Feedback communication using orthogonal signals

We consider a feedback communication system in which the forward and feedback channels are disturbed by additive noise and constrained in average power. Two block coding schemes are proposed in which the signals are orthogonal waveforms. A finite number of forward and feedback transmissions per message is made. Information received over the feedback channel is used to reduce the expected value of forward signal energy on all iterations after the first. Similarly, the expected value of feedback signal energy is reduced on all iterations after the first. These schemes, which are modifications of a feedback coding scheme due to Kramer, obtain improved error performance over one-way coding at all rates up to the forward channel capacity, provided only that the feedback channel capacity is greater than the forward channel capacity. They require less feedback power than existing feedback coding schemes to achieve a given error performance.     

有限域和剩余类环上非奇异反馈多项式的谱刻划

本文给出了有限域和剩余类环上非线性反馈移存器的非奇异反馈多项式及局部置换多项式的谱刻划，简化了素域上的现有结果，并对有限域上和剩余类环上相关免疫函数的谱特征给出了一个新的证明方法。     

Condition for the nonsingularity of a feedback shift-register over a general finite field (Corresp.)

The necessary and sufficient condition for a feedback shift-register over a general finite field to be nonsingular is established. The general condition is contrasted to the well-known necessary and sufficient condition for nonsingularity of a binary feedback shift-register.     

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).     

置换多项式在序列密码中的应用

本文讨论了一般有限域上置换多项式的表示形式及其判定条件,根据次数不超过3的置换多项式的特点,决定了一批n元非奇异反馈函数的具体表示形式,最后给出了一个求全体n元非奇异反馈函数的算法。     

Nonsingularity of Feedback Shift Registers of Degree at Most Three over a Finite Field

As a kind of generators of pseudo-random sequences, the Feedback shift register (FSR) is widely used in channel coding, cryptography and digital communication. A necessary and sufficient condition for the nonsingularity of a feedback shift register of degree at most three over a finite field is established. Using the above result, we can easily determine the nonsingularity of a feedback shift register from the algebraic normal form of the corresponding feedback function.     

σ-LFSR序列极小多项式性质研究

σ-线性反馈移位寄存器(σ-LFSR)是基于字设计的,在安全性和效率上达到较好折衷的一种反馈移位寄存器.σ-LFSR输出序列的特征多项式为有限域上的矩阵多项式.该文利用有限域上矩阵多项式环的代数结构,给出了σ-LFSR输出序列极小多项式唯一的充分必要条件.     

σ-LFSR序列极小多项式性质研究

σ-线性反馈移位寄存器(σ-LFSR)是基于字设计的,在安全性和效率上达到较好折衷的一种反馈移位寄存器。σ-LFSR输出序列的特征多项式为有限域上的矩阵多项式。该文利用有限域上矩阵多项式环的代数结构,给出了σ-LFSR输出序列极小多项式唯一的充分必要条件。     

Design of Parallel Tomlinson–Harashima Precoders

Like decision feedback equalizers (DFEs), Tomlinson-Harashima precoders (TH precoders) contain nonlinear feedback loops, which limit their use for high-speed applications. Unlike in DFEs, where the output levels of the nonlinear devices are finite, in TH precoders the output levels of the modulo devices are either infinite or finite but very large. Thus, it is difficult to apply look-ahead and pre-computation techniques to speed up TH precoders, which were successfully applied to design parallel and pipelined infinite impulse response (IIR) filters and DFEs in the past. However, a TH precoder can be viewed as an IIR filter with an input equal to the sum of the original input to the TH precoder and a finite-level compensation signal. Based on this point of view, a novel parallel architecture is proposed to speed up TH precoders. This architecture can be used in many high-speed applications, such as 10-Gb Ethernet over copper.     

Throughput Gains Using Rate and Power Control in Cooperative Relay Networks

In this letter, we use power and rate adaptation to maximize the throughput in cooperative relay networks when limited feedback links to the transmitter nodes exist. We observe that, for a finite rate of feedback, the throughput maximizing outage probability can be relatively high. This suggests using higher rate codes and allowing some outages in an effort to increase the overall network throughput. Our analysis also reveals that the relaying transmission paradigm offers significant throughput gains over direct transmission for any rate of the feedback link. Our work not only demonstrates the power of cooperative coding, but also suggests the importance of network protocols incorporating feedback to allow for throughput maximization     

A high input impedance buffer amplifier using bipolar transistors

The input impedance of conventional emitter follower circuits is limited due to the finite value of the passive emitter resistance, shunting effect of biasing resistors and that of intrinsic collector to base feedback admittance and also to the fall in current amplification factor at low operating currents. Further, the input admittance is frequency dependent because the device parameters involved therein are themselves frequency dependent. However, the shunt positive feedback incorporated in such circuits minimizes the shunting effect of the biasing network and also that of the intrinsic feedback admittance. The simulation of negative capacitance across the input terminals nullifies the effect of the presence of the otherwise positive capacity. This technique extends the bandwidth over which the input impedance remains constant. A typical buffer amplifier circuit employing five conventional epitaxial planar bipolar silicon transistors has been described in the present communication. The input impedance of which is found to be constant over a frequency range of 10 HZ to 2 KHz and its magnitude is about 25MΩ.     

Capacity of the mismatched Gaussian channel

Information capacity is determined for the additive Gaussian channel when the constraint is given in terms of a covariance different from that of the channel noise. These results, combined with previous results on capacity when the constraint covariance is the same as the noise covariance, provide a complete and general solution for the information capacity of the Gaussian channel without feedback. The results are valid for both continuous-time and discrete-time channels and require only two assumptions: the noise is due to a stochastic process with sample paths having finite energy over the observation period (w.p.1), and the constraint is given in terms of a Hilbert space norm. Such a constraint is implicit in any constraint giving finite capacity.     

On the design of globally optimal communication strategies for real-time noisy communication systems with noisy feedback

A real-time communication system with noisy feedback is considered. The system consists of a Markov source, forward and backward discrete memoryless channels, and a receiver with limited memory. The receiver can send messages to the encoder over the backward noisy channel. The encoding at the encoder and the decoding, the feedback, and the memory update at the receiver must be done in real-time. A distortion metric that does not tolerate delays is given. The objective is to design an optimal real-time communication strategy, i.e., design optimal real-time encoding, decoding, feedback, and memory update strategies to minimize a total expected distortion over a finite horizon. This problem is formulated as a decentralized stochastic optimization problem and a methodology for its sequential decomposition is presented. This results in a set of nested optimality equations that can be used to sequentially determine optimal communication strategies. The methodology exponentially simplifies the search for determining an optimal real-time communication strategy.     

Achievable Rates with Imperfect Transmitter Side Information Using a Broadcast Transmission Strategy

rdquoWe investigate the performance of the broadcast approach for various fading distributions, which correspond to different models of partial transmit channel state information (CSI). The first model considered is the quantized limited feedback. In this model, the receiver can send as feedback only a finite number of bits describing the fading gain. We derive the optimal power allocation for the broadcast approach for the quantized feedback model. For a Rayleigh fading channel, numerical results here show that if the feedback word can be longer than one bit, the broadcasting gain becomes negligible, due to diminished channel uncertainty. The second partial transmit CSI model is a stochastic Gaussian model with mean and variance information, which is commonly used for modeling the channel estimation error. In a single-input single-output (SISO) channel, this model also corresponds to the Ricean fading distribution, for which we derive maximal achievable broadcasting rates. We further consider a multiple-input single-output (MISO) channel, and derive the optimal power allocation strategy in a broadcast approach. Numerical results here show that uniform power allocation is preferable over beamforming power allocation in the region where broadcasting gain over single level coding is non-negligible.     

Remote-controlled platoon merging via coder-estimator sequence algorithm for a communication network

In this paper, a platoon-merging control system is considered as a remotely located system with a state represented by a stochastic process. In this system, it is common to encounter situations where a single decision maker controls a large number of subsystems, and observation and control signals are sent over a communication channel with finite capacity and significant transmission delays. Unlike a classical estimation problem where the observation is a continuous process corrupted by additive noise, there is a constraint that the observation must be coded and transmitted over a digital communication channel with finite capacity. A recursive coder-estimator sequence is a state estimation scheme based on observations transmitted with finite communication capacity constraint. In this paper, we introduce a stochastic model for the lead vehicle in a platoon of vehicles in a lane considering the angle between the road surface and a horizontal plane as a stochastic process. In order to merge two platoons, the lead vehicle of the following platoon is controlled by a remote control station. Using the coder-estimator sequence, the remote control station designs the feedback controller. The simulation results show that the inter-vehicle distance and the deviation from the desired inter-vehicle distance are well regulated.     

Broadcasting over uncertain channels with decoding delay constraints

We examine communication over slowly varying flat-fading additive white Gaussian noise (AWGN) channels with delayed channel state information (CSI) feedback to the transmitter and finite decoding delay constraints. Under a block-fading channel model, it is shown that a broadcast strategy maximizes the expected reliably received rate when the decoding delay constraint is one block and in certain cases when the delay constraint is two blocks. The latter requires a new analysis of underlying parallel Gaussian broadcast channels (GBCs) which are not degraded in the same direction.     

Synthesis of zero-admittance converter

A method of synthesizing a power conversion system which converts a finite value of an admittance to zero, with associated finite voltage and zero current, is presented. The synthesis method comprises a positive voltage feedback within a negative current feedback. The positive feedback loop incorporates a block of exactly specified nature and value of its transfer function providing for the zero-admittance algorithm. The negative feedback loop controls stability and dynamics of the system. A particular derivation of the zero-admittance power converter is applied in synthesizing a load-independent constant-current switch-mode power converter     

Capacity of memoryless channels and block-fading channels with designable cardinality-constrained channel state feedback

A coding theorem is proved for memoryless channels when the channel state feedback of finite cardinality can be designed. Channel state information is estimated at the receiver and a function of the estimated channel state is causally fed back to the transmitter. The feedback link is assumed to be noiseless with a finite feedback alphabet, or equivalently, finite feedback rate. It is shown that the capacity can be achieved with a memoryless deterministic feedback and with a memoryless device which select transmitted symbols from a codeword of expanded alphabet according to current feedback. To characterize the capacity, we investigate the optimization of transmission and channel state feedback strategies. The optimization is performed for both channel capacity and error exponents. We show that the design of the optimal feedback scheme is identical to the design of scalar quantizer with modified distortion measures. We illustrate the optimization using Rayleigh block-fading channels. It is shown that the optimal transmission strategy has a general form of temporal water-filling in important cases. Furthermore, while feedback enhances the forward channel capacity more effectively in low-signal-to noise ratio (SNR) region compared with that of high-SNR region, the enhancement in error exponent is significant in both high- and low-SNR regions. This indicates that significant gain due to finite-rate channel state feedback is expected in practical systems in both SNR regions.     

Outage Minimization With Limited Feedback for the Fading Relay Channel

Outage Minimization With Limited Feedback for the Fading Relay Channel In this paper, we consider practical methods to approach the theoretical performance limits in the fading relay channel under different assumptions of transmitter channel knowledge. Specifically, we consider two degrees of transmitter channel knowledge: 1) perfect feedback is available and power control is employed; and 2) no channel-state knowledge is available at the transmitters, and only spatial power allocation is possible. First, when perfect feedback is available, the optimal power-control policy determines the ultimate limits of performance for constant-rate transmission in the slow fading environment. However, in practice, perfect channel knowledge is not possible at the transmitters due to the finite capacity of the feedback links. We find practical methods to approach this performance limit through the use of power control with finite-rate feedback. The finite-rate feedback results are shown for the low-complexity, full-diversity amplify-and-forward (AF) protocol. Interestingly, we see that only a few feedback bits are needed to achieve most of the gains of the optimal perfect feedback power-control algorithm. Second, we consider the performance limit when the transmitter has no channel-state knowledge, and derive the optimal spatial power allocation between the source and relay for a given sum power constraint for the AF protocol. In the foremost practical cases of interest, equal power allocation between the source and relay is shown to be nearly optimal. Our work suggests that there is minimal power savings from using spatial power allocation at the transmitters. To obtain large performance improvements over constant power transmission, it is imperative to have feedback for each realization of the channel state to allow for temporal power control.