arXiv subjects

Jingbo Liu

Publications and source records attributed to Jingbo Liu.

65 records · Page 4Linked to original sources

arXiv2016

Brascamp-Lieb Inequality and Its Reverse: An Information Theoretic View

We generalize a result by Carlen and Cordero-Erausquin on the equivalence between the Brascamp-Lieb inequality and the subadditivity of relative entropy by allowing for random transformations (a broadcast channel). This leads to a unified perspective on several functional inequalities that have been gaining popularity in the context of proving impossibility results. We demonstrate that the information theoretic dual of the Brascamp-Lieb inequality is a convenient setting for proving properties such as data processing, tensorization, convexity and Gaussian optimality. Consequences of the latter include an extension of the Brascamp-Lieb inequality allowing for Gaussian random transformations, the determination of the multivariate Wyner common information for Gaussian sources, and a multivariate version of Nelson's hypercontractivity theorem. Finally we present an information theoretic characterization of a reverse Brascamp-Lieb inequality involving a random transformation (a multiple access channel).

cs.IT↗

arXiv2016

Key Capacity for Product Sources with Application to Stationary Gaussian Processes

We show that for product sources, rate splitting is optimal for secret key agreement using limited one-way communication between two terminals. This yields an alternative information-theoretic-converse-style proof of the tensorization property of a strong data processing inequality originally studied by Erkip and Cover and amended recently by Anantharam et al. We derive a water-filling solution of the communication-rate--key-rate tradeoff for a wide class of discrete memoryless vector Gaussian sources which subsumes the case without an eavesdropper. Moreover, we derive an explicit formula for the maximum secret key per bit of communication for all discrete memoryless vector Gaussian sources using a tensorization property and a variation on the enhanced channel technique of Weingarten et al. Finally, a one-shot information spectrum achievability bound for key generation is proved from which we characterize the communication-rate--key-rate tradeoff for stationary Gaussian processes.

cs.IT↗

arXiv2016

Smoothing Brascamp-Lieb Inequalities and Strong Converses for Common Randomness Generation

We study the infimum of the best constant in a functional inequality, the Brascamp-Lieb-like inequality, over auxiliary measures within a neighborhood of a product distribution. In the finite alphabet and the Gaussian cases, such an infimum converges to the best constant in a mutual information inequality. Implications for strong converse properties of two common randomness (CR) generation problems are discussed. In particular, we prove the strong converse property of the rate region for the omniscient helper CR generation problem in the discrete and the Gaussian cases. The latter case is perhaps the first instance of a strong converse for a continuous source when the rate region involves auxiliary random variables.

cs.IT↗

arXiv2015

Graphene terahertz modulators by ionic liquid gating

Graphene based THz modulators are promising due to the conical band structure and high carrier mobility of graphene. Here, we tune the Fermi level of graphene via electrical gating with the help of ionic liquid to control the THz transmittance. It is found that, in the THz range, both the absorbance and reflectance of the device increase proportionately to the available density of states due to intraband transitions. Compact, stable, and repeatable THz transmittance modulation up to 93% (or 99%) for a single (or stacked) device has been demonstrated in a broad frequency range from 0.1 to 2.5 THz, with an applied voltage of only 3 V at room temperature.

physics.optics↗

arXiv2015

One-Shot Mutual Covering Lemma and Marton's Inner Bound with a Common Message

By developing one-shot mutual covering lemmas, we derive a one-shot achievability bound for broadcast with a common message which recovers Marton's inner bound (with three auxiliary random variables) in the i.i.d.~case. The encoder employed is deterministic. Relationship between the mutual covering lemma and a new type of channel resolvability problem is discussed.

cs.IT↗

arXiv2015

Resolvability in Eγ with Applications to Lossy Compression and Wiretap Channels

We study the amount of randomness needed for an input process to approximate a given output distribution of a channel in the $E_γ$ distance. A general one-shot achievability bound for the precision of such an approximation is developed. In the i.i.d.~setting where $γ=\exp(nE)$, a (nonnegative) randomness rate above $\inf_{Q_{\sf U}: D(Q_{\sf X}||π_{\sf X})\le E} \{D(Q_{\sf X}||π_{\sf X})+I(Q_{\sf U},Q_{\sf X|U})-E\}$ is necessary and sufficient to asymptotically approximate the output distribution $π_{\sf X}^{\otimes n}$ using the channel $Q_{\sf X|U}^{\otimes n}$, where $Q_{\sf U}\to Q_{\sf X|U}\to Q_{\sf X}$. The new resolvability result is then used to derive a one-shot upper bound on the error probability in the rate distortion problem, and a lower bound on the size of the eavesdropper list to include the actual message in the wiretap channel problem. Both bounds are asymptotically tight in i.i.d.~settings.

cs.IT↗

arXiv2014

Robustness of Sparse Recovery via $F$-minimization: A Topological Viewpoint

A recent trend in compressed sensing is to consider non-convex optimization techniques for sparse recovery. The important case of $F$-minimization has become of particular interest, for which the exact reconstruction condition (ERC) in the noiseless setting can be precisely characterized by the null space property (NSP). However, little work has been done concerning its robust reconstruction condition (RRC) in the noisy setting. We look at the null space of the measurement matrix as a point on the Grassmann manifold, and then study the relation between the ERC and RRC sets, denoted as $Ω_J$ and $Ω_J^r$, respectively. It is shown that $Ω_J^r$ is the interior of $Ω_J$, from which a previous result of the equivalence of ERC and RRC for $\ell_p$-minimization follows easily as a special case. Moreover, when $F$ is non-decreasing, it is shown that $\overlineΩ_J\setminus\interior(Ω_J)$ is a set of measure zero and of the first category. As a consequence, the probabilities of ERC and RRC are the same if the measurement matrix $\mathbf{A}$ is randomly generated according to a continuous distribution. Quantitatively, if the null space $\mathcal{N}(\bf A)$ lies in the "$d$-interior" of $Ω_J$, then RRC will be satisfied with the robustness constant $C=\frac{2+2d}{dσ_{\min}(\mathbf{A}^{\top})}$; and conversely if RRC holds with $C=\frac{2-2d}{dσ_{\max}(\mathbf{A}^{\top})}$, then $\mathcal{N}(\bf A)$ must lie in $d$-interior of $Ω_J$. We also present several rules for comparing the performances of different cost functions. Finally, these results are capitalized to derive achievable tradeoffs between the measurement rate and robustness with the aid of Gordon's escape through the mesh theorem or a connection between NSP and the restricted eigenvalue condition.

cs.IT↗

arXiv2014

Key Capacity with Limited One-Way Communication for Product Sources

We show that for product sources, rate splitting is optimal for secret key agreement using limited one-way communication at two terminals. This yields an alternative proof of the tensorization property of a strong data processing inequality originally studied by Erkip and Cover and amended recently by Anantharam et al. We derive a `water-filling' solution of the communication-rate--key-rate tradeoff for two arbitrarily correlated vector Gaussian sources, for the case with an eavesdropper, and for stationary Gaussian processes.

cs.IT↗

arXiv2014

Polynomial complexity of polar codes for non-binary alphabets, key agreement and Slepian-Wolf coding

We consider polar codes for memoryless sources with side information and show that the blocklength, construction, encoding and decoding complexities are bounded by a polynomial of the reciprocal of the gap between the compression rate and the conditional entropy. This extends the recent results of Guruswami and Xia to a slightly more general setting, which in turn can be applied to (1) sources with non-binary alphabets, (2) key generation for discrete and Gaussian sources, and (3) Slepian-Wolf coding and multiple accessing. In each of these cases, the complexity scaling with respect to the number of users is also controlled. In particular, we construct coding schemes for these multi-user information theory problems which achieve optimal rates with an overall polynomial complexity.

cs.IT↗

arXiv2013

Graphene/liquid crystal based terahertz phase shifters

Due to its high electrical conductivity and excellent transmittance at terahertz frequencies, graphene is a promising candidate as transparent electrodes for terahertz devices. We demonstrate a liquid crystal based terahertz phase shifter with the graphene films as transparent electrodes. The maximum phase shift is 10.8 degree and the saturation voltage is 5 V with a 50 um liquid crystal cell. The transmittance at terahertz frequencies and electrical conductivity depending on the number of graphene layer are also investigated. The proposed phase shifter provides a continuous tunability, fully electrical controllability, and low DC voltage operation.

cond-mat.mtrl-sci↗

arXiv2012

Efficient Recovery of Block Sparse Signals via Zero-point Attracting Projection

In this paper, we consider compressed sensing (CS) of block-sparse signals, i.e., sparse signals that have nonzero coefficients occurring in clusters. An efficient algorithm, called zero-point attracting projection (ZAP) algorithm, is extended to the scenario of block CS. The block version of ZAP algorithm employs an approximate $l_{2,0}$ norm as the cost function, and finds its minimum in the solution space via iterations. For block sparse signals, an analysis of the stability of the local minimums of this cost function under the perturbation of noise reveals an advantage of the proposed algorithm over its original non-block version in terms of reconstruction error. Finally, numerical experiments show that the proposed algorithm outperforms other state of the art methods for the block sparse problem in various respects, especially the stability under noise.

cs.IT↗