On the Feedback Capacity of Power-Constrained Gaussian Noise Channels With Memory

For a stationary additive Gaussian-noise channel with a rational noise power spectrum of a finite-order L, we derive two new results for the feedback capacity under an average channel input power constraint. First, we show that a very simple feedback-dependent Gauss-Markov source achieves the feedback capacity, and that Kalman-Bucy filtering is optimal for processing the feedback. Based on these results, we develop a new method for optimizing the channel inputs for achieving the Cover-Pombra block-length- n feedback capacity by using a dynamic programming approach that decomposes the computation into n sequentially identical optimization problems where each stage involves optimizing O(L ²) variables. Second, we derive the explicit maximal information rate for stationary feedback-dependent sources. In general, evaluating the maximal information rate for stationary sources requires solving only a few equations by simple nonlinear programming. For first-order autoregressive and/or moving average (ARMA) noise channels, this optimization admits a closed-form maximal information rate formula. The maximal information rate for stationary sources is a lower bound on the feedback capacity, and it equals the feedback capacity if the long-standing conjecture, that stationary sources achieve the feedback capacity, holds     

Iterative timing recovery

The last decade has seen the development of iteratively decodable error-control codes of unprecedented power, whose large coding gains enable reliable communication at very low signal-to-noise ratio (SNR). A by-product of this trend is that timing recovery must be performed at an SNR lower than ever before. Conventional timing recovery ignores the presence or error-control coding and thus doomed to fail when the SNR is low enough. This article describes the iterative timing recovery, a method for implementing timing recovery in cooperation with iterative error-control decoding so as to approximate a more complicated receiver that jointly solves the timing recovery and decoding problems.     

Approaching the capacity of the MIMO Rayleigh flat-fading channel with QAM constellations, independent across antennas and dimensions

In this study we consider the challenge of reliable communication over a wireless Rayleigh flat-fading channel using multiple transmit and receive antennas. Since modern digital communication systems employ signal sets of finite cardinality, we examine the use of the quadrature amplitude modulation (QAM) constellation to approach the capacity of this channel. By restricting the channel input to the M-QAM subset of the complex-plane, the maximum achievable information rate (C/sub M-QAM/) is strictly bounded away from the channel capacity (C). We utilize a modified version of the Arimoto-Blahut algorithm to determine C/sub M-QAM/ and the probability distribution over the channel input symbols that achieves it. The results of this optimization procedure numerically indicate that the optimal input symbol distribution factors into the product of identical distributions over each real dimension of the transmitted signal. This is shown to vastly reduce the computational complexity of the optimization algorithm. Furthermore, we utilize the computed optimal channel input probability mass function (pmf) to construct capacity approaching trellis codes. These codes are implemented independent across all antennas and symbol dimensions and, if used as inner codes to outer low-density parity check (LDPC) codes, can achieve arbitrarily small error rates at signal-to-noise ratios very close to the channel capacity C/sub M-QAM/. Examples are given for a 2-transmit/2-receive antenna (2 /spl times/ 2) system.     

A Generalization of the Blahut–Arimoto Algorithm to Finite-State Channels

The classical Blahut-Arimoto algorithm (BAA) is a well-known algorithm that optimizes a discrete memoryless source (DMS) at the input of a discrete memoryless channel (DMC) in order to maximize the mutual information between channel input and output. This paper considers the problem of optimizing finite-state machine sources (FSMSs) at the input of finite-state machine channels (FSMCs) in order to maximize the mutual information rate between channel input and output. Our main result is an algorithm that efficiently solves this problem numerically; thus, we call the proposed procedure the generalized BAA. It includes as special cases not only the classical BAA but also an algorithm that solves the problem of finding the capacity-achieving input distribution for finite-state channels with no noise. While we present theorems that characterize the local behavior of the generalized BAA, there are still open questions concerning its global behavior; these open questions are addressed by some conjectures at the end of the paper. Apart from these algorithmic issues, our results lead to insights regarding the local conditions that the information-rate-maximizing FSMSs fulfill; these observations naturally generalize the well-known Kuhn-Tucker conditions that are fulfilled by capacity-achieving DMSs at the input of DMCs.     

Transfer of the horizontal patient: the effect of a friction reducing assistive device on low back mechanics

Recognizing that the transfer of bedridden patients is associated with a high rate of low back injuries, various devices have been developed to assist with sparing the patient handlers. The purpose of this study was to quantify the friction-reducing ability of three different 'sliding' patient transfer devices together with the subsequent consequences on the low back loads of people performing the transfers. Coefficients of friction of the devices were determined by 'transferring' a standard object and a 'patient' over several surfaces common to a hospital setting. Then three participants performed controlled transfers with the various devices. Electromyography to measure muscle activation levels together with external forces and kinematic positional data were collected during push, pull and twist transfers. Spine loads were estimated with a three-dimensional biomechanical static link-segment model of the human body. Simply sliding a patient on a cotton sheet (control condition) produced a coefficient of friction of 0.45. The assistive devices substantially reduced friction by well over one-half (coefficients of 0.18 - 0.21). However, when using the devices the subjects adopted a variety of postures and techniques, such that there were no consistent influences on trunk inclination, low back compression or muscle activation profiles. Direct measurement of reduced friction between the bed and the patient with a friction-reducing device together with measurement of the back loads when actually transferring a patient formed a proof of principle. Specifically, while the device lowers friction, the transfer technique adopted by the lifter must be proper to reduce low back loading and any subsequent risks of back troubles associated with patient transfers. The direction of hand forces and torso position remains important.     

List Decoding Techniques for Intersymbol Interference Channels Using Ordered Statistics

In this paper, we present a generalization of the ordered statistics decoding (OSD) techniques for the class of intersymbol interference (ISI) channels, and show decoding results for the extended Bose-Chaudhuri-Hocquenghem (eBCH) [128, 64, 22] code and the [255, 239, 17] Reed-Solomon (RS) binary image, over the PR2 partial response channel. Using the generalized OSD technique, we go on to generalize the Box-and- Match Algorithm (BMA) to the class of ISI channels. The BMA is an enhancement of OSD, and prior work has shown it to provide significant performance gain over OSD for memoryless additive white Gaussian noise (AWGN) channels. We present decoding results of the BMA for ISI channels, for the same eBCH and RS (binary image) codes, and PR2 channel. Our results show that the BMA (generalized for ISI channels) is superior to the OSD in terms of its performance/complexity trade-off. More specifically, the BMA may be tuned such that both algorithms have similar complexity, whereby the BMA still outperforms the OSD by a significant margin.     

Feedback capacity of finite-state machine channels

We consider a finite-state machine channel with a finite memory length (e.g., finite length intersymbol interference channels with finite input alphabets-also known as partial response channels). For such a finite-state machine channel, we show that feedback-dependent Markov sources achieve the feedback capacity, and that the required memory length of the Markov process matches the memory length of the channel. Further, we show that the whole history of feedback is summarized by the causal posterior channel state distribution, which is computed by the sum-product forward recursion of the Bahl-Cocke-Jelinek-Raviv (BCJR) (Baum-Welch, discrete-time Wonham filtering) algorithm. These results drastically reduce the space over which the optimal feedback-dependent source distribution needs to be sought. Further, the feedback capacity computation may then be formulated as an average-reward-per-stage stochastic control problem, which is solved by dynamic programming. With the knowledge of the capacity-achieving source distribution, the value of the capacity is easily estimated using Markov chain Monte Carlo methods. When the feedback is delayed, we show that the feedback capacity can be computed by similar procedures. We also show that the delayed feedback capacity is a tight upper bound on the feedforward capacity by comparing it to tight existing lower bounds. We demonstrate the applicability of the method by computing the feedback capacity of partial response channels and the feedback capacity of run-length-limited (RLL) sequences over binary symmetric channels (BSCs).