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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. Index Terms--Convolutional codes, decoding complexity, distance spectrum, minimal trellis.

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. Index Terms--Automatic repeat request (ARQ), burst channels, flat fading, Gilbert-Elliott channel (GEC), throughput.

This paper derives a simple closed-form expression for computing the power spectral density (PSD) of constrained sequences whose constraints are characterized by a function of an ergodic Markov process specified in terms of a Mealy machine. A suitable matrix description of the stochastic behavior of the constrained sequence is used to express its autocorrelation sequence in a compact matrix form that simplifies the calculation of the PSD. Examples of the application of this technique in cases of practical interest are provided, including differentially encoded binary sequences, source-driven binary Huffman codes, maximum entropy (d, k) codes, and convolutional- or block-encoded sequences. A unified treatment to several widely used constrained sequences is provided. Index Terms--Autocorrelation function, Fourier transform, Markov chain, Mealy machine, Moore machine, power spectral density (PSD).

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. Index Terms--Combinatorial mathematics, constrained channels, discrete noiseless channel (DNC), Shannon capacity.

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 manipulates 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 [{[differential]T(x, y)/[differential]x}.sub.x=1] (the distance spectra) without first computing the complete T(x, g). Index Terms--Convolutional codes, distance spectra, signal flow graph, transfer function.

We present an analytical method for evaluating performance bounds for a communication system that employs a convolutional code, a block interleaving with finite interleaving depth, a binary channel that exhibits statistical dependence in the occurrence of errors, and a decoder that implements the Viterbi algorithm with Hamming metric. The main idea is to apply combinatorial methods to derive a formula for bounds to first-event and bit error probabilities in terms of coefficients of a generating series. The method is used to investigate the tradeoff between coding parameters and interleaving depth to achieve a required performance. Index Terms--Coded system performance, convolutional codes, finite-state channel (FSC), generalized transfer function, generating series, Gilbert-Elliott channels.

In this paper, we investigate a method of communicating with chaos described by Hayes, Grebogi, and Ott, which uses the idea of controlling chaos by small perturbations. Although allowing the electronics controlling the output signal to remain at the low-power level, this method unavoidably incurs a capacity loss, which we calculate for a chaotic C[O.sub.2] laser model. We first determine an approximation to the laser language, by means of a forbidden set representation, and then find its Shannon capacity. Results indicate that, since the capacity loss is not significant, the tradeoff is worthwhile. Finally, we point to simple finite-state encoders that satisfy the constraints imposed by the language. Index Terms--Chaos, finite-state codes, nonlinear dynamics, Shannon capacity, symbolic dynamics.

We present in this paper 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 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. Index Terms - Concatenated codes, error statistics, Fritchman model, Rician fading.