Finite-state Markov modeling of fading channels - a survey of principles and applications <s> CONCLUSIONS AND FUTURE RESEARCH <s> An adaptive coding scheme for digital communication over time-varying channels is presented. The scheme is based on a finite-state Markov channel model. Emphasis is on the adaptation of the error protection to the actual channel state. The throughput gains that are achieved by the adaptive scheme relative to the conventional nonadaptive coding methods are demonstrated by several examples. Of special interest is the use of punctured convolutional codes with maximum-likelihood Viterbi algorithm to enable adaptive encoding and decoding without modifying the basic structure of the encoder and the decoder. > <s> BIB001 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> CONCLUSIONS AND FUTURE RESEARCH <s> Finite-state Markov channel (FSMC) models are useful for analysing radio channels with nonindependent fading, which give rise to bursty channel errors. In the paper the FSMC model is constructed by partitioning the dynamic range of the fade amplitude into finite number of intervals and representing each interval as a ‘state’ in the model. Transitions between these channel states thus characterise the physical fading process. Based on the Nakagami-m distribution, a new analytical formulation for the state transition probability is presented and validated for channels with arbitrary degrees of time-interleaving. The resultant FSMC model is shown to be applicable to a wide range of practical fading channels, including diversity-combined channels and multicarrier channels. <s> BIB002 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> CONCLUSIONS AND FUTURE RESEARCH <s> We describe parallel concatenated codes for communication over finite-state binary Markov channels. We present encoder design techniques and decoder processing modifications that utilize the a priori statistics of the channel and show that the resulting codes allow reliable communication at rates which are above the capacity of a memoryless channel with the same stationary bit error probability as the Markov channel. These codes outperform systems based on the traditional approach of using a channel interleaver to create a channel which is assumed to be memoryless. In addition, we introduce a joint estimation/decoding method that allows the estimation of the parameters of the hidden Markov model when they are not known a priori. <s> BIB003 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> CONCLUSIONS AND FUTURE RESEARCH <s> Density evolution analysis of low-density parity-check (LDPC) codes in memoryless channels is extended to the Gilbert-Elliott (GE) channel, which is a special case of a large class of channels with hidden Markov memory. In a procedure referred to as estimation decoding, the sum-product algorithm (SPA) is used to perform LDPC decoding jointly with channel-state detection. Density evolution results show (and simulation results confirm) that such decoders provide a significantly enlarged region of successful decoding within the GE parameter space, compared with decoders that do not exploit the channel memory. By considering a variety of ways in which a GE channel may be degraded, it is shown how knowledge of the decoding behavior at a single point of the GE parameter space may be extended to a larger region within the space, thereby mitigating the large complexity needed in using density evolution to explore the parameter space point-by-point. Using the GE channel as a straightforward example, we conclude that analysis of estimation decoding for LDPC codes is feasible in channels with memory, and that such analysis shows large potential gains. <s> BIB004 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> CONCLUSIONS AND FUTURE RESEARCH <s> In this paper, Rayleigh fading channel with an OFDMA system is modeled as a finite-state Markov channel (FSMC) by partitioning the received signal envelope into several intervals. With the aid of sub-band formation and property of lumpability, the size of feedback information can be reduced. This approach involves reducing an exponentially increased states of Markov channel to multiple lumpable Markov channels. The corresponding state transition probabilities and steady-state probabilities are used to predict channel states information in multiple symbol durations ahead. Some simulation examples are presented to illustrate the capability of the lumpable FSMC in channel prediction. <s> BIB005 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> CONCLUSIONS AND FUTURE RESEARCH <s> This paper addresses the problem of dynamic control for power and rate allocation in V-BLAST wireless systems over Markovian fading channels. The problem is posed as a controlled Markov decision process problem with the goal of minimizing the average transmission power with the constraint on the average delay that can be interpreted as the Quality of Service (QoS) requirement of a given application. Several structural results on the nature of the optimal randomized policies and costs are derived. In particular, it is shown that number of actions to be considered can be reduced by dividing the rate allocation problem into bit-loading problem across individual antennas and the total rate allocation based on the current buffer and channel state. Further, optimal rate allocation policies are shown to be a mixture of two pure policies that are non-decreasing in the buffer state. These results can be utilized to devise an efficient online learning algorithm for optimal rate allocation policies1. <s> BIB006 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> CONCLUSIONS AND FUTURE RESEARCH <s> We address the issue of optimal coding rate scheduling for adaptive type-I hybrid automatic repeat request wireless systems. In this scheme, the coding rate is varied depending on channel, buffer and incoming traffic conditions. In general, we consider the hidden Markov model for both time-varying flat fading channel and bursty correlated incoming traffic. It is shown that the appropriate framework for computing the optimal coding rate allocation policies is partially observable Markov decision process (POMDP). In this framework, the optimal coding rate allocation policy maximizes the reward function, which is a weighted sum of throughput and buffer occupancy with appropriate sign. Since polynomial amount of space is needed to calculate the optimal policy even for a simple POMDP problem, we investigate maximum-likelihood, voting and Q-MDP policy heuristic approaches for the purpose of efficient and real-time solution. Our results show that three heuristics perform close to completely observable system state case if the fading and/or traffic state mixing rate is slow. On the other hand, when the channel fading is fast, Q-MDP heuristic is the most throughput-efficient among considered heuristics. Also, its performance is close to the optimal coding rate allocation policy of fully observable system state case. We also explore the performances of the proposed heuristics in the bursty correlated traffic case and show that maximum-likelihood and voting heuristics consistently outperform the non-adaptive case <s> BIB007 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> CONCLUSIONS AND FUTURE RESEARCH <s> This paper presents a reduced-complexity approximate density evolution (DE) scheme for low-density parity-check (LDPC) codes in channels with memory in the form of a hidden Markov chain. This approximation is used to design degree sequences representing some of the best known LDPC code ensembles for the Gilbert-Elliott channel, and example optimizations are also given for other Markov channels. The problem of approximating the channel estimation is addressed by obtaining a specially constructed message-passing schedule in which the channel messages all approach their stable densities. It is shown that this new schedule is much easier to approximate than the standard schedule, but has the same ultimate performance in the limits of long block length and many decoding iterations. This result is extended to show that all message-passing schedules that satisfy mild conditions will have the same threshold under density evolution <s> BIB008 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> CONCLUSIONS AND FUTURE RESEARCH <s> We consider the problem of optimizing information rate upper and lower bounds for communication channels with (possibly large) memory. A recently proposed auxiliary-channel- based technique allows one to efficiently compute upper and lower bounds on the information rate of such channels. Towards tightening these bounds, we propose iterative expectation- maximization (EM) type algorithms to optimize the parameters of the auxiliary finite-state machine channel (FSMC). From a channel coding perspective, optimizing the lower bound is related to increasing the achievable mismatched information rate, i.e. the information rate of a communication system where the maximum-likelihood decoder at the receiver is matched to the auxiliary channel and not to the true channel. We provide explicit solutions for optimizing the upper bound and the difference between the upper and the lower bound and we discuss a method for the optimization of the lower bound for data-controllable channels with memory. We discuss examples of channels with memory, for which application of the developed theory results in noticeably tighter information rate bounds. <s> BIB009
Wireless communication systems that operate through fading channels have become more diverse and complex. In the last ten years, there has been a growing interest for research and development of advanced wireless communications systems that employ multicarrier (MC) techniques. So far, applications of FSMC models for fading channels has been mainly limited to single carrier (SC) communications with very few exceptions BIB002 , BIB005 . FSMC models are particulary suitable to represent and estimate the relatively fast flat-fading channel gain in each subcarrier. An unexplored avenue for research is to find appropriate FSMC models to represent MC fading channels. However, the number of TV-FFC gains to be modeled in the MC system is often much higher than in a SC system and a major challenge would be to keep the number of FSMC states to computationally manageable levels. Until now, FSMC models have been used to represent timevarying fading channels that are frequency flat. However, practical fading channels exhibit both time-varying and frequency-selective characteristics. Therefore, another direction for future research is to extend the FSMC modeling of fading channels to include frequency-selective fading channels of the form where J is the number of delayed paths and h ( j) is the fading gain of the jth path at time index , which is varying with time in a correlated manner. Again, care should be taken in the modeling stages to keep the number of FSMC states small to moderate, while accurately representing the frequency-selective fading channel. The obtained FSMC model may be then used to devise joint (and perhaps iterative) channel state estimation, equalization, and decoding techniques at the receiver. It is fair to say that a major challenge is to devise practical FSMC-based coding and decoding for fading channels (as described in application types two and three). While BIB003 - BIB004 have reported information rates higher than memoryless decoding limit by incorporating FSMC state estimation in the decoding algorithm, developing guidelines for the design of specialized LDPC and/or turbo codes to approach true FSMC capacity has been essentially an unexplored territory. A very recent work on the design of good LDPC codes for FSMC models is reported in BIB008 , which is further evidence of the current research trend in this area. It is also important to have the mismatched decoding setup in mind for testing the devised decoding algorithms. In this case, special attention is needed to optimize FSMC model parameters (such as the inclusion or exclusion of the fading phase or amplitude in the FSMC model, the number of FSMC states, memory order, and state transition probabilities) to minimize information rate loss through the actual and physical fading channel. Preliminary methodologies are reported in BIB009 for such optimizations. However, this problem certainly requires further investigation. Finally, the use of FSMC models for model-based channel prediction and adaptive coding techniques at the transmitter can be an avenue for future research activity. Modeling fading channels with a finite number of states is advantageous for channel prediction and adaptive coding, because only a few coding rates/strategies need to be developed depending on the finite number of channel states. Also, the receiver can provide feedback to the transmitter only about a few estimated channel states, which reduces the data rate on the feedback link. It is expected that the recent developments in the information theory of data-independent FSMC models with feedback will lead to the design of capacity approaching and causal adaptive coding techniques. The application of MDP and POMDP for adaptive transmission in FSMC-modeled fading channels was recently proposed in BIB001 and BIB006 - BIB007 . This area may also be further investigated and extended in the future. Given the current trends and avenues for future research, it is expected that research into new applications of FSMC models for fading channels will continue to be an active area for many years.