Cecilio Pimentel

Finite-state Markov modeling of correlated Rician-fading channels

Stochastic properties of the binary channel that describe the successes and failures of the transmission of a modulated signal over a time-correlated flat-fading channel are considered for investigation. This analysis is employed to develop Kth-order Markov models for such a burst channel. The order of the Markov model that generates accurate analytical models is estimated for a broad range of fading environments. The parameterization and accuracy of an important class of hidden Markov models, known as the Gilbert-Elliott channel (GEC), are also investigated. Fading rates are identified in which the Kth-order Markov model and the GEC model approximate the fading channel with similar accuracy. The latter model is useful for approximating slowly fading processes, since it provides a more compact parameterization.

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.

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.

Convolutional codes under a minimal trellis complexity measure

We conduct a code search, restricted to the recently introduced class of generalized punctured convolutional codes, under the minimal trellis complexity measure defined by McEliece and Lin. For the same decoding complexity and the same code rate, new codes are compared to well-known existing classes of convolutional codes. Some of the best convolutional codes (in a distance spectrum sense) of existing and new trellis complexities are tabulated.

Generalized punctured convolutional codes

This letter introduces the class of generalized punctured convolutional codes (GPCCs), which is broader than and encompasses the class of the standard punctured convolutional codes (PCCs). A code in this class can be represented by a trellis module, the GPCC trellis module, whose topology resembles that of the minimal trellis module. he GPCC trellis module for a PCC is isomorphic to the minimal trellis module. A list containing GPCCs with better distance spectrum than the best known PCCs with same code rate and trellis complexity is presented.

On the computation of weight enumerators for convolutional codes

Performance bounds for maximum-likelihood decoding of convolutional codes over memoryless channels are commonly measured using the distance weight enumerator T(x,y), also referred to as the transfer function, of the code. This paper presents an efficient iterative method to obtain T(x,y) called the state reduction algorithm. The algorithm is a systematic technique to simplify signal flow graphs that algebraically manipulate the symbolic adjacency matrix associated with the convolutional code. Next, the algorithm is modified to compute the first few terms of the series expansion of T(1,y) and {/spl part/T(x,y)//spl part/x}/sub x=1/ (the distance spectra) without first computing the complete T(x,y).

A Discrete Queue-Based Model for Capturing Memory and Soft-Decision Information in Correlated Fading Channels

A discrete (binary-input 2q-ary output) communication channel with memory is introduced to judiciously capture both the statistical memory and the soft-decision information of a time-correlated discrete fading channel (DFC) used with antipodal signaling and soft output quantization of resolution q. The discrete channel, which can be explicitly described via its binary input process and a 2q-ary noise process, is shown to be symmetric, thus admitting a simple expression for its capacity when its noise is stationary ergodic. It is observed that considerable capacity gains can be achieved due to the channels memory and the use of as few as 2 bits for soft-decision over interleaving the channel (to render it memoryless) and hard-decision demodulation (q=1). The 2q-ary noise process is next modeled via a queue-based (QB) ball-sampling mechanism to produce a mathematically tractable stationary ergodic Markovian noise source. The DFC is fitted by the QB noise model via an iterative procedure that minimizes the Kullback-Leibler divergence rate between the DFC and QB noise sources. Modeling results, measured in terms of channel noise correlation function and capacity reveal a good agreement between the two channels for a broad range of fading conditions.

A combinatorial approach to finding the capacity of the discrete noiseless channel

Shannon defined the capacity of the discrete noiseless channel (DNC) and considered a finite-state model from which the capacity can be calculated. Alternatively, the DNC may be (and often is) represented by a finite list of forbidden strings. In this correspondence, we demonstrate the application of combinatorial techniques to finding the Shannon capacity of the DNC directly from the forbidden list. In our derivations, the case of noninteger symbol durations, as introduced by Csiszar, is considered.

Minimal trellis for systematic recursive convolutional encoders

We consider high-rate systematic recursive convolutional encoders to be adopted as constituent encoders in turbo schemes. It has been shown by Douillard and Berrou that the construction of high-rate turbo codes by means of high-rate constituent encoders offers several advantages over the typical construction based on the puncturing of rate-1/2 constituent encoders. To reduce the decoding complexity associated with high-rate codes, we adopt the “minimal” trellis representation of convolutional codes introduced by McEliece and Lin. While in the literature this trellis has been obtained for nonrecursive nonsystematic generator matrices, we herein introduce the construction of the “minimal” trellis for a systematic recursive convolutional encoding matrix. We also derive expressions for the arithmetic decoding complexity when the max-log-MAP algorithm is applied over the conventional and the “minimal” trellises. Examples are provided, which show that significant savings in decoding complexity are obtained, while keeping the same error performance of conventional schemes, when the minimal trellis is used. Finally, a code search is conducted and examples are provided which indicate that a refinement in terms of decoding complexity-error performance trade-off is obtained.

Analysis of the Go-Back-

This paper develops Gilbert-Elliott channel (GEC) models for a discrete communication channel with flat fading and analyzes the throughput efficiency of the Go-Back-N scheme of the automatic repeat request (ARQ) protocol on GEC models. This protocol performance measure is then applied to determine the range of parameters of the communication system in which the binary error sequence generated by the discrete channel can be approximated by the GEC. The influence of the various parameters of the communication system on the throughput of different ARQ protocols, namely pure ARQ and type-I hybrid ARQ, is evaluated.