Information Theoretic Results for Three-User Cognitive Channels

In this paper, we introduce the three-user cognitive radio channels with asymmetric transmitter cooperation, and derive achievable rate regions under several scenarios depending on the type of cooperation and decoding capability at the receivers. Two of the most natural cooperation mechanisms for the three-user channel are considered here: cumulative message sharing (CMS) and primary-only message sharing (PMS). In addition to the message sharing mechanism, the achievable rate region is critically dependent on the decoding capability at the receivers. Here, we consider two scenarios for the decoding capability, and derive an achievable rate region for each one of them by employing a combination of superposition and Gel'fand-Pinsker coding techniques. Finally, to provide a numerical example, we consider the Gaussian channel model to plot the rate regions. In terms of achievable rates, CMS turns out to be a better scheme than PMS. However, the practical aspects of implementing such message-sharing schemes remain to be investigated.

Information-theoretic and communication-theoretic optimal power allocation for fading channels

In this paper we review the most peculiar and interesting information-theoretic and communications features of fading channels. We first describe the statistical models of fading channels which are frequently used in the analysis and design of communication systems. Next, we focus on the information theory of fading channels, by emphasizing capacity as the most important performance measure. Both single-user and multiuser transmission are examined. Further, we describe how the structure of fading channels impacts code design, and finally overview equalization of fading multipath channels.

Scheduling for Fading Channels Under Partial Channel Information

We consider a scheduler for the downlink of a wireless channel when only partial channel-state information is available at the scheduler. We characterize the network stability region and provide two throughput-optimal scheduling policies. We also derive a deterministic bound on the mean packet delay in the network. Finally, we provide a throughput-optimal policy for the network under QoS constraints when real-time and rate-guaranteed data traffic may be present.

Correlated Gaussian Sources over Orthogonal Gaussian Channels

We consider the transmission of correlated Gaussian sources over orthogonal Gaussian channels. It is shown that the Amplify and Forward (AF) scheme which simplifies the design of encoders and the decoder, performs close to the optimal scheme even at high SNR. Also, it outperforms a recently proposed scalar quantizer scheme both in performance and complexity. We also study AF when there is side information at the encoders and decoder.

Three-User Cognitive Channels with Cumulative Message Sharing: An Achievable Rate Region

In this paper, an achievable rate region for the three-user discrete memoryless interference channel with asymmetric transmitter cooperation is derived. The three-user channel facilitates different ways of message sharing between the transmitters. We introduce a manner of noncausal (genie aided) unidirectional message-sharing, which we term cumulative message sharing. We consider receivers with predetermined decoding capabilities, and define a cognitive interference channel. We then derive an achievable rate region for this channel by employing a coding scheme which is a combination of superposition and Gel'fand-Pinsker coding techniques.

Performance of Quantized Equal Gain Transmission With Noisy Feedback Channels

In this paper, new results and insights are derived for the performance of multiple-input, single-output systems with beamforming at the transmitter, when the channel state information is quantized and sent to the transmitter over a noisy feedback channel. It is assumed that there exists a per-antenna power constraint at the transmitter, hence, the equal gain transmission (EGT) beamforming vector is quantized and sent from the receiver to the transmitter. The loss in received signal-to-noise ratio (SNR) relative to perfect beamforming is analytically characterized, and it is shown that at high rates, the overall distortion can be expressed as the sum of the quantization-induced distortion and the channel error-induced distortion, and that the asymptotic performance depends on the error-rate behavior of the noisy feedback channel as the number of codepoints gets large. The optimum density of codepoints (also known as the point density) that minimizes the overall distortion subject to a boundedness constraint is shown to be the same as the point density for a noiseless feedback channel, i.e., the uniform density. The binary symmetric channel with random index assignment is a special case of the analysis, and it is shown that as the number of quantized bits gets large the distortion approaches the same as that obtained with random beamforming. The accuracy of the theoretical expressions obtained are verified through Monte Carlo simulations.

Stability of scheduled multi-access communication over quasi-static flat fading channels with random coding and independent decoding

The stability of scheduled multiaccess communication with random coding and independent decoding of messages is investigated. The number of messages that may be scheduled for simultaneous transmission is limited to a given maximum value, and the channels from transmitters to receiver are quasistatic, flat, and have independent fades. Requests for message transmissions are assumed to arrive according to an i.i.d. arrival process. Then, we show the following: (1) in the limit of large message alphabet size, the stability region has an interference limited information-theoretic capacity interpretation, (2) state-independent scheduling policies achieve this asymptotic stability region, and (3) in the asymptotic limit corresponding to immediate access, the stability region for non-idling scheduling policies is shown to be identical irrespective of received signal powers.

Stability of scheduled message communication over degraded broadcast channels

We develop a multi-class discrete-time processor-sharing queueing model for scheduled message communication over a discrete memoryless degraded broadcast channel. The framework we consider here models both the random message arrivals and the subsequent reliable communication by suitably combining techniques from queueing theory and information theory. Requests for message transmissions are assumed to arrive according to i.i.d. arrival processes. Then, (i) we derive an outer bound to the stability region of message arrival rate vectors achievable by the class of stationary scheduling policies, (ii) we show for any message arrival rate vector that satisfies the outer bound, that there exists a stationary "state-independent" policy that results in a stable system for the corresponding message arrival processes, and (iii) under an asymptotic regime, we show that the stability region of information arrival rate vectors is the information-theoretic capacity region of a degraded broadcast channel.

Optimal Receive Antenna Selection in Time-Varying Fading Channels with Practical Training Constraints

Hardware constraints, which motivate receive antenna selection, also require that various antenna elements at the receiver be sounded sequentially to obtain estimates required for selecting the `best' antenna and for coherently demodulating data thereafter. Consequently, the channel state information at different antennas is outdated by different amounts and corrupted by noise. We show that, for this reason, simply selecting the antenna with the highest estimated channel gain is not optimum. Rather, a preferable strategy is to linearly weight the channel estimates of different antennas differently, depending on the training scheme. We derive closed-form expressions for the symbol error probability (SEP) of AS for MPSK and MQAM in time-varying Rayleigh fading channels for arbitrary selection weights, and validate them with simulations. We then characterize explicitly the optimal selection weights that minimize the SEP. We also consider packet reception, in which multiple symbols of a packet are received by the same antenna. New suboptimal, but computationally efficient weighted selection schemes are proposed for reducing the packet error rate. The benefits of weighted selection are also demonstrated using a practical channel code used in third generation cellular systems. Our results show that optimal weighted selection yields a significant performance gain over conventional unweighted selection.

On Two-User Gaussian Multiple Access Channels With Finite Input Constellations

Constellation Constrained (CC) capacity regions of two-user Single-Input Single-Output (SISO) Gaussian Multiple Access Channels (GMAC) are computed for several Non-Orthogonal Multiple Access schemes (NO-MA) and Orthogonal Multiple Access schemes (O-MA). For NO-MA schemes, a metric is proposed to compute the angle(s) of rotation between the input constellations such that the CC capacity regions are maximally enlarged. Further, code pairs based on Trellis Coded Modulation (TCM) are designed with PSK constellation pairs and PAM constellation pairs such that any rate pair within the CC capacity region can be approached. Such a NO-MA scheme which employs CC capacity approaching trellis codes is referred to as Trellis Coded Multiple Access (TCMA). Then, CC capacity regions of O-MA schemes such as Frequency Division Multiple Access (FDMA) and Time Division Multiple Access (TDMA) are also computed and it is shown that, unlike the Gaussian distributed continuous constellations case, the CC capacity regions with FDMA are strictly contained inside the CC capacity regions with TCMA. Hence, for finite constellations, a NO-MA scheme such as TCMA is better than FDMA and TDMA which makes NO-MA schemes worth pursuing in practice for two-user GMAC. Then, the idea of introducing rotations between the input constellations is used to construct Space-Time Block Code (STBC) pairs for two-user Multiple-Input Single-Output (MISO) fading MAC. The proposed STBCs are shown to have reduced Maximum Likelihood (ML) decoding complexity and information-losslessness property. Finally, STBC pairs with reduced sphere decoding complexity are proposed for two-user Multiple-Input Multiple-Output (MIMO) fading MAC.

Achieving the D-MG and DMD Tradeoffs of MIMO fading channels

An overview of our recent results relating to the explicit construction of space-time block codes achieving the DMG tradeoff of the quasi-static fading channel is presented. The results include the explicit construction of D-MG optimal codes,generalization of perfect codes to any number of transmit antennas as well as optimal diversity-multiplexing-delay constructions for the MIMO ARQ Channel.

Queueing delay - error probability tradeoff for point-to-point channels with fixed length block codes

We study the tradeoff between the average error probability and the average queueing delay of messages which randomly arrive to the transmitter of a point-to-point discrete memoryless channel that uses variable rate fixed codeword length random coding. Bounds to the exponential decay rate of the average error probability with average queueing delay in the regime of large average delay are obtained. Upper and lower bounds to the optimal average delay for a given average error probability constraint are presented. We then formulate a constrained Markov decision problem for characterizing the rate of transmission as a function of queue size given an average error probability constraint. Using a Lagrange multiplier the constrained Markov decision problem is then converted to a problem of minimizing the average cost for a Markov decision problem. A simple heuristic policy is proposed which approximately achieves the optimal average cost.

A Calcium-Dependent Plasticity Rule for HCN Channels Maintains Activity Homeostasis and Stable Synaptic Learning

Theoretical and computational frameworks for synaptic plasticity and learning have a long and cherished history, with few parallels within the well-established literature for plasticity of voltage-gated ion channels. In this study, we derive rules for plasticity in the hyperpolarization-activated cyclic nucleotide-gated (HCN) channels, and assess the synergy between synaptic and HCN channel plasticity in establishing stability during synaptic learning. To do this, we employ a conductance-based model for the hippocampal pyramidal neuron, and incorporate synaptic plasticity through the well-established Bienenstock-Cooper-Munro (BCM)-like rule for synaptic plasticity, wherein the direction and strength of the plasticity is dependent on the concentration of calcium influx. Under this framework, we derive a rule for HCN channel plasticity to establish homeostasis in synaptically-driven firing rate, and incorporate such plasticity into our model. In demonstrating that this rule for HCN channel plasticity helps maintain firing rate homeostasis after bidirectional synaptic plasticity, we observe a linear relationship between synaptic plasticity and HCN channel plasticity for maintaining firing rate homeostasis. Motivated by this linear relationship, we derive a calcium-dependent rule for HCN-channel plasticity, and demonstrate that firing rate homeostasis is maintained in the face of synaptic plasticity when moderate and high levels of cytosolic calcium influx induced depression and potentiation of the HCN-channel conductance, respectively. Additionally, we show that such synergy between synaptic and HCN-channel plasticity enhances the stability of synaptic learning through metaplasticity in the BCM-like synaptic plasticity profile. Finally, we demonstrate that the synergistic interaction between synaptic and HCN-channel plasticity preserves robustness of information transfer across the neuron under a rate-coding schema. Our results establish specific physiological roles for experimentally observed plasticity in HCN channels accompanying synaptic plasticity in hippocampal neurons, and uncover potential links between HCN-channel plasticity and calcium influx, dynamic gain control and stable synaptic learning.

Information and Efficiency in the Nervous System-A Synthesis

In systems biology, questions concerning the molecular and cellular makeup of an organism are of utmost importance, especially when trying to understand how unreliable components-like genetic circuits, biochemical cascades, and ion channels, among others-enable reliable and adaptive behaviour. The repertoire and speed of biological computations are limited by thermodynamic or metabolic constraints: an example can be found in neurons, where fluctuations in biophysical states limit the information they can encode-with almost 20-60% of the total energy allocated for the brain used for signalling purposes, either via action potentials or by synaptic transmission. Here, we consider the imperatives for neurons to optimise computational and metabolic efficiency, wherein benefits and costs trade-off against each other in the context of self-organised and adaptive behaviour. In particular, we try to link information theoretic (variational) and thermodynamic (Helmholtz) free-energy formulations of neuronal processing and show how they are related in a fundamental way through a complexity minimisation lemma.

The effect of cell size and channel density on neuronal information encoding and energy efficiency

Identifying the determinants of neuronal energy consumption and their relationship to information coding is critical to understanding neuronal function and evolution. Three of the main determinants are cell size, ion channel density, and stimulus statistics. Here we investigate their impact on neuronal energy consumption and information coding by comparing single-compartment spiking neuron models of different sizes with different densities of stochastic voltage-gated Na+ and K+ channels and different statistics of synaptic inputs. The largest compartments have the highest information rates but the lowest energy efficiency for a given voltage-gated ion channel density, and the highest signaling efficiency (bits spike(-1)) for a given firing rate. For a given cell size, our models revealed that the ion channel density that maximizes energy efficiency is lower than that maximizing information rate. Low rates of small synaptic inputs improve energy efficiency but the highest information rates occur with higher rates and larger inputs. These relationships produce a Law of Diminishing Returns that penalizes costly excess information coding capacity, promoting the reduction of cell size, channel density, and input stimuli to the minimum possible, suggesting that the trade-off between energy and information has influenced all aspects of neuronal anatomy and physiology.