A Partial Ordering of General Finite-State Markov Channels Under LDPC Decoding

A partial ordering on general finite-state Markov channels is given, which orders the channels in terms of probability of symbol error under iterative estimation decoding of a low-density parity-check (LDPC) code. This result is intended to mitigate the complexity of characterizing the performance of general finite-state Markov channels, which is difficult due to the large parameter space of this class of channel. An analysis tool, originally developed for the Gilbert-Elliott channel, is extended and generalized to general finite-state Markov channels. In doing so, an operator is introduced for combining finite-state Markov channels to create channels with larger state alphabets, which are then subject to the partial ordering. As a result, the probability of symbol error performance of finite-state Markov channels with different numbers of states and wide ranges of parameters can be directly compared. Several examples illustrating the use of the techniques are provided, focusing on binary finite-state Markov channels and Gaussian finite-state Markov channels. Furthermore, this result is used to order Gilbert-Elliott channels with different marginal state probabilities, which was left as an open problem by previous work.     

Capacity analysis for finite-state Markov mapping of flat-fading channels

In this paper, time-varying flat-fading channels are modeled as first-order finite-state Markov channels (FSMC). The effect of this modeling on the channel information capacity is addressed. The approximation accuracy of the first-order memory assumption in the Markov model is validated by comparing the FSMC capacity with the channel capacity assuming perfect state information at the receiver side. The results indicate that the first-order Markovian assumption is accurate for normalized Doppler frequencies f/sub d/T /spl lsim/ 0.01, in amplitude-only quantization of the channel gain for noncoherent binary signaling. In phase-only and joint phase and amplitude quantization of the channel gain for coherent binary signaling, the first-order Markovian assumption is accurate for f/sub d/T /spl lsim/ 0.001. Furthermore, the effect of channel quantization thresholds on the FSMC capacity is studied. In high signal-to-noise ratio (SNR) conditions, nonuniform two-level amplitude quantization scheme outperforms equiprobable quantization method by 0.8-1.5 dB.     

Novel Approach for Modeling Wireless Fading Channels Using a Finite State Markov Chain

Empirical modeling of wireless fading channels using common schemes such as autoregression and the finite state Markov chain (FSMC) is investigated. The conceptual background of both channel structures and the establishment of their mutual dependence in a confined manner are presented. The novel contribution lies in the proposal of a new approach for deriving the state transition probabilities borrowed from economic disciplines, which has not been studied so far with respect to the modeling of FSMC wireless fading channels. The proposed approach is based on equal portioning of the received signal‐to‐noise ratio, realized by using an alternative probability construction that was initially highlighted by Tauchen. The associated statistical procedure shows that a first‐order FSMC with a limited number of channel states can satisfactorily approximate fading. The computational overheads of the proposed technique are analyzed and proven to be less demanding compared to the conventional FSMC approach based on the level crossing rate. Simulations confirm the analytical results and promising performance of the new channel model based on the Tauchen approach without extra complexity costs.     

Efficient rate allocation for progressive image transmission via unequal error protection over finite-state Markov channels

This paper proposes a unified framework for addressing progressive image transmission over noisy channels based on the finite-state Markov channel (FSMC) model. FSMC models are simple yet general enough to model binary symmetric, Gilbert-Elliott, and fading channels. They allow error sequence analysis that facilitates quantifying the statistical characteristics of the embedded bitstreams transmitted over FSMC in closed form. Using a concatenation of rate-compatible puncturing convolutional code and cyclic redundancy check code for error protection, we use a concatenation of rate-compatible punctured convolutional code and cyclic redundancy check code for error protection, which results in an unequal error protection (UEP) system, and find (sub-)optimal rate allocation solutions for our setup. By mapping fading channels to FSMCs, the JSCC problem is thus solved without the burden of simulations using an image-dependent lookup table. Fast algorithms are proposed to search for the optimal UEP. Experiments on embedded image bitstreams over FSMCs confirm our analytical results.     

Capacity, mutual information, and coding for finite-state Markovchannels

The finite-state Markov channel (FSMC) is a discrete time-varying channel whose variation is determined by a finite-state Markov process. These channels have memory due to the Markov channel variation. We obtain the FSMC capacity as a function of the conditional channel state probability. We also show that for i.i.d. channel inputs, this conditional probability converges weakly, and the channel's mutual information is then a closed-form continuous function of the input distribution. We next consider coding for FSMCs. In general, the complexity of maximum-likelihood decoding grows exponentially with the channel memory length. Therefore, in practice, interleaving and memoryless channel codes are used. This technique results in some performance loss relative to the inherent capacity of channels with memory. We propose a maximum-likelihood decision-feedback decoder with complexity that is independent of the channel memory. We calculate the capacity and cutoff rate of our technique, and show that it preserves the capacity of certain FSMCs. We also compare the performance of the decision-feedback decoder with that of interleaving and memoryless channel coding on a fading channel with 4PSK modulation     

Modeling End-to-End Wireless Lossy Channels: A Finite-State Markov Approach

In this paper, we present a model for wireless losses in packet transmission data networks. The model provides information about the wireless channel status that can be used in congestion control schemes. A Finite State Markov Channel (FSMC) approach is implemented to model the wireless slow fading for different modulation schemes. The arrival process statistics of the packet traces determine the channel state transition probabilities, where the statistics of both error-free and erroneous bursts are captured. Later, we establish SNR partitioning scheme that uses the transition probabilities as a basis for the state margins. The crossover probability associated with each state is calculated accordingly. We also propose an end-to-end approach to loss discrimination based on the channel state estimation at the receiver. Finally, we present a scheme for finding the channel optimal number of states as a function of the SNR. The presented FSMC approach does not restrict the state transitions to the adjacent states, nor does impose constant state duration as compared to some literature studies. We validate our model by experimental packet traces. Our simulation results show the feasibility of building a fading channel model for better wireless-loss awareness.     

噪声功率时变的瑞利慢衰落信道有限状态Markov模型

对衰落信道的准确建模对于自适应无线通信、认知无线电等应用中的信道预测具有重要意义。针对噪声功率存在时变特性的无线通信应用环境,提出了一种新的瑞利衰落信道的有限状态Markov模型。通过将接收信号的衰落电平进行离散化处理,建立了衰落电平区间与Markov模型状态之间的一一对应关系,推导了门限电平与状态转移概率和状态分布概率之间的理论关系式,并在此基础上提出了一种易于实现的基于等概率的信道模型。理论分析与仿真结果表明:在噪声功率时变的条件下,已有的基于信噪比的模型失效,而该模型能准确反映信道的衰落特性,最大相对误差小于7%。      

Finite-state Markov model for Rayleigh fading channels

We form a finite-state Markov channel model to represent Rayleigh fading channels. We develop and analyze a methodology to partition the received signal-to-noise ratio (SNR) into a finite number of states according to the time duration of each state. Each state corresponds to a different channel quality indicated by the bit-error rate (BER). The number of states and SNR partitions are determined by the fading speed of the channel. Computer simulations are performed to verify the accuracy of the model     

Markov error structure for throughput analysis of adaptive modulation systems combined with ARQ over correlated fading channels

We introduce an analytical method that uses a finite-state Markov chain (FSMC) as an error model, for estimating the performance of adaptive modulation systems (AMSs) combined with automatic repeat request (ARQ) schemes in correlated slow fading channels. For the throughput performance evaluation of wireless packet networks, conventionally, we have assumed independent block fading, which may also be suitable to represent fast fading channels. However, in slow fading channels, error rates of consecutive packets are highly correlated and we cannot simply assume independent error structure in performance evaluations. We propose a multistate Markov error structure for AMS in correlated fading channels, which is also described by a finite-state Markov chain (FSMC) and we also present throughput-estimation methods for AMS combined with ARQ, using the proposed Markov error structure.     

Mathematical modeling of rayleigh fading channels based on finite state markov chains

To mathematically model the Rayleigh fading channel, we propose a new method to partition the received Signalto-Noise ratio (SNR) range into a finite number of states and construct a finite state Markov chain (FSMC). Our method is based on the assumption that the transitions of the FSMC occur only between adjacent states. We provide numerical and simulation results to verify that our method constructs an accurate FSMC and our method outperforms existing methods.     

Finite-state Markov Model for Lognormal,Chi-square (Central), Chi-square (Non-central), and <Emphasis Type="Italic">K</Emphasis>-distributions

This paper formulates a finite-state Markov channel model to represent received signal-to-noise (SNR) ratios having lognormal, K-distribution, chi-square (central) and chi-square (non-central) distributions in a slow fading channel. The range of the SNRs is partitioned into a finite number of states following earlier works in literature. Performance measures like level crossing rates, steady-state probabilities, transition probabilities, and state-time durations are derived, and numerical results are plotted and discussed for the FSMC models for all the distributions.

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).     

An average error probability evaluation in a fading environment using finite state Markov channel for LEO satellite communication system

Recent research shows that fading channels have a much larger capacity than anticipated with traditional approaches. This modern view on fading channels encouraged us to characterize these channels more precisely for better identification and use of wireless channel capacity.Since the Markov model is a natural way to approximate a channel with memory, many people have considered finite state first-order Markov modeling for describing a wireless communication channel.In this paper, we first introduce the relationship between a physical fading channel and the corresponding finite state Markov Model (FSMC) in case of low earth orbit (LEO) satellite communication system, which can be used for performance evaluation in an M-order quadrature amplitude-modulation (MQAM) transmission scheme by deriving an analytical expression of average bit error rate in Rayleigh fading channel. By establishing the FSMC, we show that the FSMC is accurate enough to evaluate the performance of MQAM modulation scheme to be implemented on board a LEO satellite communication system.     

Finite-State Markov Wireless Channel Modeling for Railway Tunnel Environments

In recent years,high-speed railways(HSRs)have developed rapidly with a high transportation capacity and high comfort level.A tunnel is a complex high-speed rail terrain environment.It is very important to establish an accurate channel propagation model for a railway tunnel environment to improve the safety of HSR operation.In this paper,a method for finite-state Markov chain(FSMC)channel modeling with least squares fitting based on non-uniform interval division is proposed.First,a path loss model is obtained according to measured data.The communication distance between the transmitter and receiver in the tunnel is non-uniformly divided into several large non-overlapping intervals based on the path loss model.Then,the Lloyd-Max quantization method is used to determine the threshold of the signal-to-noise ratio(SNR)and the channel state quantization value and obtain the FSMC state transition probability matrix.Simulation experiments show that the proposed wireless channel model has a low mean square error(MSE)and can accurately predict the received signal power in a railway tunnel environment.     

On Information Rates of Time-Varying Fading Channels Modeled as Finite-State Markov Channels

We study information rates of time-varying flatfading channels (FFC) modeled as finite-state Markov channels (FSMC). FSMCs have two main applications for FFCs: modeling channel error bursts and decoding at the receiver. Our main finding in the first application is that receiver observation noise can more adversely affect higher-order FSMCs than lower-order FSMCs, resulting in lower capacities. This is despite the fact that the underlying higher-order FFC and its corresponding FSMC are more predictable. Numerical analysis shows that at low to medium SNR conditions (SNR ≲12 dB) and at medium to fast normalized fading rates (0.01 ≲fDT ≲0.10), FSMC information rates are non-increasing functions of memory order. We conclude that BERs obtained by low-order FSMC modeling can provide optimistic results. To explain the capacity behavior, we present a methodology that enables analytical comparison of FSMC capacities with different memory orders. We establish sufficient conditions that predict higher/lower capacity of a reduced-order FSMC, compared to its original high-order FSMC counterpart. Finally, we investigate the achievable information rates in FSMC-based receivers for FFCs. We observe that high-order FSMC modeling at the receiver side results in a negligible information rate increase for normalized fading rates fDT ≲0.01.     

Upper Bounds on the Rate of LDPC Codes for a Class of Finite-State Markov Channels

In this correspondence, we consider the class of finite-state Markov channels (FSMCs) in which the channel behaves as a binary symmetric channel (BSC) in each state. Upper bounds on the rate of LDPC codes for reliable communication over this class of FSMCs are found. A simple upper bound for all noninverting FSMCs is first derived. Subsequently, tighter bounds are derived for the special case of Gilbert-Elliott (GE) channels. Tighter bounds are also derived over the class of FSMCs considered. The latter bounds hold almost-surely for any sequence of randomly constructed LDPC codes of given degree distributions. Since the bounds are derived for optimal maximum-likelihood decoding, they also hold for belief propagation decoding. Using the derivations of the bounds on the rate, some lower bounds on the density of parity check matrices for given performance over FSMCs are derived     

Performance of Hybrid Error Control Schemes of Satellite Channels

The effectiveness of hybrid error control schemes involving forward error correction (FEC) and automatic repeat request (ARQ) is examined for satellite channels. The principal features of the channel are: large round-trip transmission delay due to the satellite link, and burst errors introduced by the terrestrial links that connect the users to the satellite link. The performance is estimated for two channels described by Fritchman's simple partitioned finite-state Markov model, and is compared to that obtainable if the channel is considered as a binary symmetric channel of the same bit error probability. Results show that the hybrid schemes offer substantial improvement over ARQ and FEC, and that an optimum exists for the number of errors corrected to obtain maximum throughput efficiency.     

Capacity and zero-error capacity of Ising channels

Simple binary symmetric one- and two-dimensional channel systems called Ising channels are investigated. The one-dimensional version is a certain binary finite-state channel with input intersymbol interference. Its zero-error capacity is determined together with lower and upper bounds to its Shannon capacity. For the two-dimensional channel system, a lower bound is obtained for the zero-error capacity, and an efficient zero-error coding scheme is developed     

Capacity and coding for the Gilbert-Elliot channels

The Gilbert-Elliott channel, a varying binary symmetric channel, with crossover probabilities determined by a binary-state Markov process, is treated. In general, such a channel has a memory that depends on the transition probabilities between the states. A method of calculating the capacity of this channel is introduced and applied to several examples, and the question of coding is addressed. In the conventional usage of varying channels, a code suitable for memoryless channels is used in conjunction with an interleaver, with the decoder considering the deinterleaved symbol stream as the output of a derived memoryless channel. The transmission rate is limited by the capacity of this memoryless channel, which is often considerably less than the capacity of the original channel. A decision-feedback decoding algorithm that completely recovers this capacity loss is introduced. It is shown that the performance of a system incorporating such an algorithm is determined by an equivalent genie-aided channel, the capacity of which equals that of the original channel. The calculated random coding exponent of the genie-aided channel indicates a considerable increase in the cutoff rate over that of the conventionally derived memoryless channel     

Modeling of high error rate binary communication channels (Corresp.)

Most of the existing mathematical models for binary communication channels describe low error rate wire lines satisfactorily. For typical high error rate channels, like the ultrahigh frequency (UHF) or very high frequency (VHF) wideband data channel encountered in military uses, finite-state as well as denumerable infinite state Markov chain models do not achieve an accurate characterization. The above models, including some more recent compound models, are compared against data from the actual channel using the multigap distribution as a tool. A modification of a compound model is shown that allows more accurate modeling of a wider class of channels including the high error rate radio channel.