptotics of the maximal throughput of communication over AWGN channels by $n$ channel uses under a covert constraint in terms of an upper bound $\delta$ of Kullback-Leibler divergence (KL divergence). It is shown that the first and second order asymptotics of the maximal throughput are $\sqrt{n\delta \log e}$ and $(2)^{1/2}(n\delta)^{1/4}(\log e)^{3/4}\cdot Q^{-1}(\epsilon)$, respectively. The technique we use in the achievability is quasi-$\varepsilon$-neighborhood notion from information geometry. We prove that if the generating distribution of the codebook is close to Dirac measure in the weak sense, then the corresponding output distribution at the adversary satisfies covert constraint in terms of most common divergences. This helps link the local differential geometry of the distribution of noise with covert constraint. For the converse, the optimality of Gaussian distribution for minimizing KL divergence under second order moment constraint is extended from dimension $1$ to dimension $n$. It helps to establish the upper bound on the average power of the code to satisfy the covert constraint, which further leads to the direct converse bound in terms of covert metric

Fundamental Limits of Communication with Low Probability of Detection

This paper considers the problem of communication over a discrete memoryless channel (DMC) or an additive white Gaussian noise (AWGN) channel subject to the constraint that the probability that an adversary who observes the channel outputs can detect the communication is low. Specifically, the relative entropy between the output distributions when a codeword is transmitted and when no input is provided to the channel must be sufficiently small. For a DMC whose output distribution induced by the "off" input symbol is not a mixture of the output distributions induced by other input symbols, it is shown that the maximum amount of information that can be transmitted under this criterion scales like the square root of the blocklength. The same is true for the AWGN channel. Exact expressions for the scaling constant are also derived.Comment: Version to appear in IEEE Transactions on Information Theory; minor typos in v2 corrected. Part of this work was presented at ISIT 2015 in Hong Kon

Digital Watermarking, Fingerprinting and Compression: An Information-Theoretic Perspective

The ease with which digital data can be duplicated and distributed over the media and the Internethas raised many concerns about copyright infringement.In many situations, multimedia data (e.g., images, music, movies, etc) are illegally circulated, thus violatingintellectual property rights. In an attempt toovercome this problem, watermarking has been suggestedin the literature as the most effective means for copyright protection and authentication. Watermarking is the procedure whereby information (pertaining to owner and/or copyright) is embedded into host data, such that it is:(i) hidden, i.e., not perceptually visible; and(ii) recoverable, even after a (possibly malicious) degradation of the protected work. In this thesis,we prove some theoretical results that establish the fundamental limits of a general class of watermarking schemes. The main focus of this thesis is the problem ofjoint watermarking and compression of images, whichcan be briefly described as follows: due to bandwidth or storage constraints, a watermarked image is distributed in quantized form, using $R_Q$ bits per image dimension, and is subject to some additional degradation (possibly due to malicious attacks). The hidden message carries $R_W$ bits per image dimension. Our main result is the determination of the region of allowable rates $(R_Q, R_W)$, such that: (i) an average distortion constraint between the original and the watermarked/compressed image is satisfied, and (ii) the hidden message is detected from the degraded image with very high probability. Using notions from information theory, we prove coding theorems that establish the rate regionin the following cases: (a) general i.i.d. image distributions,distortion constraints and memoryless attacks, (b) memoryless attacks combined with collusion (for fingerprinting applications), and (c) general---not necessarily stationary or ergodic---Gaussian image distributions and attacks, and average quadratic distortion constraints. Moreover, we prove a multi-user version of a result by Costa on the capacity of a Gaussian channel with known interference at the encoder

One-shot achievability and converse bounds of Gaussian random coding in AWGN channels under covert constraint

The achievability and converse bounds on the throughput of covert communication over AWGN channels are investigated in this paper. By re-visiting [8], several new achievability bounds on maximal and average probability of error based on random coding scheme are presented, which leads to results on achievability bounds when the codewords are generated from Gaussian distribution and then selected from a subset under maximal power constraint. The bounds provide us the framework for analyzing the maximal throughput under covert constraint of total variation distance