Generalized degrees of freedom region for MIMO interference channel with feedback

We consider two-user MIMO broadcast and interference channels in which confidential messages intended for each receiver are kept secret from the other receiver. The confidential secrecy rates are nonconvex functions of transmit covariance matrices, which makes it intractable to find optimal transmit covariance matrices analytically. In the MIMO broadcast channels, we prove the weighted secrecy sum rate maximization has zero duality gap and KKT conditions are necessary conditions for the optimal solution. We apply the block successive lower-bound maximization technique to nonconvex weighted secrecy sum rate maximization problems. We also derive numerical algorithms for MIMO interference channels and Gaussian wiretap channels with a cooperative jammer. Every limit point achieved by the proposed algorithms is a local optimal solution that satisfies the KKT conditions. Numerical results show that the proposed algorithms outperform existing suboptimal algorithms in terms of secrecy rates.

In order to explore the compatibility of blind interference alignment schemes with channel knowledge based beamforming and zero-forcing schemes, in this work we initiate the study of the degrees of freedom (DoF) of the two-user MIMO interference channel (IC) where Transmitter 1 is equipped with reconfigurable antennas and has no channel knowledge while Transmitter 2 has partial channel knowledge but no reconfigurable antennas. In particular we focus on two challenging examples to show how blind interference alignment, rate-splitting and partial zero-forcing schemes may be combined in non-trivial ways. Limited generalizations of these examples to broader parameter regimes are also presented.

We study the following natural question: Which cryptographic primitives (if any) can be realized by functions with constant input locality, namely functions in which every bit of the input influences only a constant number of bits of the output? This continues the study of cryptography in low complexity classes. It was recently shown by Applebaum et al. (FOCS 2004) that, under standard cryptographic assumptions, most cryptographic primitives can be realized by functions with constant output locality, namely ones in which every bit of the output is influenced by a constant number of bits from the input. We (almost) characterize what cryptographic tasks can be performed with constant input locality. On the negative side, we show that primitives which require some form of non-malleability (such as digital signatures, message authentication, or non-malleable encryption) cannot be realized with constant input locality. On the positive side, assuming the intractability of certain problems from the domain of error correcting codes (namely, hardness of decoding a random binary linear code or the security of the McEliece cryptosystem), we obtain new constructions of one-way functions, pseudorandom generators, commitments, and semantically-secure public-key encryption schemes whose input locality is constant. Moreover, these constructions also enjoy constant output locality and thus they give rise to cryptographic hardware that has constant-depth, constant fan-in and constant fan-out. As a byproduct, we obtain a pseudorandom generator whose output and input locality are both optimal (namely, 3).

Energy efficiency (EE) optimization is investigated for a multi-user cognitive radio network (CRN) over multiple-input-multiple-output (MIMO) interference channels (ICs). To reduce the system overhead due to information exchange among the secondary CR uses (SUs), the EE optimization problem is formulated as a non-cooperative game, where each SU transmitter competes against the other SU pairs by optimizing its transmit covariance matrix. Specifically, each multi-antenna SU maximizes locally its energy efficiency in terms of the number of bits transmitted per unit energy consumption, subject to the per-SU transmit power constraint and the primary user (PU) perceived total interference constraint. It is proved that the formulated non-cooperative game admits at least one Nash equilibrium (NE), and the sufficient condition for a unique NE is derived subsequently. Primal decomposition is employed in the local EE optimization problem to relax the coupling PU perceived interference constraint such that fully distributed operation is allowed. A distributed iterative EE optimization algorithm (DIEEOA) is then proposed to obtain the unique NE, which is shown to converge to the global optimum. Linear precoding techniques are employed to mitigate the impacts of multi-user interference and imperfect channel state information (CSI). Through numerical simulations, effectiveness of the proposed scheme is validated and the system setting parameters' impacts on the performance are studied.

Fast radio broadcasting with advice

It is very important that the radar sensor network has autonomous capabilities such as self-managing, etc. Quite often, MIMO interference channels are applied to radar sensor networks, and for self-managing purpose, interference management in MIMO interference channels is critical. Interference alignment (IA) has the potential to dramatically improve system throughput by effectively mitigating interference in multi-user networks at high signal-to-noise (SNR). However, the implementation of IA predominantly relays on perfect and global channel state information (CSI) at all transceivers. A large amount of CSI has to be fed back to all transmitters, resulting in a proliferation of feedback bits. Thus, IA with limited feedback has been introduced to reduce the sum feedback overhead. In this paper, by exploiting the advantage of heterogeneous path loss, we first investigate the throughput of IA with limited feedback in interference channels while each user transmits multi-streams simultaneously, then we get the upper bound of sum rate in terms of the transmit power and feedback bits. Moreover, we propose a dynamic feedback scheme via bit allocation to reduce the throughput loss due to limited feedback. Simulation results demonstrate that the dynamic feedback scheme achieves better performance in terms of sum rate.

In a K-pair-user two-way Gaussian interference channel (IC), 2K messages and 2K transmitters/receivers form a Gaussian K-user IC in the forward direction (K messages) and another Gaussian K-user IC in the backward direction (K messages) which operate simultaneously in full-duplex mode. All nodes are permitted to interact, i.e. adapt current channel inputs to past received signals. We derive a new sum-rate outer bound for linear deterministic and Gaussian noise channels allowing for interaction, but show that for symmetric scenarios and certain interference regimes (moderately weak and strong), non-interactive schemes achieve to within a constant gap of this outer bound. That is, interaction for symmetric channels in certain interference regimes may only improve the sum-rate by a constant number of bits per channel use.

This paper studies a two-user Gaussian interference channel with an in-band-reception and out-of-band-transmission relay, where the link between the relay and the two receivers is modeled as a degraded broadcast channel. It is shown that a generalized hash-and-forward (GHF) relaying strategy can achieve the capacity region of this channel to within a constant number of bits in a certain weak relay regime, where the transmitter-to-relay link gains are not unboundedly stronger than the interference links between the transmitters and the receivers. In such a regime, the GHF relaying strategy can be performed in an incremental fashion, where the relay message to one receiver is a degraded version of the message to the other receiver. A generalized-degree-of-freedom analysis reveals that in the symmetric channel setting, each common relay bit can improve the sum rate roughly by about one bit or two bits asymptotically, and the rate gain can be thought as coming solely from the improvement of the common message rates.

Previously, the authors have shown that linear precoding with only private streams can have unbounded gap to the sum capacity of the two-user multi-input single-output (MISO) broadcast channel (BC), and that rate-splitting (RS) combined with zero-forcing (ZF) can reduce the gap to a constant number of bits per channel use. In this paper, we extend the investigation to the general K-user multiple-input multiple-output (MIMO) channel. We propose a RS scheme with minimum mean square error (MMSE) precoding. First, we show that the proposed scheme achieves the whole capacity region to within a constant gap in the two-user case. Second, we prove that the proposed scheme does not enjoy the same optimality in the three-user case in general. Third, we provide a simple pathological example showing why RS with linear precoding does not work beyond the two-user case. The current study reveals a fundamental gap between the transmitter-side and the receiver-side interference mitigation.

We consider a fast fading 2-receiver Broadcast channel (BC), where one of the recievers is legitimate and the other is malicious/unintended. The instantaneous Channel State Information (CSI) is assumed to be known only at the receivers (CSIR). The secrecy capacity of this channel is characterized within 11 bits irrespective of fading statistics and Signal-to- Noise Ratios (SNRs). This is achieved by deriving a new upper bound to the secrecy capacity of the channel and two new lower bounds. The upper bound is derived by approximating Complementary Cumulative Distribution Functions (CCDFs) of the two links by corresponding staircase functions and has the desirable property of easy computability for arbitrary fading statistics. The smaller lower bound, although looser, has a form which can be analytically compared with the upper bound and facilitates the approximate secrecy capacity characterization. It is proved that, the so called Binary Expansion Signaling with Reverse Stripping (BES-RS) scheme can achieve a secrecy rate larger than both these lower bounds. This result establishes BES-RS scheme as a practically implementable coding scheme that can achieve the secrecy capacity of the FWC within a constant number of bits, where the constant is universal across all fading statistics and SNR. Explicit numerical computation of these bounds shows that the difference between the secrecy rate achievable by the BES-RS scheme and the upper bound is much smaller than the aforementioned universal constant. This in turn suggests that, much of the gap of 11 bits originates from the loosness introduced to bring the two bounds in a compatiable form.

We exhibit a two-prover perfect zero-knowledge proof system for 3-SAT. In this protocol, the verifier asks a single message to each prover, whose size grows logarithmically in the size of the 3-SAT formula. Each prover's answer consists of only a constant number of bits. The verifier will always accept correct proofs. Given an unsatisfiable formula S the verifier will reject with probability at least ?((|S| - max-sat(S))/|S|, where max-sat(S) denotes the maximum number of clauses of S that may be simultaneously satisfied, and |S| denotes the total number of clauses of S. Using a recent result by Arora et al [2], we can construct for any language in NP a protocol with the property that any nonmember of the language be rejected with constant probability.

Fast periodic graph exploration with constant memory

This paper deals with the problem of multicasting a set of discrete\nmemoryless correlated sources (DMCS) over a cooperative relay network.\nNecessary conditions with cut-set interpretation are presented. A \\emph{Joint\nsource-Wyner-Ziv encoding/sliding window decoding} scheme is proposed, in which\ndecoding at each receiver is done with respect to an ordered partition of other\nnodes. For each ordered partition a set of feasibility constraints is derived.\nThen, utilizing the sub-modular property of the entropy function and a novel\ngeometrical approach, the results of different ordered partitions are\nconsolidated, which lead to sufficient conditions for our problem. The proposed\nscheme achieves operational separation between source coding and channel\ncoding. It is shown that sufficient conditions are indeed necessary conditions\nin two special cooperative networks, namely, Aref network and finite-field\ndeterministic network. Also, in Gaussian cooperative networks, it is shown that\nreliable transmission of all DMCS whose Slepian-Wolf region intersects the\ncut-set bound region within a constant number of bits, is feasible. In\nparticular, all results of the paper are specialized to obtain an achievable\nrate region for cooperative relay networks which includes relay networks and\ntwo-way relay networks.\n

We study the problem of constructing locally computable universal one-way hash functions (UOWHFs) $$\mathcal {H}:\{0,1\}^n \rightarrow \{0,1\}^m$$ . A construction with constant output locality, where every bit of the output depends only on a constant number of bits of the input, was established by Applebaum et al. (SIAM J Comput 36(4):845–888, 2006). However, this construction suffers from two limitations: (1) it can only achieve a sublinear shrinkage of $$n-m=n^{1-\epsilon }$$ and (2) it has a super-constant input locality, i.e., some inputs influence a large super-constant number of outputs. This leaves open the question of realizing UOWHFs with constant output locality and linear shrinkage of $$n-m= \epsilon n$$ , or UOWHFs with constant input locality and minimal shrinkage of $$n-m=1$$ . We settle both questions simultaneously by providing the first construction of UOWHFs with linear shrinkage, constant input locality and constant output locality. Our construction is based on the one-wayness of “random” local functions—a variant of an assumption made by Goldreich (Studies in Complexity and Cryptography, 76–87, 2011; ECCC 2010). Using a transformation of Ishai et al. (STOC, 2008), our UOWHFs give rise to a digital signature scheme with a minimal additive complexity overhead: signing n-bit messages with security parameter $$\kappa $$ takes only $$O(n+\kappa )$$ time instead of $$O(n\kappa )$$ as in typical constructions. Previously, such signatures were only known to exist under an exponential hardness assumption. As an additional contribution, we obtain new locally computable hardness amplification procedures for UOWHFs that preserve linear shrinkage.

We study the problem of constructing locally computable Universal One-Way Hash Functions (UOWHFs) \(\mathcal{H}:\{0,1\}^n \rightarrow \{0,1\}^m\). A construction with constant output locality, where every bit of the output depends only on a constant number of bits of the input, was established by [Applebaum, Ishai, and Kushilevitz, SICOMP 2006]. However, this construction suffers from two limitations: (1) It can only achieve a sub-linear shrinkage of n − m = n 1 − ε; and (2) It has a super-constant input locality, i.e., some inputs influence a large super-constant number of outputs. This leaves open the question of realizing UOWHFs with constant output locality and linear shrinkage of n − m = εn, or UOWHFs with constant input locality and minimal shrinkage of n − m = 1.We settle both questions simultaneously by providing the first construction of UOWHFs with linear shrinkage, constant input locality, and constant output locality. Our construction is based on the one-wayness of “random” local functions – a variant of an assumption made by Goldreich (ECCC 2000). Using a transformation of [Ishai, Kushilevitz, Ostrovsky and Sahai, STOC 2008], our UOWHFs give rise to a digital signature scheme with a minimal additive complexity overhead: signing n-bit messages with security parameter κ takes only O(n + κ) time instead of O(nκ) as in typical constructions. Previously, such signatures were only known to exist under an exponential hardness assumption. As an additional contribution, we obtain new locally-computable hardness amplification procedures for UOWHFs that preserve linear shrinkage.KeywordsHash FunctionLinear ShrinkageRandom StringPseudorandom GeneratorInput LocalityThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.