Noiseless Link Research Articles

Diamond Message Set Groupcasting: From an Inner Bound for the DM Broadcast Channel to the Capacity Region of the Combination Network

Multiple groupcasting over the broadcast channel (BC) is studied in a special setting. In particular, an inner bound is obtained for the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> -receiver discrete memoryless (DM) BC for the diamond message set which consists of four groupcast messages: one desired by all receivers, one by all but two receivers, and two more desired by all but each one of those two receivers. The inner bound is based on rate-splitting and superposition coding and is given in explicit form herein as a union over coding distributions of four-dimensional polytopes. This inner bound is then shown to be the capacity for a certain class of partially ordered DM BCs with order defined via the less noisy condition. When specialized to the so- called combination network, which is a class of three-layer (two-hop) broadcast networks parameterized by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2^{K}{-}1$ </tex-math></inline-formula> finite-and-arbitrary-capacity noiseless links from the source node in the first layer to as many nodes of the second layer, our top-down approach from the DM BC to the combination network yields an explicit inner bound as a single polytope via the identification of a single coding distribution. This inner bound consists of inequalities which are then identified to be within the class of generalized cut-set outer bounds recently obtained by Salimi et al for broadcast networks. We hence establish the capacity region of the general <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> -user combination network for the diamond message set, and do so in explicit and structured form. Such a result implies a certain strength of our inner bound for the DM BC in that it (a) produces a hitherto unknown capacity region when specialized to the combination network and (b) may capture many combinatorial aspects of the capacity region of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> -receiver DM BC itself for the diamond message set. Moreover, we extend that inner bound by adding binning to it. As in the no-binning case, we provide the more general inner bound in explicit form.

Multiple Access Channel Simulation

We study the problem of simulating a two-user multiple-access channel (MAC) over a multiple access network of noiseless links. Two encoders observe independent and identically distributed (i.i.d.) copies of a source random variable each, while a decoder observes i.i.d. copies of a side-information random variable. There are rate-limited noiseless communication links between each encoder and the decoder, and there is independent pairwise shared randomness between all the three possible pairs of nodes. The decoder has to output approximately i.i.d. copies of another random variable jointly distributed with the two sources and the side information. We are interested in the rate tuples which permit this simulation. This setting can be thought of as a multi-terminal generalization of the point-to-point channel simulation problem studied by Bennett et al. (2002) and Cuff (2013). When the pairwise shared randomness between the encoders is absent, the setting reduces to a special case of MAC simulation using another MAC studied by Haddadpour et al. (2013). We establish that the presence of encoder shared randomness can strictly improve the communication rate requirements. We first show that the inner bound derived from Haddadpour et al. (2013) is tight when the sources at the encoders are conditionally independent given the side-information at the decoder. This result recovers the existing results on point-to-point channel simulation and function computation over such multi-terminal networks. We then explicitly compute the communication rate regions for an example both with and without the encoder shared randomness and demonstrate that its presence strictly reduces the communication rates. Inner and outer bounds for the general case are also obtained.

Distributed Hypothesis Testing over Noisy Broadcast Channels

This paper studies binary hypothesis testing with a single sensor that communicates with two decision centers over a memoryless broadcast channel. The main focus lies on the tradeoff between the two type-II error exponents achievable at the two decision centers. In our proposed scheme, we can partially mitigate this tradeoff when the transmitter has a probability larger than 1/2 to distinguish the alternate hypotheses at the decision centers, i.e., the hypotheses under which the decision centers wish to maximize their error exponents. In the cases where these hypotheses cannot be distinguished at the transmitter (because both decision centers have the same alternative hypothesis or because the transmitter’s observations have the same marginal distribution under both hypotheses), our scheme shows an important tradeoff between the two exponents. The results in this paper thus reinforce the previous conclusions drawn for a setup where communication is over a common noiseless link. Compared to such a noiseless scenario, here, however, we observe that even when the transmitter can distinguish the two hypotheses, a small exponent tradeoff can persist, simply because the noise in the channel prevents the transmitter to perfectly describe its guess of the hypothesis to the two decision centers.

Stealthy Communication Over Adversarially Jammed Multipath Networks

We consider the problem of stealthy communication over a multipath network in the presence of an active adversary. The multipath network consists of multiple parallel noiseless links, and the adversary is able to eavesdrop and jam a subset of links. We consider two types of jamming- erasure jamming and overwrite jamming. We require the communication to be both stealthy and reliable, i.e., the adversary should be unable to detect whether or not meaningful communication is taking place, while the legitimate receiver should reconstruct any potential messages from the transmitter with high probability simultaneously. We provide inner and outer bounds on the stealthy capacities under both adversarial erasure and adversarial overwrite jamming.

The Capacity of Anonymous Communications

We consider the communication scenario where $K$ transmitters are each connected to a common receiver with an orthogonal noiseless link. One of the transmitters has a message for the receiver, who is prohibited from learning anything in the information theoretic sense about which transmitter sends the message (transmitter anonymity is guaranteed). The capacity of anonymous communications is the maximum number of bits of desired information that can be anonymously communicated per bit of total communication. For this anonymous communication problem over a parallel channel with $K$ transmitters and one receiver, we show that the capacity is $1/K$ , i.e., to communicate 1 bit anonymously, each transmitter must send a 1 bit signal. Furthermore, it is required that each transmitter has at least 1 bit correlated randomness (that is independent of the messages and is not available to the receiver) per message bit and the size of correlated randomness at all $K$ transmitters is at least $K-1$ bits per message bit.

Noisy Beam Alignment Techniques for Reciprocal MIMO Channels

Future multi-input multi-output (MIMO) wireless communications systems will use beamforming as a first-step towards realizing the capacity requirements necessitated by the exponential increase in data demands. The focus of this work is on beam alignment for time-division duplexing (TDD) systems, for which we propose a number of novel algorithms. These algorithms seek to obtain good estimates of the optimal beamformer/combiner pair (which are the dominant singular vectors of the channel matrix). They are motivated by the power method, an iterative algorithm to determine eigenvalues and eigenvectors through repeated matrix multiplication. In contrast to the basic power method which considers only the most recent iteration and assumes noiseless links, the proposed techniques consider information from all the previous iterations of the algorithm and combine them in different ways. The first technique (Sequential Least-Squares method) sequentially constructs a least-squares estimate of the channel matrix, which is then used to calculate the beamformer/combiner pair estimate. The second technique (Summed Power method) aims to mitigate the effect of noise by using a linear combination of the previously tried beams to calculate the next beam, providing improved performance in the low-SNR regime (typical for mmWave systems) with minimal complexity/feedback overhead. A third technique (Least-Squares Initialized Summed Power method) combines the good performance of the first technique at the high-SNR regime with the low-complexity advantage of the second technique by priming the summed power method with initial estimates from the sequential method.

Communication and Randomness Lower Bounds for Secure Computation

In secure multiparty computation (MPC), mutually distrusting users collaborate to compute a function of their private data without revealing any additional information about their data to other users. While it is known that information theoretically secure MPC is possible among $n$ users (connected by secure and noiseless links and have access to private randomness) against the collusion of less than $n/2$ users in the honest-but-curious model, relatively less is known about the communication and randomness complexity of secure computation. In this work, we employ information theoretic techniques to obtain lower bounds on the amount of communication and randomness required for secure MPC. We restrict ourselves to a concrete interactive setting involving 3 users under which all functions are securely computable against corruption of a single user in the honest-but-curious model. We derive lower bounds for both the perfect security case (i.e., zero-error and no leakage of information) and asymptotic security (where the probability of error and information leakage vanish as block-length goes to $\infty$). Our techniques include the use of a data processing inequality for residual information (i.e., the gap between mutual information and G\'acs-K\"orner common information), a new information inequality for 3-user protocols, and the idea of distribution switching. Our lower bounds are shown to be tight for various functions of interest. In particular, we show concrete functions which have "communication-ideal" protocols, i.e., which achieve the minimum communication simultaneously on all links in the network, and also use minimum amount of randomness. Also, we obtain the first explicit example of a function that incurs a higher communication cost than the input length in the secure computation model of "Feige, Kilian, and Naor [STOC, 1994]", who had shown that such functions exist.

Joint quantisation levels and power optimisation in uplink network multiple‐input and multiple‐output under constraint backhaul

This article studies the performance of the cooperative system where each base station (BS) is connected to a central processor (CP) via a noiseless and rate-limited backhaul link. The single-user compress-and-forward scheme is deployed at the BSs, and the problem for jointly setting the quantisation noise and the transmit power levels is left open. The authors formulate the weighted sum-rate (WSR) problem of optimising quantisation and transmit power levels for K-users and B-BSs situation. However, the problem is non-convex and difficult to be solved directly by conventional convex methods. In this work, an algorithm is proposed to solve the optimisation problem and achieve its global optimality. More importantly, the authors reveal the reason for the effect of the quantisation levels on the performance of cooperative system. Lower and upper bounds of quantisation levels are derived under the given signal to interference noise ratio (SINR) requirements. The lower and upper bounds are then demonstrated to be rather close to the numerical results. It is also numerically shown that the proposed algorithm can achieve the global optimality and is robust with respect to different multi-user situations.

Low-Complexity Interactive Algorithms for Synchronization From Deletions, Insertions, and Substitutions

Consider two remote nodes having binary sequences $X$ and $Y$, respectively. $Y$ is an edited version of ${X}$, where the editing involves random deletions, insertions, and substitutions, possibly in bursts. The goal is for the node with $Y$ to reconstruct $X$ with minimal exchange of information over a noiseless link. The communication is measured in terms of both the total number of bits exchanged and the number of interactive rounds of communication. This paper focuses on the setting where the number of edits is $o(\tfrac{n}{\log n})$, where $n$ is the length of $X$. We first consider the case where the edits are a mixture of insertions and deletions (indels), and propose an interactive synchronization algorithm with near-optimal communication rate and average computational complexity of $O(n)$ arithmetic operations. The algorithm uses interaction to efficiently split the source sequence into substrings containing exactly one deletion or insertion. Each of these substrings is then synchronized using an optimal one-way synchronization code based on the single-deletion correcting channel codes of Varshamov and Tenengolts (VT codes). We then build on this synchronization algorithm in three different ways. First, it is modified to work with a single round of interaction. The reduction in the number of rounds comes at the expense of higher communication, which is quantified. Next, we present an extension to the practically important case where the insertions and deletions may occur in (potentially large) bursts. Finally, we show how to synchronize the sources to within a target Hamming distance. This feature can be used to differentiate between substitution and indel edits. In addition to theoretical performance bounds, we provide several validating simulation results for the proposed algorithms.

Achievable rate regions for many‐to‐one Gaussian interference channel with a fusion centre

This paper considers a many-to-one Gaussian interference channel with a fusion centre (FC) where there is a K -user interference channel in which only one relay (receiver) faces interference while the remaining K-1 receivers are interference free. All the relays communicate information about their observed sequence to the FC through noiseless links at communication rate R 0. First, by analysing traditional relaying schemes, i.e., Decode and Forward, Compress and Forward and Compute and Forward, three rate-regions for this setting are derived. Then, based on nested lattice codes, a new achievable rate-region is provided. Based on the proposed scheme, one can design a transmission scheme that can recover both integer and non-integer linear combination of messages. Numerical examples show that if channel gains are integer, the proposed scheme performs similarly to the compute-and-forward scheme. In the case of non-integer channel gains, the proposed scheme outperforms other relaying schemes at high signal-to-noise ratios. Finally, it is shown that if the channel gains are larger than one and if the rate of each relay-to-FC link equals to the capacity of an AWGN channel, then the proposed scheme can achieve the capacity region in high SNR regime.

A Theory of Network Equivalence – Part II: Multiterminal Channels

A technique for bounding the capacities of networks of independent channels is introduced. Parts I and II treat point-to-point and multiterminal channels, respectively. Bounds are derived using a new tool called a bounding model. Channel 1 is an upper (lower) bounding model for channel 2 if replacing channel 2 by channel 1 in any network yields a new network whose capacity region is a superset (subset) of the capacity region of the original network. This paper derives bounding models from noiseless links, with lower bounding models corresponding to points in the channel's capacity region and upper bounding models corresponding to points in a new channel characterization called an emulation region. Replacing all channels in a network by their noiseless upper (lower) bounding models yields a network of lossless links whose capacity region is a superset (subset) of the capacity region for the original network. This converts a general (often stochastic) network into a network coding instance, enabling the application of tools and results derived in that domain. A channel's upper and lower bounding models differ when the channel can carry more information in some networks than in others. Bounding the difference between upper and lower bounding models bounds both the accuracy of the technique and the price of separating source-network coding from channel coding.

The Multisession Multilayer Broadcast Approach for Two Cooperating Receivers—How Many Sessions Are Required?

We consider the problem of transmission of a common message from a single source to two cooperating destination users, exhibiting different signal-to-noise ratios (SNR). The cooperation is performed over a noiseless link with a total capacity limit <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">coop</sub> , which the users may utilize for conversation. In order to maximize the achievable throughput, it is suggested to employ a multilayer broadcast approach combined with multisession cooperation, such that every session another layer can be decoded. Since the cooperation link is limited, an efficient cooperation scheme is required. The relaying user performs compression which utilizes the side information of the decoder in the Wyner-Ziv (WZ) spirit. In multisession cooperation the compression is in the form of successive-refinement WZ coding. After the first user decodes a layer, the minimal required information is sent back to the second user to allow both of them to decode the message. The minimal required information is achievable with random coding using a binning strategy. While it is expected that multisession cooperation will be more efficient than a single-session cooperation we show that the maximal throughput is achieved with a single session cooperation. This is shown for the nonfading channel and for the ergodic fading case. Nonetheless, for the block fading channel it is already known that multilayering and multisession outperforms single session cooperation.