Rate vs. distortion trade-off for channels with state information

A problem of state information transmission over a state-dependent discrete memoryless channel (DMC) with independent and identically distributed (i.i.d.) states, known strictly causally at the transmitter is investigated. It is shown that block-Markov encoding coupled with channel state estimation conditioned on treating the decoded message and received channel output as side information at the decoder yields the minimum state estimation error. This same channel can also be used to send additional independent information at the expense of a higher channel state estimation error. The optimal tradeoff between the rate of the independent information that can be reliably transmitted and the state estimation error is characterized via the capacity-distortion function. It is shown that any optimal tradeoff pair can be achieved via a simple rate-splitting technique, whereby the transmitter appropriately allocates its rate between pure information transmission and state estimation.

We consider the problem of optimal probing of communication channel at the encoder for discrete memoryless channels (DMC) with i.i.d. states. The encoder generates an action sequence dependent on the message with which it probes the channel and hence acquires partial state information. This is further used causally or non-causally to generate channel input symbols while decoder may or may not have partial channel state information. We call the maximum achievable rate for such systems as the `Probing Capacity'. In this paper we characterize this capacity when channel inputs are allowed to depend causally or non-causally on partially observed state sequence.We motivate the problem by addressing the issue of characterizing the essential trade-off between the capacity and the cost `to observe or not to observe' the channel states at the encoder.

The best reconstructions of the history of life will use both molecular time estimates and fossil data. Errors in molecular rate estimation typically are unaccounted for and no attempts have been made to quantify this uncertainty comprehensively. Here, focus is primarily on fossil calibration error because this error is least well understood and nearly universally disregarded. Our quantification of errors in the synapsid-diapsid calibration illustrates that although some error can derive from geological dating of sedimentary rocks, the absence of good stem fossils makes phylogenetic error the most critical. We therefore propose the use of calibration ages that are based on the first undisputed synapsid and diapsid. This approach yields minimum age estimates and standard errors of 306.1 +/- 8.5 MYR for the divergence leading to birds and mammals. Because this upper bound overlaps with the recent use of 310 MYR, we do not support the notion that several metazoan divergence times are significantly overestimated because of serious miscalibration (sensuLee 1999). However, the propagation of relevant errors reduces the statistical significance of the pre-K-T boundary diversification of many bird lineages despite retaining similar point time estimates. Our results demand renewed investigation into suitable loci and fossil calibrations for constructing evolutionary timescales.

On the fast-fading discrete memoryless channels (DMCs) with channel state information at the receiver a necessary and sufficient condition is determined for the tilted channel associated with an input distribution to be the product of a tilted channel state distribution and the tilted channel associated with the same input distribution on the non-fading DMC for the given channel state. On fading channels for which constituent channels associated with different channel states share a common Augustin capacity-achieving input distribution aforementioned necessary and sufficient condition is shown to hold, and a parametric form for the sphere packing exponent (SPE) is obtained in terms of the tilted channel state distribution and the tilted channel of the nonfading DMC for the given channel state. The SPE of fast-fading binary erasure and binary symmetric channels with channel state information at the receiver are analyzed as examples.

We consider the problem of scheduling transmissions over a wireless downlink when channel state information (CSI) is not available to the transmitter. We assume channel states are time varying and evolve according to a Markov Chain. We show that using current QLI does not stabilize the system due to correlations between backlog and channel state. We show that the throughput optimal scheduling policy in this context must use delayed queue length information (QLI). We characterize the extent to which QLI must be delayed as a function of the channel state statistics.

We study the task of localizing multipartite entanglement in pure quantum states onto a subsystem by measuring the remaining systems. To this end, we fix a multipartite entanglement measure and consider two quantities: the multipartite entanglement of assistance (MEA), defined as the entanglement measure averaged over the post-measurement states and maximized over arbitrary measurements; and the localizable multipartite entanglement (LME), defined in the same way but restricted to only local single-system measurements. Both quantities generalize previously considered bipartite entanglement localization measures. In our work we choose the n-tangle, the genuine multipartite entanglement concurrence and the concentratable entanglement (CE) as the underlying seed measure, and discuss the resulting MEA and LME quantities. First, we prove easily computable upper and lower bounds on MEA and LME and establish Lipschitz-continuity for the n-tangle and CE-based LME and MEA. Using these bounds we investigate the typical behavior of entanglement localization by deriving concentration inequalities for the MEA evaluated on Haar-random states and performing numerical studies for small tractable system sizes. We then turn our attention to protocols that transform graph states. We give a simple criterion based on a matrix equation to decided whether states with a specified n-tangle value can be obtained from a given graph state, providing no-go theorems for a broad class of such graph state transformations beyond the usual “local Clifford plus local Pauli measurement” framework. This analysis is generalized to weighted graph states, which provide a realistic error model in current experiments preparing graph state. Our entanglement localization framework certifies the near-optimality of recently discussed local-measurement protocols to transform uniformly weighted line graph states into GHZ states, even when considering arbitrary entangled measurements. Finally, we demonstrate how our MEA and LME quantities can be used to detect critical phenomena such as phase transitions in transversal field Ising models. Since entanglement localization is operationally relevant throughout quantum networking and measurement-based quantum computation, our framework of results based on the MEA and LME has the potential for broad applications in these fields.

We study the two-user discrete memoryless compound multiple access channel (MAC) with common message and two specially correlated channel states each known non-causally by one of the encoders. Two channel states are correlated in the sense of Slepian-Wolf (SW) in which two correlated states are modeled by three independent states: a common state and two private states. By using superposition coding, binning scheme and jointly decoding, we propose several achievable rates for various cases of the two-user compound MAC with non-causal Slepian-Wolf channel states available at encoders and common message or conferencing encoders. Also, we show that the obtained achievable rate regions are optimal when perfect states are known at both decoders as well.

Spectrum sensing use current primary user (PU) received signal to detect PU channel state at current time, however PU channel state in near future using previous detected channel state information can secure an efficient utilization of unoccupied spectrum, also can help in preventing harmful interference with PU and solving problem of latency between spectrum sensing and data transmission which caused by hardware implementation. In this paper, an algorithm Based on K-Nearest Neighbor (KNN) Classifier and Kalman Filter is proposed to detect and predict future of primary user channel state the spectrum holes. The new algorithm based on training KNN classifier over a set containing some frame time slots energy test statistics along with their corresponding decisions about presence or absence of primary user transmission, so as to predict decisions for new unclassified time slot, then utilize Kalman filter to track PU primary user channel state by next expected spectrum holes based on previously detected hole. Experimental results show that proposed approach is efficient and easy to implement for detecting and tracking predicting PU channel state. KEYWORD: Channel state tracking; Channel state prediction; K-nearest neighbor classifier; Kalman Filter; Spectrum sensing time slot

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We consider the two-user MISO broadcast channel where the transmitter has imperfect knowledge on the current channel state, in addition to delayed channel state information. The degree of freedom region is completely characterized. The optimal scheme smoothly bridges between the scheme recently proposed by Maddah-Ali and Tse with no current state information and a simple zero-forcing beamforming with perfect current state information. The essential ingredients of this scheme lie in the quantization and multicasting of the overheard interferences, while broadcasting new private messages.

We study an analog of the well-known Gel’fand Pinsker channel which uses quantum states for the transmission of the data. We consider the case where both the sender’s inputs to the channel and the channel states are to be taken from a finite set (the cq-channel with state information at the sender). We distinguish between causal and non-causal channel state information input by the sender. The receiver remains ignorant, throughout. We give a single-letter description of the capacity in the first case. In the second case we present two different regularized expressions for the capacity. It is an astonishing and unexpected result of our work that a simple change from causal to non-causal channel state information by the encoder causes the complexity of a numerical computation of the capacity formula to change from trivial to seemingly difficult. Still, even the non-single letter formula allows one to draw nontrivial conclusions, for example regarding the continuity of the capacity with respect to changes in the system parameters. The direct parts of both coding theorems are based on a special class of positive operator valued measurements (POVMs) which are derived from orthogonal projections onto certain representations of the symmetric groups. This approach supports a reasoning that is inspired by the classical method of types. In combination with the non-commutative union bound these POVMs yield an elegant method of proof for the direct part of the coding theorem in the first case.

We propose a new subcarrier allocation algo- rithm for Orthogonal Frequency Division Multiple Access (OFDMA) that gives fair allocation of capacity to multiple users with different channel and traffic characteristics. This is achieved by utilizing buffer state information and mea- sured traffic statistics in addition to channel state feedback. Multiuser diversity gains are achieved in the proposed al- gorithm by scheduling across both time (buffering) and fre- quency (subcarriers). Simulation results are shown to illus- trate (a) improved capacity allocation and throughput, and (b) larger admissible traffic when compared to the existing algorithms.

This paper fully determines the degree-of-freedom (DoF) region of two-user interference channels with arbitrary number of transmit and receive antennas in the case of isotropic and independent (or block-wise independent) fading, where the channel state information is available to the receivers but not to the transmitters. Thus, the DoF gap between previous upper and lower bounds due to the authors, Vaze and Varanasi, and Huang, Jafar, Shamai, and Vishwanath is closed. The DoF result characterizes the capacity region to the first order of the logarithm of the signal-to-noise ratio (SNR) in the high-SNR regime. The DoF region is achievable by using random Gaussian codebooks independent of the channel states, which implies that it is impossible to increase the DoF using beamforming and interference alignment in the absence of channel state information at the transmitters.

The impact of inaccurate channel state information at the transmitter for a variable rate variable power multilevel quadrature amplitude modulation (VRVP-MQAM) system over a Rayleigh flat-fading channel is investigated. A system model is proposed with rate and power adaptation based on the estimates of instantaneous signal-to-noise ratio (SNR) and bit error rate (BER). A pilot symbol assisted modulation scheme is used for SNR estimation. The BER estimator is derived using a maximum a posteriori approach and a simplified closed-form solution is obtained as a function of only the second order statistical characterization of the channel state imperfection. Based on the proposed system model, rate and power adaptation is derived for the optimization of spectral efficiency subject to an average power constraint and an instantaneous BER requirement. The performance of the VRVP-MQAM system under imperfect channel state information (CSI) is evaluated. We show that the proposed VRVP-MQAM system that employs optimal solutions based on the statistical characterization of CSI imperfection achieves a higher spectral efficiency as compared to an ideal CSI assumption based method.

We propose a compression/transmission scheme that allows the quality of the reconstructed signal to gracefully degrade as the channel quality drops, as well as steadily improve with the channel improvement. The main idea is to partition the channel and/or network resources into m units (e.g., sub-bands, packets) and compress the source independently m times to perfectly match single unit resources, thus creating m independently distorted source versions. Consequently, we create a multiple-description, joint source-channel like architecture, that enables efficient reconstruction starting from a single received description with improvements onward. We further split the compression rate in two parts, allocating one to a rate-distortion optimal encoder, and the other to transmitting uncoded source symbols. We show how this architecture can easily leverage modularity in terms of adjustable rate-splitting ratio and the maximum number of descriptions, e.g., through software parameters, to simultaneously and robustly (i.e. avoiding the cliff effect) achieve operating points close to rate-distortion curve for many channel states. We demonstrate how statistical description of channel states (or performance statistics of content delivery network) can be used to set the two parameters constructively in terms of converging to optimal operation in the range of interest.