Finite-state Markov Channel Research Articles

Distributed Optimal Relay Selection in Wireless Cooperative Networks With Finite-State Markov Channels

Relay selection is crucial in improving the performance of wireless cooperative networks. Most previous works for relay selection use the current observed channel conditions to make the relay-selection decision for the subsequent frame. However, this <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">memoryless</i> channel assumption is often not realistic given the time-varying nature of some mobile environments. In this paper, we consider finite-state Markov channels in the relay-selection problem. Moreover, we also incorporate adaptive modulation and coding, as well as residual relay energy in the relay-selection process. The objectives of the proposed scheme are to increase spectral efficiency, mitigate error propagation, and maximize the network lifetime. The formulation of the proposed relay-selection scheme is based on recent advances in stochastic control algorithms. The obtained relay-selection policy has an indexability property that dramatically reduces the computation and implementation complexity. In addition, there is no need for a centralized control point in the network, and relays can freely join and leave from the set of potential relays. Simulation results are presented to show the effectiveness of the proposed scheme.

On Symbol Versus Bit Interleaving for Block-Coded Binary Markov Channels

We examine bit- and symbol-interleaving strategies for linear nonbinary block codes (under bounded-distance decoding) over the family of binary additive noise finite-state Markov channel (FSMC) models with memory. We derive a simple analytical sufficient condition under which perfect (i.e., with infinite interleaving depth) symbol interleaving outperforms perfect bit interleaving in terms of the probability of codeword error (PCE). It is shown that the well-known Gilbert-Elliott channel (GEC) with positive noise-correlation coefficient and the recently introduced Markovian queue-based channel (QBC) of memory M satisfy this condition. This result has widely been illustrated numerically (without proof) in the literature, particularly for the GEC. We also provide examples of binary FSMC models for which the reverse result holds, i.e., perfect bit interleaving outperforming perfect symbol interleaving. Finally, a numerical PCE study of imperfect symbol-interleaved nonbinary codes over the QBC indicates that there is a linear relationship between the optimal interleaving depth and a function of a single parameter of the QBC.

Packet-Based Modeling of Reed–Solomon Block-Coded Correlated Fading Channels Via a Markov Finite Queue Model

We consider the transmission of a Reed-Solomon (RS) code over a binary modulated time-correlated flat Rician fading channel with hard-decision demodulation. We define a binary packet (symbol) error sequence that indicates whether an RS symbol is successfully transmitted across the discrete (fading) channel whose input enters the modulator and whose output exits the demodulator. We then approximate the packet error sequence of the discrete channel (DC) using the recently developed queue-based channel (QBC), which is a simple finite-state Markov channel model with <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> th-order Markovian additive noise. In other words, we use the QBC to model the binary DC at the packet level. We propose a general framework for determining the probability of codeword error (PCE) for QBC models. We evaluate the modeling accuracy by comparing the simulated PCE for the DC with the numerically evaluated PCE for the QBC. Modeling results identify accurate low-order QBC models for a wide range of fading conditions and reveal that modeling the DC at the packet level is an efficient tool for nonbinary coding performance evaluation over binary channels with memory.

Design and Analysis of Successive Decoding With Finite Levels for the Markov Channel

This paper proposes a practical successive decoding scheme with finite levels for the finite-state Markov channels (FSMCs) where there is no a priori state information at the transmitter or the receiver. The design employs either a random interleaver or a deterministic interleaver with an irregular pattern and an optional iterative estimation and decoding procedure within each level. The interleaver design criteria may be the achievable rate or the extrinsic information transfer (EXIT) chart, depending on the receiver type. For random interleavers, the optimization problem is solved efficiently using a pilot-utility function, while for deterministic interleavers, a good construction is given using empirical rules. Simulation results demonstrate that the new successive decoding scheme combined with irregular low-density parity-check (LDPC) codes can approach the identically and uniformly distributed (i.u.d.) input capacity on the Markov-fading channel using only a few levels.

Ordering Finite-State Markov Channels by Mutual Information

In this paper, an ordering result is given for Markov channels with respect to mutual information, under the assumption of an independent and identically distributed (i.i.d.) input distribution. For those Markov channels in which the capacity-achieving input distribution is i.i.d., this allows ordering of the channels by capacity. The complexity of analyzing general Markov channels is mitigated by this ordering, since it is possible to immediately determine that a wide class of channels, with different numbers of states, has a smaller mutual information than a given channel.

Rate adaptation using acknowledgement feedback in finite-state markov channels with collisions

We investigate packet-by-packet rate adaptation so as to maximize the throughput. We consider a finite-state Markov channel (FSMC) with collisions, which models channel fading as well as collisions due to multi-user interference. To limit the amount of feedback data, we only use past packet acknowledgements (ACKs) and past rates as channel state information. The maximum achievable throughput is computationally prohibitive to determine, thus we employ a two-pronged approach. Firstly, we derive new upper bounds on the maximum achievable throughput, which are tighter than previously known ones. Secondly, we propose the particle-filter-based rate adaptation (PRA), which employs a particle filter to estimate the a posteriori channel distribution. The PRA can easily be implemented even when the number of available rates is large. Numerical studies show that the PRA performs within one dB of SNR to the proposed upper bounds for a slowly time-varying channel, even in the presence of multi-user interference.

Modeling of Single-Step Power Control Scheme in Finite-State Markov Channel and Its Impact on Queuing Performance

In this paper, we analyze the queuing performance in the finite-state Markov channel (FSMC) when the single-step power control (SSPC) scheme is adopted. To start with, an SSPC model and its extended power control error (PCE) model are proposed and described in detail. Such models can emulate the behaviors of the interaction between the SSPC and an FSMC and the variation of the PCE with high accuracy. Furthermore, the packet error rate that has been recently analyzed by Lee and Chang is adopted to evaluate the service rate, the time average queuing length, and the probability mass function (PMF) of the queuing length variation. Based on these results, a queuing variation model is proposed to emulate the queuing variation in the FSMC. The flooring phenomenon of the queuing length is observed under a particular requirement of an overflow probability when the SNR value is greater than a certain value. This indicates that the tradeoff among the SNR, the buffer size of the queue, and the overflow probability exists. Hence, two different approaches to select the optimal target SNR of the SSPC and the maximum buffer size of the queue under the requested queuing buffer overflow probability are proposed. The improvement of the SSPC, its impact on the system, and the validity of the proposed models are shown in this paper as well.

The Error Exponent of Variable-Length Codes Over Markov Channels With Feedback

The error exponent of Markov channels with feedback is studied in the variable-length block-coding setting. Burnashev's classic result is extended to finite-state ergodic Markov channels. For these channels, a single-letter characterization of the reliability function is presented, under the assumption of full causal output feedback, and full causal observation of the channel state both at the transmitter and at the receiver side. Tools from stochastic control theory are used in order to treat channels with intersymbol interference (ISI). Specifically, the convex-analytic approach to Markov decision processes is adopted in order to handle problems with stopping time horizons induced by variable-length coding schemes.

Coherent continuous-phase frequency-shift keying: Parameter optimization and code design

The symmetric information rate of a modulation-constrained transmission system is the information-theoretic limit on performance under the assumption that the inputs are independent and uniformly distributed. The symmetric information rate for continuous-phase frequency-shift keying (CPFSK) over an AWGN channel may be estimated by considering the system to be a finite-state Markov channel and executing a BCJR-like algorithm. In this paper, the estimated symmetric information rate is used along with the exact expression for the 99% power bandwidth to determine the information-theoretic tradeoff between energy and spectral efficiency for CPFSK modulation. Using this tradeoff, the code rate and modulation index are jointly optimized for a particular spectral efficiency and alphabet size. Codes are then designed for the optimized system. The codes are comprised of variable nodes (which represent irregular repetition codes), check nodes (which represent single parity-check codes), and an interleaver connecting the variable and check nodes. The degree distributions of the code are optimized from the system's EXIT chart by using linear programming. Additional details of the code design, including labeling and interleaver design, are also discussed. Simulation results show that the optimized coded systems achieve bit error rates within 0.4 dB of the information-theoretic limits at BER = 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> .

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

We study information rates of time-varying flat-fading 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 lsim 12 dB) and at medium to fast normalized fading rates (0.01 lsim fDT lsim 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 lsim 0.01.

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.

Finite-state Markov Model for Lognormal, Chi-square (Central), Chi-square (Non-central), and K-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.

On the Capacity of Time-Varying Channels With Periodic Feedback

The capacity of time-varying channels with periodic feedback at the transmitter is evaluated. It is assumed that the channel-state information (CSI) is perfectly known at the receiver and is fed back to the transmitter at the regular time intervals. The system capacity is investigated in two cases: 1) finite-state Markov channel, and 2) additive white Gaussian noise channel with time-correlated fading. In the first case, it is shown that the capacity is achievable by multiplexing multiple codebooks across the channel. In the second case, the channel capacity and the optimal adaptive coding is obtained. It is shown that the optimal adaptation can be achieved by a single Gaussian codebook, while adaptively allocating the total power based on the side information at the transmitter.

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.

Adaptive Transmission of Multi-Layered Video over Wireless Fading Channels

In this paper, adaptive transmission of scalable multi-layered video with quality of service (QoS) assurance over wireless channels is studied. By properly formulating the channel fading as a finite state Markov channel (FSMC) model, three rate adaptation schemes, namely, assured-rate-allocation, neighbor- interleaving, and swing-loaded schemes, are proposed to exploit the inherent multiplexing gain. An analytical model for QoS performance evaluation of video transmission over time-varying erroneous channels is derived. The accuracy of the analytical model is validated by simulations. Analytical and simulation results demonstrate that the proposed rate adaptation schemes can effectively improve the channel utilization and the system throughput.

Low-density generator matrix codes for indoor and markov channels

We propose a modified algorithm for decoding of linear codes with low-density generator matrix (LDGM codes) over finite-state binary Markov channels. In order to avoid error floors, a serial concatenation of two LDGM codes is utilized. The hidden Markov model representing the channel is incorporated into the graph corresponding to the code, and the message passing algorithm is modified accordingly. The proposed scheme clearly outperforms systems in which the channel statistics are not exploited in the decoding process, allowing reliable communication at rates which are above the capacity of a memoryless channel with the same stationary bit error probability as the Markov channel. The proposed technique can be successfully applied for real wireless channels that can be modeled with hidden Markov models, such as indoor channels. In this case, the hidden Markov model representing the wireless channel can be estimated jointly with the decoding process

A Novel Analytical Framework for Integrated Cross-Layer Study of Call-Level and Packet-Level QoS in Wireless Mobile Multimedia Networks

We present a novel integrated analytical framework for analyzing the quality-of-service (QoS) performance measures in a wireless mobile multimedia network. The framework integrates physical, radio link, and network layer parameters and protocols to analyze the call-level and packet-level performances. In the network layer, call admission control (CAC) is responsible for deciding whether an incoming call can be accepted or not so that the performances of the ongoing calls do not deteriorate below the acceptable level. Also, an adaptive channel allocation (ACA) scheme is used to maximize the utilization of the radio resources. In the data link layer, queue management and error control are used for non-real-time loss-sensitive traffic. In the physical layer, a finite state Markov channel (FSMC) is used to model channel fading, and adaptive modulation is used for rate adaptation according to channel quality. Various call-level and packet-level QoS measures for real-time, non-real-time, and best-effort traffic are obtained. The analytical results are validated by extensive simulations. Examples of the applications of the presented analytical framework are also provided

Vector quantisation for finite‐state Markov channels and application to wireless communications

AbstractVector quantisation for joint source‐channel (JSC) coding over a finite‐state Markov channel (FSMC) is studied. In particular, minimum mean square error (MMSE) decoding of a vector quantised source in the absence of channel state information (CSI) is considered. Based on hidden Markov modelling of the channel output, two decoding strategies are proposed. The first one is a soft‐decoder which estimates the source reconstruction vectors directly from a sequence of channel output samples. The second one is a hard‐decoder based on joint maximum a posteriori (MAP) probability estimation of channel symbols and channel states. An iterative procedure for designing JSC optimised vector quantisers (VQs) is also proposed. Finally, the design of VQs for wireless channels using a finite‐state model is examined. Experimental results are provided for a Gauss‐Markov source and flat‐fading wireless channels. A comparison with an idealised tandem source‐channel coding system is also provided to demonstrate the advantage of the proposed JSC coding approach. Copyright © 2007 John Wiley &amp; Sons, Ltd.

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

A Successive Decoding Strategy for Channels With Memory

This paper presents a new technique for communication over channels with memory where the channel state is unknown at the transmitter and receiver. A deep interleaver combined with successive decoding decomposes a channel with memory into an array of parallel memoryless channels on which a conventional coding system can operate individually. The problems of joint channel estimation and decoding thus are separated without loss of capacity. This technique achieves channel capacity and so may be used to evaluate the capacities of different channels. A general information-theoretic framework is developed and applied to intersymbol interference (ISI), finite-state Markov, and Rayleigh-fading channels. A full system implementation, which performs within 1.1 dB of the channel capacity upper bound, is presented for the Rayleigh-fading channel