254 research outputs found

    Information Recovery from Pairwise Measurements

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    A variety of information processing tasks in practice involve recovering nn objects from single-shot graph-based measurements, particularly those taken over the edges of some measurement graph G\mathcal{G}. This paper concerns the situation where each object takes value over a group of MM different values, and where one is interested to recover all these values based on observations of certain pairwise relations over G\mathcal{G}. The imperfection of measurements presents two major challenges for information recovery: 1) inaccuracy\textit{inaccuracy}: a (dominant) portion 1p1-p of measurements are corrupted; 2) incompleteness\textit{incompleteness}: a significant fraction of pairs are unobservable, i.e. G\mathcal{G} can be highly sparse. Under a natural random outlier model, we characterize the minimax recovery rate\textit{minimax recovery rate}, that is, the critical threshold of non-corruption rate pp below which exact information recovery is infeasible. This accommodates a very general class of pairwise relations. For various homogeneous random graph models (e.g. Erdos Renyi random graphs, random geometric graphs, small world graphs), the minimax recovery rate depends almost exclusively on the edge sparsity of the measurement graph G\mathcal{G} irrespective of other graphical metrics. This fundamental limit decays with the group size MM at a square root rate before entering a connectivity-limited regime. Under the Erdos Renyi random graph, a tractable combinatorial algorithm is proposed to approach the limit for large MM (M=nΩ(1)M=n^{\Omega(1)}), while order-optimal recovery is enabled by semidefinite programs in the small MM regime. The extended (and most updated) version of this work can be found at (http://arxiv.org/abs/1504.01369).Comment: This version is no longer updated -- please find the latest version at (arXiv:1504.01369

    The capacity region of broadcast channels with intersymbol interference and colored Gaussian noise

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    We derive the capacity region for a broadcast channel with intersymbol interference (ISI) and colored Gaussian noise under an input power constraint. The region is obtained by first defining a similar channel model, the circular broadcast channel, which can be decomposed into a set of parallel degraded broadcast channels. The capacity region for parallel degraded broadcast channels is known. We then show that the capacity region of the original broadcast channel equals that of the circular broadcast channel in the limit of infinite block length, and we obtain an explicit formula for the resulting capacity region. The coding strategy used to achieve each point on the convex hull of the capacity region uses superposition coding on some or all of the parallel channels and dedicated transmission on the others. The optimal power allocation for any point in the capacity region is obtained via a multilevel water-filling. We derive this optimal power allocation and the resulting capacity region for several broadcast channel models

    The Impact of CSI and Power Allocation on Relay Channel Capacity and Cooperation Strategies

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    Capacity gains from transmitter and receiver cooperation are compared in a relay network where the cooperating nodes are close together. Under quasi-static phase fading, when all nodes have equal average transmit power along with full channel state information (CSI), it is shown that transmitter cooperation outperforms receiver cooperation, whereas the opposite is true when power is optimally allocated among the cooperating nodes but only CSI at the receiver (CSIR) is available. When the nodes have equal power with CSIR only, cooperative schemes are shown to offer no capacity improvement over non-cooperation under the same network power constraint. When the system is under optimal power allocation with full CSI, the decode-and-forward transmitter cooperation rate is close to its cut-set capacity upper bound, and outperforms compress-and-forward receiver cooperation. Under fast Rayleigh fading in the high SNR regime, similar conclusions follow. Cooperative systems provide resilience to fading in channel magnitudes; however, capacity becomes more sensitive to power allocation, and the cooperating nodes need to be closer together for the decode-and-forward scheme to be capacity-achieving. Moreover, to realize capacity improvement, full CSI is necessary in transmitter cooperation, while in receiver cooperation optimal power allocation is essential.Comment: Accepted for publication in IEEE Transactions on Wireless Communication

    Joint design of vector quantizers and RCPC channel codes for Rayleigh fading channels

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    We study the performance of joint source and channel codes designed to minimize end-to-end distortion over a Rayleigh fading channel. We consider two joint code designs. The first joint code uses a sequential design: a standard vector quantizer (VQ) source code is designed for a perfect channel (noiseless and distortionless) and then an RCPC channel code is optimized relative to the VQ and the channel statistics. The second design jointly optimizes a channel optimized VQ (COVQ) and an RCPC channel code through an iterative design process. We consider both hard-decision and soft-decision decoding for the channel codes. In both designs the bit allocation between the source and channel codes is optimized. At this optimal bit allocation, the performance of the iterative joint design and the simpler sequential design are nearly the same over the range of SNR values that we considered. Both code designs outperform standard COVQ and by up to 6 dB, and this performance improvement is most pronounced at low SNRs
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