arXiv subjects

Cong Ling

Publications and source records attributed to Cong Ling.

At least 55 records · Page 3Linked to original sources

arXiv2020

Coded Caching in Multi-server System with Random Topology

Cache-aided content delivery is studied in a multi-server system with $P$ servers and $K$ users, each equipped with a local cache memory. In the delivery phase, each user connects randomly to any $ρ$ out of $P$ servers. Thanks to the availability of multiple servers, which model small-cell base stations (SBSs), demands can be satisfied with reduced storage capacity at each server and reduced delivery rate per server; however, this also leads to reduced multicasting opportunities compared to the single-server scenario. A joint storage and proactive caching scheme is proposed, which exploits coded storage across the servers, uncoded cache placement at the users, and coded delivery. The delivery \textit{latency} is studied for both \textit{successive} and \textit{parallel} transmissions from the servers. It is shown that, with successive transmissions the achievable average delivery latency is comparable to the one achieved in the single-server scenario, while the gap between the two depends on $ρ$, the available redundancy across the servers, and can be reduced by increasing the storage capacity at the SBSs. The optimality of the proposed scheme with uncoded cache placement and MDS-coded server storage is also proved for successive transmissions.

cs.IT↗

arXiv2019

On Low-complexity Lattice Reduction Algorithms for Large-scale MIMO Detection: the Blessing of Sequential Reduction

Lattice reduction is a popular preprocessing strategy in multiple-input multiple-output (MIMO) detection. In a quest for developing a low-complexity reduction algorithm for large-scale problems, this paper investigates a new framework called sequential reduction (SR), which aims to reduce the lengths of all basis vectors. The performance upper bounds of the strongest reduction in SR are given when the lattice dimension is no larger than 4. The proposed new framework enables the implementation of a hash-based low-complexity lattice reduction algorithm, which becomes especially tempting when applied to large-scale MIMO detection. Simulation results show that, compared to other reduction algorithms, the hash-based SR algorithm exhibits the lowest complexity while maintaining comparable error performance.

cs.IT↗

arXiv2019

Semantically Secure Lattice Codes for Compound MIMO Channels

We consider compound multi-input multi-output (MIMO) wiretap channels where minimal channel state information at the transmitter (CSIT) is assumed. Code construction is given for the special case of isotropic mutual information, which serves as a conservative strategy for general cases. Using the flatness factor for MIMO channels, we propose lattice codes universally achieving the secrecy capacity of compound MIMO wiretap channels up to a constant gap (measured in nats) that is equal to the number of transmit antennas. The proposed approach improves upon existing works on secrecy coding for MIMO wiretap channels from an error probability perspective, and establishes information theoretic security (in fact semantic security). We also give an algebraic construction to reduce the code design complexity, as well as the decoding complexity of the legitimate receiver. Thanks to the algebraic structures of number fields and division algebras, our code construction for compound MIMO wiretap channels can be reduced to that for Gaussian wiretap channels, up to some additional gap to secrecy capacity.

cs.IT↗

arXiv2019

Deterministic Sampling Decoding: Where Sphere Decoding Meets Lattice Gaussian Distribution

In this paper, the paradigm of sphere decoding (SD) based on lattice Gaussian distribution is studied, where the sphere radius $D>0$ in the sense of Euclidean distance is characterized by the initial pruning size $K>1$, the standard deviation $σ>0$ and a regularization term $ρ_{σ,\mathbf{y}}(Λ)>0$ ($Λ$ denotes the lattice, $\mathbf{y}$ is the query point). In this way, extra freedom is obtained for analytical diagnosis of both the decoding performance and complexity. Based on it, the equivalent SD (ESD) algorithm is firstly proposed, and we show it is exactly the same with the classic Fincke-Pohst SD but characterizes the sphere radius with $D=σ\sqrt{2\ln K}$. By fixing $σ$ properly, we show that the complexity of ESD measured by the number of visited nodes is upper bounded by $|S|<nK$, thus resulting in a tractable decoding trade-off solely determined by $K$. In order to further exploit the decoding potential, the regularized SD (RSD) algorithm based on Klein's sampling probability is proposed, which achieves a better decoding trade-off than the equivalent SD by fully utilizing the regularization terms. Moreover, besides the designed criterion of pruning threshold, another decoding criterion named as candidate protection is proposed to solve the decoding problems in the cases of small $K$, which generalizes both the regularized SD and equivalent SD from maximum likelihood (ML) decoding to bounded distance decoding (BDD). Finally, simulation results based on MIMO detection are presented to confirm the tractable decoding trade-off of the proposed lattice Gaussian distribution-based SD algorithms.

cs.IT↗

arXiv2019

On the Polarization of Rényi Entropy

Existing polarization theories have mostly been concerned with Shannon's information measures, such as Shannon entropy and mutual information, and some related measures such as the Bhattacharyya parameter. In this work, we extend polarization theories to a more general information measure, namely, the Rényi entropy. Our study shows that under conditional Rényi entropies of different orders, the same synthetic sub-channel may exhibit opposite extremal states. This result reveals more insights into the polarization phenomenon on the micro scale (probability pairs) rather than on the average scale.

cs.IT↗

arXiv2019

Ring Compute-and-Forward over Block-Fading Channels

The Compute-and-Forward protocol in quasi-static channels normally employs lattice codes based on the rational integers $\mathbb{Z}$, Gaussian integers $\mathbb{Z}\left[i\right]$ or Eisenstein integers $\mathbb{Z}\left[ω\right]$, while its extension to more general channels often assumes channel state information at transmitters (CSIT). In this paper, we propose a novel scheme for Compute-and-Forward in block-fading channels without CSIT, which is referred to as Ring Compute-and-Forward because the fading coefficients are quantized to the canonical embedding of a ring of algebraic integers. Thanks to the multiplicative closure of the algebraic lattices employed, a relay is able to decode an algebraic-integer linear combination of lattice codewords. We analyze its achievable computation rates and show it outperforms conventional Compute-and-Forward based on $\mathbb{Z}$-lattices. By investigating the effect of Diophantine approximation by algebraic conjugates, we prove that the degrees-of-freedom (DoF) of the optimized computation rate is ${n}/{L}$, where $n$ is the number of blocks and $L$ is the number of users.

cs.IT↗

arXiv2019

Coprime Sensing via Chinese Remaindering over Quadratic Fields, Part II: Generalizations and Applications

The practical application of a new class of coprime arrays based on the Chinese remainder theorem (CRT) over quadratic fields is presented in this paper. The proposed CRT arrays are constructed by ideal lattices embedded from coprime quadratic integers. The geometrical constructions and theoretical foundations were discussed in the accompanying paper in great detail, while this paper focuses on aspects of the application of the proposed arrays in two-dimensional (2D) remote sensing. A generalization of CRT arrays based on two or more pairwise coprime ideal lattices is proposed with closed-form expressions on sensor locations, the total number of sensors and the achievable DOF. The issues pertaining to the coprimality of any two quadratic integers are also addressed to explore all possible ideal lattices. Exploiting the symmetry of lattices, sensor reduction methods are discussed with the coarray remaining intact for economic maximization. In order to extend conventional angle estimation techniques based on uniformly distributed arrays to the method that can exploit any coarray configurations based on lattices, this paper introduces a hexagon-to-rectangular transformation to 2D spatial smoothing, providing the possibility of finding more compact sensor arrays. Examples are provided to verify the feasibility of the proposed methods.

eess.SP↗

arXiv2019

Coprime Sensing via Chinese Remaindering over Quadratic Fields, Part I: Array Designs

A coprime antenna array consists of two or more sparse subarrays featuring enhanced degrees of freedom (DOF) and reduced mutual coupling. This paper introduces a new class of planar coprime arrays, based on the theory of ideal lattices. In quadratic number fields, a splitting prime $p$ can be decomposed into the product of two distinct prime ideals, which give rise to the two sparse subarrays. Their virtual difference coarray enjoys a quadratic gain in DOF, thanks to the generalized Chinese Remainder Theorem (CRT). To enlarge the contiguous aperture of the coarray, we present hole-free symmetric CRT arrays with simple closed-form expressions. The ring of Gaussian integers and the ring of Eisenstein integers are considered as examples to demonstrate the procedure of designing coprime arrays. With Eisenstein integers, our design yields a difference coarray that is a subset of the hexagonal lattice, offering a significant gain in DOF over the rectangular lattice, given the same physical areas.

eess.SP↗

arXiv2019

Practical Functional Regenerating Codes for Broadcast Repair of Multiple Nodes

A code construction and repair scheme for optimal functional regeneration of multiple node failures is presented, which is based on stitching together short MDS codes on carefully chosen sets of points lying on a linearized polynomial. The nodes are connected wirelessly, hence all transmissions by helper nodes during a repair round are available to all the nodes being repaired. The scheme is simple and practical because of low subpacketization, low I/O cost and low computational cost. Achievability of the minimum-bandwidth regenerating (MBR) point, as well as an interior point, on the optimal storage-repair bandwidth tradeoff curve is shown. The subspace properties derived in the paper provide insight into the general properties of functional regenerating codes.

cs.IT↗

arXiv2019

On the Optimality of Gauss's Algorithm over Euclidean Imaginary Quadratic Fields

In this paper, we continue our previous work on the reduction of algebraic lattices over imaginary quadratic fields for the special case when the lattice is spanned over a two dimensional basis. In particular, we show that the algebraicvariant of Gauss algorithm returns a basis that corresponds to the successive minima of the lattice in polynomial time if the chosen ring is Euclidean.

cs.IT↗

arXiv2018

Construction of Capacity-Achieving Lattice Codes: Polar Lattices

In this paper, we propose a new class of lattices constructed from polar codes, namely polar lattices, to achieve the capacity $\frac{1}{2}\log(1+\SNR)$ of the additive white Gaussian-noise (AWGN) channel. Our construction follows the multilevel approach of Forney \textit{et al.}, where we construct a capacity-achieving polar code on each level. The component polar codes are shown to be naturally nested, thereby fulfilling the requirement of the multilevel lattice construction. We prove that polar lattices are \emph{AWGN-good}. Furthermore, using the technique of source polarization, we propose discrete Gaussian shaping over the polar lattice to satisfy the power constraint. Both the construction and shaping are explicit, and the overall complexity of encoding and decoding is $O(N\log N)$ for any fixed target error probability.

cs.IT↗

arXiv2018

Lattice Gaussian Sampling by Markov Chain Monte Carlo: Bounded Distance Decoding and Trapdoor Sampling

Sampling from the lattice Gaussian distribution plays an important role in various research fields. In this paper, the Markov chain Monte Carlo (MCMC)-based sampling technique is advanced in several fronts. Firstly, the spectral gap for the independent Metropolis-Hastings-Klein (MHK) algorithm is derived, which is then extended to Peikert's algorithm and rejection sampling; we show that independent MHK exhibits faster convergence. Then, the performance of bounded distance decoding using MCMC is analyzed, revealing a flexible trade-off between the decoding radius and complexity. MCMC is further applied to trapdoor sampling, again offering a trade-off between security and complexity. Finally, the independent multiple-try Metropolis-Klein (MTMK) algorithm is proposed to enhance the convergence rate. The proposed algorithms allow parallel implementation, which is beneficial for practical applications.

cs.IT↗

arXiv2018

Coded Computation Against Distributed Straggling Channel Decoders in the Cloud for Gaussian Uplink Channels

The uplink of a Cloud Radio Access Network (CRAN) architecture is studied, where decoding at the cloud takes place at distributed decoding processors. To mitigate the impact of straggling decoders in the cloud, the cloud re-encodes the received frames via a linear code before distributing them to the decoding processors. Focusing on Gaussian channels, and assuming the use of lattice codes at the users, in this paper the maximum user rate is derived such that all the servers can reliably recover the linear combinations of the messages corresponding to the employed linear code at the cloud. Furthermore, two analytical upper bounds on the frame error rate (FER) as a function of the decoding latency are developed, in order to quantify the performance of the cloud's linear code in terms of the tradeoff between FER and decoding latency at the cloud.

cs.IT↗

arXiv2018

Polar Coding Strategies for the Interference Channel with Partially-Joint Decoding

Existing polar coding schemes for the two-user interference channel follow the original idea of Han and Kobayashi, in which component messages are encoded independently and then mapped by some deterministic functions (i.e., homogeneous superposition coding). In this paper, we propose a new polar coding scheme for the interference channel based on the heterogeneous superposition coding approach of Chong, Motani and Garg. We prove that fully-joint decoding (the receivers simultaneously decode both senders' common messages and the intended sender's private message) in the Han-Kobayashi strategy can be simplified to two types of partially-joint decoding, which are friendly to polar coding with practical decoding algorithms. The proposed coding scheme requires less auxiliary random variables and no deterministic functions, and can be efficiently constructed. Further, we extend this result to interference networks and show that the proposed partially-joint decoding scheme is a general method for designing heterogeneous superposition polar coding schemes in interference networks.

cs.IT↗

arXiv2018

Storage-Repair Bandwidth Trade-off for Wireless Caching with Partial Failure and Broadcast Repair

Repair of multiple partially failed cache nodes is studied in a distributed wireless content caching system, where $r$ out of a total of $n$ cache nodes lose part of their cached data. Broadcast repair of failed cache contents at the network edge is studied; that is, the surviving cache nodes transmit broadcast messages to the failed ones, which are then used, together with the surviving data in their local cache memories, to recover the lost content. The trade-off between the storage capacity and the repair bandwidth is derived. It is shown that utilizing the broadcast nature of the wireless medium and the surviving cache contents at partially failed nodes significantly reduces the required repair bandwidth per node.

cs.DC↗

arXiv2018

Achieving AWGN Channel Capacity With Lattice Gaussian Coding

We propose a new coding scheme using only one lattice that achieves the $\frac{1}{2}\log(1+\SNR)$ capacity of the additive white Gaussian noise (AWGN) channel with lattice decoding, when the signal-to-noise ratio $\SNR>e-1$. The scheme applies a discrete Gaussian distribution over an AWGN-good lattice, but otherwise does not require a shaping lattice or dither. Thus, it significantly simplifies the default lattice coding scheme of Erez and Zamir which involves a quantization-good lattice as well as an AWGN-good lattice. Using the flatness factor, we show that the error probability of the proposed scheme under minimum mean-square error (MMSE) lattice decoding is almost the same as that of Erez and Zamir, for any rate up to the AWGN channel capacity. We introduce the notion of good constellations, which carry almost the same mutual information as that of continuous Gaussian inputs. We also address the implementation of Gaussian shaping for the proposed lattice Gaussian coding scheme.

cs.IT↗

arXiv2018

Almost universal codes for MIMO wiretap channels

Despite several works on secrecy coding for fading and MIMO wiretap channels from an error probability perspective, the construction of information-theoretically secure codes over such channels remains an open problem. In this paper, we consider a fading wiretap channel model where the transmitter has only partial statistical channel state information. Our channel model includes static channels, i.i.d. block fading channels, and ergodic stationary fading with fast decay of large deviations for the eavesdropper's channel. We extend the flatness factor criterion from the Gaussian wiretap channel to fading and MIMO wiretap channels, and establish a simple design criterion where the normalized product distance / minimum determinant of the lattice and its dual should be maximized simultaneously. Moreover, we propose concrete lattice codes satisfying this design criterion, which are built from algebraic number fields with constant root discriminant in the single-antenna case, and from division algebras centered at such number fields in the multiple-antenna case. The proposed lattice codes achieve strong secrecy and semantic security for all rates $R<C_b-C_e-κ$, where $C_b$ and $C_e$ are Bob and Eve's channel capacities respectively, and $κ$ is an explicit constant gap. Furthermore, these codes are almost universal in the sense that a fixed code is good for secrecy for a wide range of fading models. Finally, we consider a compound wiretap model with a more restricted uncertainty set, and show that rates $R<\bar{C}_b-\bar{C}_e-κ$ are achievable, where $\bar{C}_b$ is a lower bound for Bob's capacity and $\bar{C}_e$ is an upper bound for Eve's capacity for all the channels in the set.

cs.IT↗

arXiv2018

AWGN-Goodness is Enough: Capacity-Achieving Lattice Codes based on Dithered Probabilistic Shaping

In this paper we show that any sequence of infinite lattice constellations which is good for the unconstrained Gaussian channel can be shaped into a capacity-achieving sequence of codes for the power-constrained Gaussian channel under lattice decoding and non-uniform signalling. Unlike previous results in the literature, our scheme holds with no extra condition on the lattices (e.g. quantization-goodness or vanishing flatness factor), thus establishing a direct implication between AWGN-goodness, in the sense of Poltyrev, and capacity-achieving codes. Our analysis uses properties of the discrete Gaussian distribution in order to obtain precise bounds on the probability of error and achievable rates. In particular, we obtain a simple characterization of the finite-blocklength behavior of the scheme, showing that it approaches the optimal dispersion coefficient for \textit{high} signal-to-noise ratio. We further show that for \textit{low} signal-to-noise ratio the discrete Gaussian over centered lattice constellations can not achieve capacity, and thus a shift (or "dither") is essentially necessary.

cs.IT↗