Finite-state Channel Model Research Articles

Random coding bound for channels with memory decoding function with partial overlapping. Part 2. Examples and Discussion

Introduction:Suboptimal random coding exponent Er*(R; ψ) for a wide class of finite-state channel models using a mismatched decoding function tp was obtained and presented in the first part of this work. We used tp function represented as a product of a posteriori probabilities of non-overlapped input subblocks of length 2B+1 relative to the overlapped output subblocks of length 2W+1. It has been shown that the computation of function Er*(R; ψ) is reduced to the calculation of the largest eigenvalue of a square non-negative matrix of an order depending on the B and W values.Purpose:Toillustrate the approach developed in the first part of this study with its application to various channel modelled as a probabilistic finite-state machine.Results:We consider channels with state transitions not depending on the input symbol (channels with freely evolving states), and channels with deterministic state transitions, in particular, intersymbol interference channels. We present and discuss numerical results of calculating this random coding exponent in a full range of code rates for some of channel models for which similar results were not obtained before. Practical computations were carried out for relatively small values of B and W. Nevertheless, even for small values of these parameters a good correspondence with some known results for optimal decoding was shown.

Markovian‐based framework for cooperative channel selection in cognitive radio networks

The authors propose Markovian-based spectrum sensing policies in a cognitive radio system that leverages past sensing outcomes of several cooperating secondary users (SUs) to decide which channel (of primary users – PUs) should be sensed by each SU at a given time. These policies are based on a new finite-state channel model that captures the fading condition as well as the occupancy state for each primary channel. The multiuser extension of this model is useful when multiple spatially distributed SUs share their sensing outcomes. The proposed schemes allow the asynchronous sensing outcomes obtained by the SUs over different slots to be fused together and converted into a posteriori probabilities for the current states of the primary channels. As the detection threshold in a spectrum detector balances the trade-off between the false-alarm and miss probabilities for detecting primary signals in a single primary channel, a design parameter is introduced to allow the system designer to devise policies with different levels of aggressiveness. The authors evaluate the optimality and complexity of the proposed sensing policies and show that our schemes significantly increase secondary use of the spectrum and/or reduce interference with PUs compared to a random selection policy or a cooperative sensing policy based on a two-state channel model.

Coding for High-Density Recording on a 1-D Granular Magnetic Medium

In terabit-density magnetic recording, several bits of data can be replaced by the values of their neighbors in the storage medium. As a result, errors in the medium are dependent on each other and also on the data written. We consider a simple one-dimensional combinatorial model of this medium. In our model, we assume a setting where binary data is sequentially written on the medium and a bit can erroneously change to the immediately preceding value. We derive several properties of codes that correct this type of errors, focusing on bounds on their cardinality. We also define a probabilistic finite-state channel model of the storage medium, and derive lower and upper estimates of its capacity. A lower bound is derived by evaluating the symmetric capacity of the channel, i.e., the maximum transmission rate under the assumption of the uniform input distribution of the channel. An upper bound is found by showing that the original channel is a stochastic degradation of another, related channel model whose capacity we can compute explicitly.

Effective capacity region of two-user opportunistic spectrum access

The effective capacity region of the two-user opportunistic spectrum access (OSA) system in Rayleigh fading environment is derived in this paper. Although OSA is a contemporary research topic, little attention has been given to the capacity analysis under quality-of-service (QoS) constraints. Hence, we use the effective capacity, which is a powerful tool to analyze the QoS requirements in wireless communication systems, to study the sustainable packet arrival rate of the secondary users while meeting statistical QoS constraints. We derive the effective capacity region of the two-user OSA system and propose a method to obtain the capacity region boundary. In addition, by combining the finite state channel model and the activity of the primary user, an extended finite state channel model for the two-user OSA system is also proposed.

A channel representation method for the study of hybrid retransmission-based error control

In this paper, we present a methodology to obtain a channel description tailored on performance evaluation for incremental redundancy hybrid automatic repeat request schemes. Such techniques counteract channel errors by using data coding and transmitting parts of the codeword over different channel realizations. We focus on coding performance models where the error probability is asymptotically zero if the channel parameters of these realizations fall within a given region. To map this region in a compact but still precise manner, we adopt a finite-state channel model. This approach is quite common in the literature; however, differently from existing work, we propose a novel method to derive efficient channel partitioning rules, i.e., a code-matched quantization of the channel state. Such a representation enables the use of accurate Markov models to study the system performance. Compared to existing channel representation methods, our proposed technique leads to a more accurate evaluation of higher layer statistics while at the same time keeping the computational complexity low.

A Novel Approach for Modeling a Hybrid ARQ (Automatic Repeat Request) Based on the Hidden Markov Model

In this letter, we propose a novel approach for use in the analytical modeling of the overall performance of a Hybrid ARQ (type I and II) together with arbitrary channel model, based on Hidden Markov Model (HMM). Using the combined HMM model developed for involved ARQ protocols with the finite state channel model, such critical performance measure as throughput and delay can be derived in closed form. Analytical results are derived for Stop-and-Wait as well as Go-back-N type together with the type I and type II Hybrid ARQ scheme adopted. We compare the analytical results along with the simulation results in order to check the correctness our model, and show the efficiency of our approach by applying it to realistic environments such as the CDMA IS-95 system with its derived equations.

Enumeration of Markov chains and burst error statistics for finite state channel models

The analysis of a communication system operating over finite state channel (FSC) models includes the calculation of the probability of subsets of error sequences. These probabilities are known as burst error statistics. The study of the statistical description of the error process has immediate applications in the modeling of real channels and in the design of coding schemes for channels with memory. We present a method to derive analytic expressions for burst error statistics of FSC models with an arbitrary number of states. We follow the theory of enumeration of constrained sequences to obtain an expression for the generating series which enumerates all permissible error sequences that constitute the burst event of interest. We will show that the probability of this event is obtained by acting on the generating series with a linear mapping. Such an approach allows the derivation of various burst error statistics used in the design of a coded system for FSC models.

Concatenated coding performance for FSK modulation on time-correlated Rician fading channels

We present an analytical method for evaluating the performance of noninterleaved concatenated codes over channels modeled as a nonfrequency selective correlated Rician fading channel with a known power spectral density. The main idea is to model the communication system from the modulator input to the demodulator output as a finite state channel (FSC) model, and apply powerful enumeration techniques to such a discrete channel in order to gain useful information on the system performance. The concatenated scheme makes use of two codes; Reed-Solomon codes are employed for the outer code, and binary block codes are used as the inner code. Next, the method is extended to study the effect on the performance when an interleaving with finite depth is incorporated into the communication system. A comparison between symbol and bit interleaving is made. Finally, we study the potential gain produced when channel information is passed on to the outer decoder in the form of an erasure symbol. In all cases, analytical expressions for the probability of the number of error symbols produced by the FSC model were obtained in terms of a coefficient in a formal power series. This is an interesting alternative approach with respect to computer simulations.

Modeling burst channels using partitioned Fritchman's Markov models

Discrete models based on functions of Markov chains (also referred to as hidden Markov models or finite-state channel (FSC) models) have been used to characterize the error process in communication channels with memory. One important property of these models is that the probability of any observed sequence can be expressed as a linear combination of the probability of a finite set of sequences of finite length, the so-called basis sequences. In this paper, we express the parameters of a class of FSC models as a simple function of the probability of the basis sequences. Based on this approach, we propose a new method for the parameterization of the Fritchman (1967) channel with single-error state as well as the interesting cases of Fritchman channels with more than one error state and the Gilbert-Elliott channel ((GEC) nonrenewal models). To illustrate the method, FSC models for the nonfrequency-selective Rician fading channel are presented. The number of states and the probability of state transitions are estimated for a given set of fading parameters.