We propose a non-orthogonal multiple access (NOMA) scheme based on three-dimensional chaotic attractors, which we denote chaos-NOMA. In this system, the chaotic signals transmitted by each user are generated from the state variables of the attractor. We employ a principal component analysis algorithm for dimensionality reduction and obtain an orthonormal basis and a signal constellation for the chaotic signals. The dynamical properties of these signals result in the transmission of time-varying waveforms, modeled as an intrinsic noise. Depending on factors such as the number of users and the power difference of the transmitted signals, this intrinsic noise can lead to a performance curve exhibiting an error floor. We propose a neural network architecture coupled to the demodulator to mitigate the impact of the intrinsic noise.

Constrained sequences have been used in many storage systems as well as in data transmission schemes. These sequences are usually described by a deterministic graph. The graph with the fewest vertices is obtained, in general, via a two-step procedure: The first step is to generate an initial graph, and the second one is to apply a vertex-minimization algorithm to identify classes of equivalent vertices. Applying the new concept of constraint set this work presents a new splitting algorithm to determine the vertices of the minimal presentation without determining an initial graph. Thus the transition function that connects the vertices is calculated over a smaller set, reducing the computation efforts for constructing this graph.

The performance and complexity of turbo decoding using rate k/n constituent codes are investigated. The conventional, minimal and sectionalized trellis modules of the constituent convolutional codes are utilized. The performance metric is the bit error rate (BER), while complexity is analyzed based on the number of multiplications, summations and comparisons required by the max-log-MAP decoding algorithm. Our results show that the performance depends on how the systematic bits are grouped in a trellis module. The best performance is achieved when the k systematic bits are grouped together in the same section of the module, so that the log-likelihood ratio (LLR) of the k-bit vector is calculated at once. This is a characteristic of the conventional trellis module and of some of the sectionalizations of the minimal trellis module. Moreover, we show that it is possible to considerably reduce the decoding complexity with respect to the conventional trellis if a particular sectionalization of the minimal trellis module is utilized. In some cases, this sectionalization is found within the best performing group, while in some other cases a small performance loss can be traded off for a large complexity reduction.

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 channel's 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.

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.

A discrete fading channel (DFC) consisting of a binary modulated time-correlated Rayleigh fading channel used in conjunction with coherent soft-decision demodulation of resolution q is considered. The capacity of the binary input 2q-ary output DFC, which can be explicitly expressed in terms of a non-binary noise discrete channel with stationary ergodic 2q-ary noise, is evaluated in terms of q and the fading parameters. It is observed that considerable capacity gains can be achieved due to the channel's statistical 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 DFC is next fitted by a recently introduced analytically tractable queue-based (QB) Markovian noise model. The QB parameters are estimated via an iterative procedure that minimizes the Kullback-Leibler divergence rate between the DFC and QB noise sources. Modeling results, measured in terms of both channel noise correlation function and capacity reveal a good agreement between the two channels for a broad range of fading conditions.

A discrete (binary-input 2q-ary output) communication channel with memory is introduced with the objective to judiciously capture both the statistical memory and the soft-decision information of time-correlated fading channels modulated via binary phase-shift keying and coherently demodulated with an output quantizer of resolution q. It is shown that the discrete channel can be explicitly described in terms of its binary input process and a 2q-ary noise process. It is also shown that the channel is symmetric and admits a simple expression for its capacity when its noise is stationary ergodic. The 2q-ary noise process is next modeled via a generalized version of the recently studied binary queue-based channel (2007) to produce a mathematically tractable stationary ergodic M'th order Markovian noise source with 2q+ 2 parameters. Numerical results indicate that the capacity of the discrete channel with q = 2, 3 is substantially improved over the cases of perfect channel interleaving (which yields an equivalent memoryless channel) and of hard-decision demodulation (q = 1). These results point to potentially large performance gains achievable by designing coding schemes for this discrete channel that exploit both its memory and soft-decision information, as opposed to ignoring either of them.

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.

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.

This paper has two purposes the first of which is to introduce a precise definition of redundancy in homophonic coding and the second is to introduce a perfect homophonic coding technique. The new homophonic coding technique generalizes often with advantage an earlier scheme due to Rocha and Masseys.

In this paper, we investigate the behavior of the distance spectrum of convolutional codes when the decoding complexity is measured by the total number of edge symbols per information bit in the minimal trellis module representing the code. We conduct a code search restricted to the recently introduced class of generalized punctured convolutional codes, which is broad enough to contain good codes and yet has structural properties that facilitate the code search. New good convolutional codes are tabulated. For the same decoding complexity and the same code rate, the new codes have slightly better distance spectrum than the best known punctured convolutional codes. When compared to the best known unit-memory convolutional codes of the same rate, the new codes typically have improved free distance for a given decoding complexity, or about the same distance spectrum is achieved with much lower decoding complexity. Under this decoding complexity measure, the behaviour that higher decoding complexity implies better distance spectrum remains valid.

This work develops finite state channel (FSC) models for a discrete communication channel with flat fading and analyzes the throughput efficiency of the Go-Back-N (GBN) scheme of the automatic repeat request protocol on FSC 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 two classes of FSC models: first-order Markov and Gilbert-Elliott channel. The influence of the various parameters of the communication system on the throughput of the GBN protocol is evaluated

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).

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.

We investigate a method of communicating with chaos described by Hayes, Grebogi, and Ott (19913), 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 CO/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 (1963) capacity. The 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.

We study the performance of a decision feedback decoder (DFD) for convolutional codes over an interleaved burst channel. The DFD adaptively estimates channel reliability information from previous decisions. The effect of error propagation, finite interleaving and the length of the initial training sequence is explicitly studied. A binary Gilbert-Elliott channel is used to model the correlation structure of the error process. Comparison of the DFD and the hard decision decoding with Hamming metric reveals a crossover between the performance curves, depending on the interleaving parameters and channel statistics.

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.

The analysis of a communication system operating over finite state channel (FSC) models includes the calculation of the probability of subsets of error sequences. In this paper we first present an analytical method for evaluating the performance of non-interleaved Reed-Solomon (RS) codes over channels modeled as FSC models with an arbitrary number of states. The main idea is to express the probability of the number of error symbols produced by the channel in terms of a coefficient in a formal power series. Next, the method is extended to study the effect on the performance when an interleaving with finite depth is incorporated into the communication system. The general expressions are specialized for a Gilbert-Elliott channel (GEC) with known model parameters, and numerical results are derived.

Continuous phase modulation (CPM) signals may be precoded by a convolutional code followed by a mapping rule. Better codes may, however, be obtained by a more general code formed by a finite state machine. We provide improved codes for one such finite state machine. A new description of codes and design rules are presented. Better results are demonstrated for the partial response CPM schemes and previous optimum results are matched for the full response case. Tests of an M-algorithm decoder achieve near maximum-likelihood performance with only a fraction of the complexity of the Viterbi algorithm.>