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TOC Alert for Publication# 18 2018October 22<![CDATA[Table of contents]]>6411C1C4147<![CDATA[IEEE Transactions on Information Theory publication information]]>6411C2C2112<![CDATA[Reducing Guesswork via an Unreliable Oracle]]>$X$ , and Bob is trying to guess its value by asking questions of the form “is $X=x$ ?”. Alice answers truthfully and the game terminates once Bob guesses correctly. Before the game begins, Bob is allowed to reach out to an oracle, Carole, and ask her any yes/no question, i.e., a question of the form “is $Xin A$ ?”. Carole is known to lie with a given probability $p$ . What should Bob ask Carole if he would like to minimize his expected guessing time? When Carole is always truthful ($p=0$ ), it is not difficult to check that Bob should order the symbol probabilities in descending order and ask Carole whether the index of $X$ with respect to this order is even or odd. We show that this strategy is almost optimal for any lying probability $p$ , up to a small additive constant upper bounded by 1/4. We discuss a connection to the cutoff rate of the BSC with feedback.]]>641169416953373<![CDATA[Capacity Results on Multiple-Input Single-Output Wireless Optical Channels]]>641169546966604<![CDATA[Strong Functional Representation Lemma and Applications to Coding Theorems]]>$X$ and $Y$ , it is possible to represent $Y$ as a function of $(X,Z)$ such that $Z$ is independent of $X$ and $I(X;Z|Y)le log (I(X;Y)+1)+4$ bits. We use this strong functional representation lemma (SFRL) to establish a bound on the rate needed for one-shot exact channel simulation for general (discrete or continuous) random variables, strengthening the results by Harsha et al. and Braverman and Garg, and to establish new and simple achievability results for one-shot variable-length lossy source coding, multiple description coding, and Gray–Wyner system. We also show that the SFRL can be used to reduce the channel with state noncausally known at the encoder to a point-to-point channel, which provides a simple achievability proof of the Gelfand–Pinsker theorem.]]>641169676978348<![CDATA[A Variational Characterization of Rényi Divergences]]>641169796989270<![CDATA[The Minrank of Random Graphs]]>minrank of a directed graph $G$ is the minimum rank of a matrix $M$ that can be obtained from the adjacency matrix of $G$ by switching some ones to zeros (i.e., deleting edges) and then setting all diagonal entries to one. This quantity is closely related to the fundamental information-theoretic problems of (linear) index coding (Bar-Yossef et al.), network coding (Effros et al.), and distributed storage (Mazumdar, ISIT, 2014). We prove tight bounds on the minrank of directed Erdős–Rényi random graphs $G(n,p)$ for all regimes of $pin [{0,1}]$ . In particular, for any constant $p$ , we show that $mathsf {minrk}(G) = Theta (n/log n)$ with high probability, where $G$ is chosen from $G(n,p)$ . This bound gives a near quadratic improvement over the previous best lower bound of $Omega (sqrt {n})$ (Haviv and Langberg), and partially settles an open problem raised by Lubetzky and Stav. Our lower bound matches the well-known upper bound obtained by the “clique covering” solution and settles the linear index coding problem for random knowledge graphs.]]>641169906995252<![CDATA[Noisy Broadcast Networks With Receiver Caching]]>capacity-memory tradeoff of this network (the largest rate at which messages can be reliably communicated for given cache sizes). The lower bound is achieved by means of a joint cache-channel coding scheme and significantly improves over traditional schemes based on the separate cache-channel coding. In particular, it is shown that the joint cache-channel coding offers new global caching gains that scale with the number of strong receivers in the network. The upper bound uses bounding techniques from degraded broadcast channels and introduces an averaging argument to capture the fact that the contents of the cache memories are designed before knowing users’ demands. The derived upper bound is valid for all stochastically degraded broadcast channels. The lower and upper bounds match for a single weak receiver (and any number of strong receivers) when the cache size does not exceed a certain threshold. Improved bounds are presented for the special case of a single weak and a single strong receiver with two files and the bounds are shown to match over a large range of cache sizes.]]>6411699670161214<![CDATA[Distributed Detection in Ad Hoc Networks Through Quantized Consensus]]>a posteriori detector is optimal; 2) the Neyman–Pearson criterion with a constant type-I error probability constraint; and 3) the Neyman–Pearson criterion with an exponential type-I error probability constraint. Leveraging recent development in distributed consensus reaching using bounded quantizers with possibly unbounded data (which are log-likelihood ratios of local observations in the context of distributed detection), we design a one-bit deterministic quantizer with a controllable threshold that leads to desirable consensus error bounds. The obtained bounds are key to establishing the optimal asymptotic detection performance. In addition, we examine the non-asymptotic performance of the proposed approach and show that the type-I and type-II error probabilities at each node can be made arbitrarily close to the centralized ones simultaneously when a continuity condition is satisfied.]]>641170177030685<![CDATA[Making Recommendations Bandwidth Aware]]>6411703170501632<![CDATA[Improved Converses and Gap Results for Coded Caching]]>6411705170621439<![CDATA[Distributed Averaging With Random Network Graphs and Noises]]>641170637080603<![CDATA[Private Information Retrieval From MDS Coded Data in Distributed Storage Systems]]>$(n,k,d)$ maximum distance separable code to store the data reliably on unreliable storage nodes. Some of these nodes can be spies which report to a third party, such as an oppressive regime, which data is being requested by the user. An information theoretic PIR scheme ensures that a user can satisfy its request while revealing no information on which data is being requested to the nodes. A user can trivially achieve PIR by downloading all the data in the DSS. However, this is not a feasible solution due to its high communication cost. We construct PIR schemes with low download communication cost. When there is $b=1$ spy node in the DSS, in other words, no collusion between the nodes, we construct PIR schemes with download cost $frac {1}{1-R}$ per unit of requested data ($R=k/n$ is the code rate), achieving the information theoretic limit for linear schemes. The proposed schemes are universal since they depend on the code rate, but not on the generator matrix of the code. Also, if $bleq n-delta k$ nodes collude, with $delta =lfloor {frac {n-b}{k}}rfloor $ , we construct linear PIR schemes with download cost $frac {b+delta k}{delta }$ .]]>641170817093804<![CDATA[Coding for Racetrack Memories]]>$d$ deletions with $d+1$ heads if the heads are well separated. Similar results are provided for burst of deletions, sticky insertions, and combinations of both deletions and sticky i-
sertions.]]>641170947112445<![CDATA[The Velocity of the Propagating Wave for Spatially Coupled Systems With Applications to LDPC Codes]]>6411711371311378<![CDATA[On Constructing Primitive Roots in Finite Fields With Advice]]>$p^{n}$ elements of characteristic $p$ remains to be a hard computational problem with the bottlenecks coming from both locating a small set of possible candidates and also factoring $p^{n}-1$ in order to test these candidates. Kopparty et al. (2016) have introduced a question of designing a fast algorithm to find primitive roots with a short advice from an oracle. Trivially, for an $m$ -bit prime $p$ , such a primitive root can be fully described by about $mn$ bits of information received from an all-powerful oracle. Here, we have shown that one can achieve this in polynomial time and with about $(1/2+o(1))m + O(log n)$ bits of advice.]]>641171327136205<![CDATA[Locally Repairable Codes With Unequal Local Erasure Correction]]>641171377152349<![CDATA[On the Finite Length Scaling of <inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula>-Ary Polar Codes]]>$q$ -ary alphabet is studied. Recently, it has been shown that the blocklength of polar codes with prime alphabet size scales polynomially with respect to the inverse of the gap between code rate and channel capacity. However, except for the binary case, the degree of the polynomial in the bound is extremely large. In this paper, a different approach to computing the degree of this polynomial for any prime alphabet size is shown. This approach yields a lower degree polynomial for various values of the alphabet size that were examined. It is also shown that even lower degree polynomial can be computed with an additional numerical effort.]]>6411715371701416<![CDATA[Lower Bounds on the Covering Radius of the Non-Binary and Binary Irreducible Goppa Codes]]>641171717177366<![CDATA[Asymptotically Optimal Regenerating Codes Over Any Field]]>et al., we obtain two explicit families regenerating codes. These codes approach the cut-set bound as the reconstruction degree increases and may be realized over any given finite field if the file size is large enough. Essentially, these codes constitute a constructive proof that the cut-set bound does not imply a field size restriction, unlike some known bounds for ordinary linear codes. The first construction attains the cut-set bound at the MBR point asymptotically for all parameters, whereas the second one attains the cut-set bound at the MSR point asymptotically for low-rate parameters. Even though these codes require a large file size, this restriction is trivially satisfied in most conceivable distributed storage scenarios, that are the prominent motivation for regenerating codes.]]>641171787187683<![CDATA[Explicit MDS Codes With Complementary Duals]]>641171887193236<![CDATA[The Wiretapped Diamond-Relay Channel]]>$M$ relays through orthogonal links and the relays transmit to the destination over a wireless multiple-access channel in the presence of an eavesdropper. The eavesdropper not only observes the relay transmissions through another multiple-access channel but also observes a certain number of source-relay links. The legitimate terminals know neither the eavesdropper’s channel state information nor the location of source-relay links revealed to the eavesdropper except the total number of such links. For this wiretapped diamond-relay channel, we establish the optimal secure d.o.f. In the achievability part, our proposed scheme uses the source-relay links to transmit a judiciously constructed combination of message symbols, artificial noise symbols, and fictitious message symbols associated with secure network coding. The relays use a combination of beamforming and interference alignment in their transmission scheme. For the converse part, we take a genie-aided approach assuming that the location of wiretapped links is known.]]>641171947207624<![CDATA[GDoF Region of the MISO BC: Bridging the Gap Between Finite Precision and Perfect CSIT]]>$K=2$ user MISO BC, i.e., the wireless broadcast channel where a transmitter equipped with $K=2$ antennas sends independent messages to $K=2$ receivers each of which is equipped with a single antenna, the generalized degrees of freedom (GDoFs) region are characterized for arbitrary channel strength and channel uncertainty levels for each of the channel coefficients. The result is extended to K>2 users under additional restrictions which include the assumption of symmetry.]]>641172087217432<![CDATA[Almost Universal Codes for MIMO Wiretap Channels]]>$R< C_{b}-C_{e}-kappa $ , where $C_{b}$ and $C_{e}$ are Bob and Eve’s channel capacities, respectively, and $kappa $ 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}-kappa $ 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.]]>641172187241721<![CDATA[Asymptotic Analysis and Spatial Coupling of Counter Braids]]>et al. in 2007 for per-flow measurements on high-speed links which can be decoded with low complexity using message passing (MP). CBs achieve an asymptotic compression rate (under optimal decoding) that matches the entropy lower bound of the flow size distribution. In this paper, we apply the concept of spatial coupling to CBs to improve the performance of the original CBs and analyze the performance of the resulting spatially-coupled CBs (SC-CBs). We introduce an equivalent bipartite graph representation of CBs with identical iteration-by-iteration finite-length and asymptotic performance. Based on this equivalent representation, we then analyze the asymptotic performance of single-layer CBs and SC-CBs under the MP decoding algorithm proposed by Lu et al.. In particular, we derive the potential threshold of the uncoupled system and show that it is equal to the area threshold. We also derive the Maxwell decoder for CBs and prove that the potential threshold is an upper bound on the Maxwell decoding threshold, which, in turn, is a lower bound on the maximum a posteriori (MAP) decoding threshold. We then show that the area under the extended MP extrinsic information transfer curve (defined for the equivalent graph), computed for the expected residual CB graph when a peeling decoder equivalent to the MP decoder stops, is equal to zero precisely at the area threshold. This, combined with the analysis of the Maxwell decoder and simulation results, leads us to the conjecture that the potential threshold is, in fact, equal to the Maxwell decoding threshold and hence a lower bound on the MAP decoding threshold. Interestingly, SC-CBs do not show the well-known phenomenon of threshold saturation of the MP decoding threshold to the potential threshold characteristic of spatially-coupled low-density parity-check codes and other coupled systems. However, SC-C-
s yield better MP decoding thresholds than their uncoupled counterparts. Finally, we also consider SC-CBs as a compressed sensing scheme and show that low undersampling factors can be achieved.]]>6411724272631143<![CDATA[Finite Sample Analysis of Approximate Message Passing Algorithms]]>$beta _{0}$ from a noisy measurement $y=A beta _{0} + w$ . AMP is a low-complexity, scalable algorithm for this problem. Under suitable assumptions on the measurement matrix $A$ , AMP has the attractive feature that its performance can be accurately characterized in the large system limit by a simple scalar iteration called state evolution. Previous proofs of the validity of state evolution have all been asymptotic convergence results. In this paper, we derive a concentration inequality for AMP with Gaussian matrices with independent and identically distributed (i.i.d.) entries and finite dimension $n times N$ . The result shows that the probability of deviation from the state evolution prediction falls exponentially in $n$ . This provides theoretical support for empirical findings that have demonstrated excellent agreement of AMP performance with state evolution predictions for moderately large dimensions. The concentration inequality also indicates that the number of AMP iterations $t$ can grow no faster than order $({log n}/{log log n})$ fo-
the performance to be close to the state evolution predictions with high probability. The analysis can be extended to obtain similar non-asymptotic results for AMP in other settings such as low-rank matrix estimation.]]>641172647286474<![CDATA[Median-Truncated Nonconvex Approach for Phase Retrieval With Outliers]]>median-truncated Wirtinger flow and median-reshaped Wirtinger flow, both of which provably recover the signal from a near-optimal number of measurements when the measurement vectors are composed of independent and identically distributed Gaussian entries, up to a logarithmic factor, even when a constant fraction of the measurements is adversarially corrupted. We further show that both algorithms are stable in the presence of additional dense bounded noise. Our analysis is accomplished by developing non-trivial concentration results of median-related quantities, which may be of independent interest. We provide numerical experiments to demonstrate the effectiveness of our approach.]]>6411728773101120<![CDATA[Tensor SVD: Statistical and Computational Limits]]>641173117338838<![CDATA[Distributed Testing With Cascaded Encoders]]>641173397348839<![CDATA[Forest Learning From Data and its Universal Coding]]>$n$ samples of $p$ variables, assuming that the structure is a forest, using the Chow–Liu algorithm. Specifically, for incomplete data, we construct two model selection algorithms that complete in $O(p^{2})$ steps: one obtains a forest with the maximum posterior probability given the data and the other obtains a forest that converges to the true one as $n$ increases. We show that the two forests are generally different when some values are missing. In addition, we present estimations for benchmark data sets to demonstrate that both algorithms work in realistic situations. Moreover, we derive the conditional entropy provided that no value is missing, and we evaluate the per-sample expected redundancy for the universal coding of incomplete data in terms of the number of non-missing samples.]]>641173497358723<![CDATA[Physical-Layer Security in TDD Massive MIMO]]>no training-phase jamming attack in which the adversary jams only the data communication and eavesdrops both the data communication and the training. Specifically, we show that the secure degrees of freedom (SDoF) attained in the presence of such an attack are identical to the maximum DoF attainable under no attack. Furthermore, we evaluate the number of base station (BS) antennas necessary in order to establish information theoretic security without even a need for Wyner encoding for a given rate of information leakage to the attacker. Next, we show that things are completely different once the adversary starts jamming the training phase. Specifically, we consider the pilot contamination attack, called training-phase jamming in which the adversary jams and eavesdrops both the training and the data communication. We show that under such an attack, the maximum achieved SDoF is identical to zero. Furthermore, the maximum achievable secure rates of users also vanish, even in the asymptotic regime in the number of the BS antennas. We finally address this attack and show that, under training-phase jamming, if the number of pilot signals is scaled in a certain way and the pilot signal assignments can be hidden from the adversary, the users achieve an SDoF identical to the maximum achievable DoF under no attack.]]>641173597380891<![CDATA[The Conditional Common Information in Classical and Quantum Secret Key Distillation]]>conditional common information (cCI) and the coarse-grained conditional common information (ccCI). Both quantities are shown to be useful technical tools in the study of classical and quantum resource transformations. In particular, the ccCI is shown to have an operational interpretation as the optimal rate of secret key extraction from an eavesdropped classical source $p_{XYZ}$ when Alice ($X$ ) and Bob ($Y$ ) are unable to communicate but share common randomness with the eavesdropper Eve ($Z$ ). Moving to the quantum setting, we consider two different ways of generating a tripartite quantum state from classical correlations $p_{XYZ}$ : 1) coherent encodings $sum _{xyz}sqrt {p_{xyz}} |xyzrangle $ and 2) incoherent encodings $sum _{xyz}p_{xyz} |xyzrangle langle xyz|$ . We study how well can Alice and Bob extract secret key from these quantum sources using quantum operations compared with the extraction of key from the underlying classical sources $p_{XYZ}$ using classical operations. While the power of quantum mechanics increases Alice and Bob’s ability to generate shared randomness, it also equips Eve with a greater arsenal of eavesdropping attacks. Therefore, it is not obvious wh-
gains the greatest advantage for distilling secret key when replacing a classical source with a quantum one. We first demonstrate that the classical key rate of $p_{XYZ}$ is equivalent to the quantum key rate for an incoherent quantum encoding of the distribution. For coherent encodings, we next show that the classical and quantum rates are generally incomparable, and in fact, their difference can be arbitrarily large in either direction. Finally, we introduce a “zoo” of entangled tripartite states all characterized by the conditional common information of their encoded probability distributions. Remarkably, for these states almost all entanglement measures, such as Alice and Bob’s entanglement cost, squashed entanglement, and relative entropy of entanglement, can be sharply bounded or even exactly expressed in terms of the conditional common information. In the latter case, we thus present a rare instance in which the various entropic entanglement measures of a quantum state can be explicitly calculated.]]>641173817394614<![CDATA[Expected Communication Cost of Distributed Quantum Tasks]]>641173957423740<![CDATA[Polar Codes for Arbitrary Classical-Quantum Channels and Arbitrary cq-MACs]]>$O(Nlog N)$ operations, where $N$ is the blocklength of the code. A quantum successive cancellation decoder for the constructed codes is proposed. It is shown that the probability of error of this decoder decays faster than $2^{-N^{beta }}$ for any $beta < ({1}/{2})$ .]]>641174247442363<![CDATA[Comments on “Improving Compressed Sensing With the Diamond Norm”–Saturation of the Norm Inequalities Between Diamond and Nuclear Norm]]>641174437445176<![CDATA[Blank page]]>6411B7446B74463<![CDATA[Blank page]]>6411B7447B74484<![CDATA[IEEE Transactions on Information Theory information for authors]]>6411C3C366