Communication complexity

About: Communication complexity is a research topic. Over the lifetime, 3870 publications have been published within this topic receiving 105832 citations.

Strong communication complexity or generating quasi-random sequences from two communicating semi-random sources

Abstract: The semi-random source, defined by Santha and Vazirani, is a general mathematical mode for imperfect and correlated sources of randomness (physical sources such as noise dicdes). In this paper an algorithm is presented which efficiently generates “high quality” random sequences (quasirandom bit-sequences) from two independent semi-random sources. The general problem of extracting “high quality” bits is shown to be related to communication complexity theory, leading to a definition of strong communication complexity of a boolean function. A hierarchy theorem for strong communication complexity classes is proved; this allows the previous algorithm to be generalized to one that can generate quasi-random sequences from two communicating semi-random sources

Noncoherent MIMO Communication: Grassmannian Constellations and Efficient Detection

Abstract: This paper considers the design of both a transmitter and a receiver for noncoherent communication over a frequency-flat, richly scattered multiple-input multiple-output (MIMO) channel. The design is guided by the fact that at high signal-to-noise ratios (SNRs), the ergodic capacity of the channel can be achieved by input signals that are isotropically distributed on the (compact) Grassmann manifold. The first part of the paper considers the design of Grassmannian constellations that MIMIC the isotropic distribution. A subspace perturbation analysis is used to determine an appropriate metric for the distance between Grassmannian constellation points, and using this metric, greedy, direct and rotation-based techniques for designing constellations are proposed. These techniques offer different tradeoffs between the minimum distance of the constellation and the design complexity. In addition, the rotation-based technique results in constellations that have lower storage requirements and admit a natural ldquoquasi-set-partitioningrdquo binary labeling.

Rounds in communication complexity revisited

Abstract: The $k$-round two-party communication complexity was studied in the deterministic model by [14] and [4] and in the probabilistic model by [20] and [6]. We present new lower bounds that give (1) randomization is more powerful than determinism in $k$-round protocols, and (2) an explicit function which exhibits an exponential gap between its $k$ and $(k-1)$-round randomized complexity. We also study the three party communication model, and exhibit an exponential gap in 3-round protocols that differ in the starting player. Finally, we show new connections of these questions to circuit complexity, that motivate further work in this direction.

Efficient multi-party computation with dispute control

Abstract: Secure multi-party computation (MPC) allows a set of n players to securely compute an agreed function of their inputs, even when up to t players are under the control of an (active or passive) adversary. In the information-theoretic model MPC is possible if and only if t < n/2 (where active security with t ≥ n/3 requires a trusted key setup). Known passive MPC protocols require a communication of $\mathcal{O}(n^2)$ field elements per multiplication. Recently, the same communication complexity was achieved for active security with t < n/3. It remained an open question whether $\mathcal{O}(n^2)$ complexity is achievable for n/3 ≤ t < n/2. We answer this question in the affirmative by presenting an active MPC protocol that provides optimal (t < n/2) security and communicates only $\mathcal{O}(n^2)$ field elements per multiplication. Additionally the protocol broadcasts $\mathcal{O}(n^3)$ field elements overall, for the whole computation. The communication complexity of the new protocol is to be compared with the most efficient previously known protocol for the same model, which requires broadcastingΩ(n5) field elements per multiplication. This substantial reduction in communication is mainly achieved by applying a new technique called dispute control: During the course of the protocol, the players keep track of disputes that arise among them, and the ongoing computation is adjusted such that known disputes cannot arise again. Dispute control is inspired by the player-elimination framework. However, player elimination is not suited for models with t ≥ n/3.

Low-complexity resource allocation and its application to distributed antenna systems [Coordinated and Distributed MIMO]

Abstract: The aim of this tutorial article is to present low-complexity resource allocation approaches that rely on chunks of subcarriers for downlink distributed antenna systems. The chunk-based resource allocation approach is first introduced for single-antenna base stations with the consideration of guaranteeing an average bit error rate constraint per chunk and is compared to subcarrier-based allocation. How it can be combined with maximal ratio transmission and zero-forcing beamforming for base stations with many antennas is then described. Finally, we discuss how the techniques can be applied to DASs. It is shown that in typical wireless environments chunk based resource allocation coupled with MRT and ZFB in the DAS can reduce the complexity of resource allocation significantly at the cost of negligible performance loss compared to subcarrier-based allocation.