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A performance analysis of a slow frequency-hopped, noncoherent binary frequency-shift keying (SFH/NCBFSK) communication system with rate 1/2 convolutional coding and soft decision Viterbi detection in the presence of partial-band noise jamming is performed. The effect of additive white Gaussian noise is also considered. The analysis is performed for both a non-fading channel and a Ricean fading channel. The system's performance is severely degraded by partial-band noise jamming. By way of comparison the analysis is also performed when the system utilizes hard decision Viterbi detection and for a system utilizing noise-normalized combining with soft decision Viterbi detection. In both cases a significant increase in the system's immunity to the effects of partial-band noise jamming is achieved.

The convolutional sparse model has recently gained increasing attention in the signal and image processing communities, and several methods have been proposed for solving the pursuit problem emerging from it -- in particular its convex relaxation, Basis Pursuit. In the first of this two-part work, we have provided a theoretical back-bone for this model, providing guarantees for the uniqueness of the sparsest solution and for the success of pursuit algorithms by introducing the notion of stripe sparsity and other related measures. Herein, we extend the analysis to a noisy regime, thereby considering signal perturbations and model deviations. We address questions of stability of the sparsest solutions and the success of pursuit algorithms, both greedy and convex. Classical definitions such as the RIP are generalized to the convolutional model, and existing notions such as the ERC are connected to our setting. On the algorithmic side, we demonstrate how to solve the global pursuit problem by using simple local processing, thus offering a first of its kind bridge between global modeling of signals and their patch-based local treatment.

Motion compensation is a fundamental technology in video coding to remove the temporal redundancy between video frames. To further improve the coding efficiency, sub-pel motion compensation has been utilized, which requires interpolation of fractional samples. The video coding standards usually adopt fixed interpolation filters that are derived from the signal processing theory. However, as video signal is not stationary, the fixed interpolation filters may turn out less efficient. Inspired by the great success of convolutional neural network (CNN) in computer vision, we propose to design a CNN-based interpolation filter (CNNIF) for video coding. Different from previous studies, one difficulty for training CNNIF is the lack of ground-truth since the fractional samples are actually not available. Our solution for this problem is to derive the "ground-truth" of fractional samples by smoothing high-resolution images, which is verified to be effective by the conducted experiments. Compared to the fixed half-pel interpolation filter for luma in High Efficiency Video Coding (HEVC), our proposed CNNIF achieves up to 3.2% and on average 0.9% BD-rate reduction under low-delay P configuration.

Motion compensation is a fundamental technology in video coding to remove the temporal redundancy between video frames. To further improve the coding efficiency, sub-pel motion compensation has been utilized, which requires interpolation of fractional samples. The video coding standards usually adopt fixed interpolation filters that are derived from the signal processing theory. However, as video signal is not stationary, the fixed interpolation filters may turn out less efficient. Inspired by the great success of convolutional neural network (CNN) in computer vision, we propose to design a CNN-based interpolation filter (CNNIF) for video coding. Different from previous studies, one difficulty for training CNNIF is the lack of ground-truth since the fractional samples are actually not available. Our solution for this problem is to derive the "ground-truth" of fractional samples by smoothing high-resolution images, which is verified to be effective by the conducted experiments. Compared to the fixed half-pel interpolation filter for luma in High Efficiency Video Coding (HEVC), our proposed CNNIF achieves up to 3.2% and on average 0.9% BD-rate reduction under low-delay P configuration.

We propose an efficient Adaptive Random Convolutional Network Coding (ARCNC) algorithm to address the issue of field size in random network coding. ARCNC operates as a convolutional code, with the coefficients of local encoding kernels chosen randomly over a small finite field. The lengths of local encoding kernels increase with time until the global encoding kernel matrices at related sink nodes all have full rank. Instead of estimating the necessary field size a priori, ARCNC operates in a small finite field. It adapts to unknown network topologies without prior knowledge, by locally incrementing the dimensionality of the convolutional code. Because convolutional codes of different constraint lengths can coexist in different portions of the network, reductions in decoding delay and memory overheads can be achieved with ARCNC. We show through analysis that this method performs no worse than random linear network codes in general networks, and can provide significant gains in terms of average decoding delay in combination networks.

We propose an efficient Adaptive Random Convolutional Network Coding (ARCNC) algorithm to address the issue of field size in random network coding. ARCNC operates as a convolutional code, with the coefficients of local encoding kernels chosen randomly over a small finite field. The lengths of local encoding kernels increase with time until the global encoding kernel matrices at related sink nodes all have full rank. Instead of estimating the necessary field size a priori, ARCNC operates in a small finite field. It adapts to unknown network topologies without prior knowledge, by locally incrementing the dimensionality of the convolutional code. Because convolutional codes of different constraint lengths can coexist in different portions of the network, reductions in decoding delay and memory overheads can be achieved with ARCNC. We show through analysis that this method performs no worse than random linear network codes in general networks, and can provide significant gains in terms of average decoding delay in combination networks.

We present a general theory of entanglement-assisted quantum convolutional coding. The codes have a convolutional or memory structure, they assume that the sender and receiver share noiseless entanglement prior to quantum communication, and they are not restricted to possess the Calderbank-Shor-Steane structure as in previous work. We provide two significant advances for quantum convolutional coding theory. We first show how to "expand" a given set of quantum convolutional generators. This expansion step acts as a preprocessor for a polynomial symplectic Gram-Schmidt orthogonalization procedure that simplifies the commutation relations of the expanded generators to be the same as those of entangled Bell states (ebits) and ancilla qubits. The above two steps produce a set of generators with equivalent error-correcting properties to those of the original generators. We then demonstrate how to perform online encoding and decoding for a stream of information qubits, halves of ebits, and ancilla qubits. The upshot of our theory is that the quantum code designer can engineer quantum convolutional codes with desirable error-correcting properties without having to worry about the commutation relations of these generators.

We show how to protect a stream of quantum information from decoherence induced by a noisy quantum communication channel. We exploit preshared entanglement and a convolutional coding structure to develop a theory of entanglement-assisted quantum convolutional coding. Our construction produces a Calderbank-Shor-Steane (CSS) entanglement-assisted quantum convolutional code from two arbitrary classical binary convolutional codes. The rate and error-correcting properties of the classical convolutional codes directly determine the corresponding properties of the resulting entanglement-assisted quantum convolutional code. We explain how to encode our CSS entanglement-assisted quantum convolutional codes starting from a stream of information qubits, ancilla qubits, and shared entangled bits.

Multiple Instance Learning (MIL) is commonly utilized in weakly supervised whole slide image (WSI) classification. MIL techniques typically involve a feature embedding step using a pretrained feature extractor, then an aggregator that aggregates the embedded instances into predictions. Current efforts aim to enhance these sections by refining feature embeddings through self-supervised pretraining and modeling correlations between instances. In this paper, we propose a convolutional sparsely coded MIL (CSCMIL) that utilizes convolutional sparse dictionary learning to simultaneously address these two aspects. Sparse dictionary learning consists of filters or kernels that are applied with convolutional operations and utilizes an overly comprehensive dictionary to represent instances as sparse linear combinations of atoms, thereby capturing their similarities. Straightforwardly built into existing MIL frameworks, the suggested CSC module has an affordable computation cost. Experiments on various datasets showed that the suggested CSC module improved performance by 3.85% in AUC and 4.50% in accuracy, equivalent to the SimCLR pretraining (4.21% and 4.98%) significantly of current MIL approaches.

A performance analysis of a slow frequency-hopped, noncoherent binary frequency-shift keying (SFH/NCBFSK) communication system with rate 1/2 convolutional coding and soft decision Viterbi detection in the presence of partial-band noise jamming is performed. The effect of additive white Gaussian noise is also considered. The analysis is performed for both a non-fading channel and a Ricean fading channel. The system's performance is severely degraded by partial-band noise jamming. By way of comparison the analysis is also performed when the system utilizes hard decision Viterbi detection and for a system utilizing noise-normalized combining with soft decision Viterbi detection. In both cases a significant increase in the system's immunity to the effects of partial-band noise jamming is achieved.

The purpose of this thesis is to model a satellite communication system with VSATs, using Spread Spectrum CDMA methods and Forward Error Correction (FEC). Walsh codes and PN sequences are used to generate a CDMA system and FEC is used to further improve the performance. Convolutional and block coding methods are examined and the results are obtained for each different case, including concatenated use of the codes. The performance of the system is given in terms of Bit Error Rate (BER). As observed from the results, the performance is mainly affected by the number of users and the code rates.

We present algorithms for initializing a convolutional network coding scheme in networks that may contain cycles. An initialization process is needed if the network is unknown or if local encoding kernels are chosen randomly. During the initialization process every source node transmits basis vectors and every sink node measures the impulse response of the network. The impulse response is then used to find a relationship between the transmitted and the received symbols, which is needed for a decoding algorithm and to find the set of all achievable rates. Unlike acyclic networks, for which it is enough to transmit basis vectors one after another, the initialization of cyclic networks is more involved, as pilot symbols interfere with each other and the impulse response is of infinite duration.

The celebrated sparse representation model has led to remarkable results in various signal processing tasks in the last decade. However, despite its initial purpose of serving as a global prior for entire signals, it has been commonly used for modeling low dimensional patches due to the computational constraints it entails when deployed with learned dictionaries. A way around this problem has been proposed recently, adopting a convolutional sparse representation model. This approach assumes that the global dictionary is a concatenation of banded Circulant matrices. Although several works have presented algorithmic solutions to the global pursuit problem under this new model, very few truly-effective guarantees are known for the success of such methods. In the first of this two-part work, we address the theoretical aspects of the sparse convolutional model, providing the first meaningful answers to corresponding questions of uniqueness of solutions and success of pursuit algorithms. To this end, we generalize mathematical quantities, such as the $\ell_0$ norm, the mutual coherence and the Spark, to their counterparts in the convolutional setting, which intrinsically capture local measures of the global model. In a companion paper, we extend the analysis to a noisy regime, addressing the stability of the sparsest solutions and pursuit algorithms, and demonstrate practical approaches for solving the global pursuit problem via simple local processing.

Sparse and convolutional constraints form a natural prior for many optimization problems that arise from physical processes. Detecting motifs in speech and musical passages, super-resolving images, compressing videos, and reconstructing harmonic motions can all leverage redundancies introduced by convolution. Solving problems involving sparse and convolutional constraints remains a difficult computational problem, however. In this paper we present an overview of convolutional sparse coding in a consistent framework. The objective involves iteratively optimizing a convolutional least-squares term for the basis functions, followed by an L1-regularized least squares term for the sparse coefficients. We discuss a range of optimization methods for solving the convolutional sparse coding objective, and the properties that make each method suitable for different applications. In particular, we concentrate on computational complexity, speed to {\epsilon} convergence, memory usage, and the effect of implied boundary conditions. We present a broad suite of examples covering different signal and application domains to illustrate the general applicability of convolutional sparse coding, and the efficacy of the available optimization methods.

Most of multipath multimedia streaming proposals use Forward Error Correction (FEC) approach to protect from packet losses. However, FEC does not sustain well burst of losses even when packets from a given FEC block are spread over multiple paths. In this article, we propose an online multipath convolutional coding for real-time multipath streaming based on an on-the-fly coding scheme called Tetrys. We evaluate the benefits brought out by this coding scheme inside an existing FEC multipath load splitting proposal known as Encoded Multipath Streaming (EMS). We demonstrate that Tetrys consistently outperforms FEC in both uniform and burst losses with EMS scheme. We also propose a modification of the standard EMS algorithm that greatly improves the performance in terms of packet recovery. Finally, we analyze different spreading policies of the Tetrys redundancy traffic between available paths and observe that the longer propagation delay path should be preferably used to carry repair packets.

Most of multipath multimedia streaming proposals use Forward Error Correction (FEC) approach to protect from packet losses. However, FEC does not sustain well burst of losses even when packets from a given FEC block are spread over multiple paths. In this article, we propose an online multipath convolutional coding for real-time multipath streaming based on an on-the-fly coding scheme called Tetrys. We evaluate the benefits brought out by this coding scheme inside an existing FEC multipath load splitting proposal known as Encoded Multipath Streaming (EMS). We demonstrate that Tetrys consistently outperforms FEC in both uniform and burst losses with EMS scheme. We also propose a modification of the standard EMS algorithm that greatly improves the performance in terms of packet recovery. Finally, we analyze different spreading policies of the Tetrys redundancy traffic between available paths and observe that the longer propagation delay path should be preferably used to carry repair packets.

An analysis of the performance of a binary phase shift keying (BPSK) communication system employing fast frequency hopped (FFH) spread spectrum modulation under conditions of hostile partial band noise interference is performed in this thesis. The data are assumed to be encoded using convolutional coding and the receivers are assumed to use soft decision Viterbi decoding. The receiver structures to be examined are the conventional FFH/BPSK receiver with diversity the conventional FFH/BPSK receiver with diversity and the assumption of perfect side information and the noise normalized FFH/BPSK combining receiver with diversity. The FFH/BPSK noise normalized receiver with diversity minimizes the effects of hostile partial band noise interference and alleviates the effects of fading. The effect of inaccurate measurement of the noise power present in each hop is also examined and it is found that noise measurement error does not significantly degrade receiver performance. For the conventional FFH/BPSK receiver with perfect side information the effect of a Ricean fading channel is also examined.

We outline a quantum convolutional coding technique for protecting a stream of classical bits and qubits. Our goal is to provide a framework for designing codes that approach the ``grandfather'' capacity of an entanglement-assisted quantum channel for sending classical and quantum information simultaneously. Our method incorporates several resources for quantum redundancy: fresh ancilla qubits, entangled bits, and gauge qubits. The use of these diverse resources gives our technique the benefits of both active and passive quantum error correction. We can encode a classical-quantum bit stream with periodic quantum gates because our codes possess a convolutional structure. We end with an example of a ``grandfather'' quantum convolutional code that protects one qubit and one classical bit per frame by encoding them with one fresh ancilla qubit, one entangled bit, and one gauge qubit per frame. We explicitly provide the encoding and decoding circuits for this example.

"June 1998."

The performance of coherent and noncoherent RAKE receivers over a fading channel in the presence of pulse-noise interference and additive white Gaussian noise is analyzed. Coherent RAKE receivers require a pilot tone for coherent demodulation. Using a first order phase-lock-loop to recover a pilot tone with additive white Gaussian noise causes phase distortions at the phase-lock-loop output, which produce an irreducible phase noise error floor for soft decision Viterbi decoding. Both coherent and noncoherent RAKE receivers optimized for additive white Gaussian noise perform poorly when pulse-noise interference is present. When soft decision convolutional coding is considered, the performance degrades as the duty cycle of the pulse-noise interference signal decreases. The reverse is true for hard decision Viterbi decoding, since fewer bits experience interference and bit errors with high noise variance cannot dominate the decision statistics. Soft decision RAKE receiver optimized for pulse-noise interference and additive white Gaussian noise performed the best for both the coherent and noncoherent RAKE receivers. This receiver scales the received signal by the inverse of the variance on a bit-by-bit basis to minimize the effect of pulse-noise interference. The efficacy is demonstrated by analytical results, which reveal that this receiver reduces the probability of bit error down to the irreducible phase noise error floor when pulse-noise interference is present. This demonstrates how important it is to design the receiver for the intended operational environment.

In source coding, either with or without side information at the decoder, the ultimate performance can be achieved by means of random binning. Structured binning into cosets of performing channel codes has been successfully employed in practical applications. In this letter it is formally shown that various convolutional- and turbo-syndrome decoding algorithms proposed in literature lead in fact to the same estimate. An equivalent implementation is also delineated by directly tackling syndrome decoding as a maximum a posteriori probability problem and solving it by means of iterative message-passing. This solution takes advantage of the exact same structures and algorithms used by the conventional channel decoder for the code according to which the syndrome is formed.

We show how extra entanglement shared between sender and receiver reduces the memory requirements for a general entanglement-assisted quantum convolutional code. We construct quantum convolutional codes with good error-correcting properties by exploiting the error-correcting properties of an arbitrary basic set of Pauli generators. The main benefit of this particular construction is that there is no need to increase the frame size of the code when extra shared entanglement is available. Then there is no need to increase the memory requirements or circuit complexity of the code because the frame size of the code is directly related to these two code properties. Another benefit, similar to results of previous work in entanglement-assisted convolutional coding, is that we can import an arbitrary classical quaternary code for use as an entanglement-assisted quantum convolutional code. The rate and error-correcting properties of the imported classical code translate to the quantum code. We provide an example that illustrates how to import a classical quaternary code for use as an entanglement-assisted quantum convolutional code. We finally show how to "piggyback" classical information to make use of the extra shared entanglement in the code.

Subband Speech Coding and Matched Convolutional Channel Coding for Mobile Radio Channels DOI: 10.1109/78.91143

Convolutional neural networks (CNN) have led to many state-of-the-art results spanning through various fields. However, a clear and profound theoretical understanding of the forward pass, the core algorithm of CNN, is still lacking. In parallel, within the wide field of sparse approximation, Convolutional Sparse Coding (CSC) has gained increasing attention in recent years. A theoretical study of this model was recently conducted, establishing it as a reliable and stable alternative to the commonly practiced patch-based processing. Herein, we propose a novel multi-layer model, ML-CSC, in which signals are assumed to emerge from a cascade of CSC layers. This is shown to be tightly connected to CNN, so much so that the forward pass of the CNN is in fact the thresholding pursuit serving the ML-CSC model. This connection brings a fresh view to CNN, as we are able to attribute to this architecture theoretical claims such as uniqueness of the representations throughout the network, and their stable estimation, all guaranteed under simple local sparsity conditions. Lastly, identifying the weaknesses in the above pursuit scheme, we propose an alternative to the forward pass, which is connected to deconvolutional, recurrent and residual networks, and has better theoretical guarantees.

Cell ensembles, originally proposed by Donald Hebb in 1949, are subsets of synchronously firing neurons and proposed to explain basic firing behavior in the brain. Despite having been studied for many years no conclusive evidence has been presented yet for their existence and involvement in information processing such that their identification is still a topic of modern research, especially since simultaneous recordings of large neuronal population have become possible in the past three decades. These large recordings pose a challenge for methods allowing to identify individual neurons forming cell ensembles and their time course of activity inside the vast amounts of spikes recorded. Related work so far focused on the identification of purely simulta- neously firing neurons using techniques such as Principal Component Analysis. In this paper we propose a new algorithm based on sparse convolution coding which is also able to find ensembles with temporal structure. Application of our algorithm to synthetically generated datasets shows that it outperforms previous work and is able to accurately identify temporal cell ensembles even when those contain overlapping neurons or when strong background noise is present.

We consider an \textit{Adaptive Random Convolutional Network Coding} (ARCNC) algorithm to address the issue of field size in random network coding for multicast, and study its memory and decoding delay performances through both analysis and numerical simulations. ARCNC operates as a convolutional code, with the coefficients of local encoding kernels chosen randomly over a small finite field. The cardinality of local encoding kernels increases with time until the global encoding kernel matrices at related sink nodes have full rank.ARCNC adapts to unknown network topologies without prior knowledge, by locally incrementing the dimensionality of the convolutional code. Because convolutional codes of different constraint lengths can coexist in different portions of the network, reductions in decoding delay and memory overheads can be achieved. We show that this method performs no worse than random linear network codes in terms of decodability, and can provide significant gains in terms of average decoding delay or memory in combination, shuttle and random geometric networks.

Higher-dimensional analogs of the predictable degree property and column reducedness are defined, and it is proved that the two properties are equivalent. It is shown that every multidimensional convolutional code has, what is called, a minimal reduced polynomial resolution. It is uniquely determined (up to isomorphism) and leads to a number of important integer invariants of the code generalizing classical Forney's indices.

The performance analysis of a differential phase shift keyed (DPSK) communications system, operating in a Rayleigh fading environment, employing convolutional coding and diversity processing is presented. The receiver is the conventional square-law DPSK receiver using soft-decision convolutional decoding. The computationally efficient union bound technique is utilized to evaluate the system performance. The coded and uncoded system performances of various diversity combining techniques are evaluated and compared. The combining techniques considered include equal gain combining (EGC), selection combining (SC), and a generalization of SC, whereby two or three signals with the two or three largest amplitudes are noncoherently combined. This generalized method is called second or third order SC and denoted as SC2 or SC3, respectively. Numerical results indicate that coded systems with SC2 and SC3 techniques significantly enhance the bit-error rate (BER) performance relative to that achievable with SC

Lossy image and video compression algorithms yield visually annoying artifacts including blocking, blurring, and ringing, especially at low bit-rates. To reduce these artifacts, post-processing techniques have been extensively studied. Recently, inspired by the great success of convolutional neural network (CNN) in computer vision, some researches were performed on adopting CNN in post-processing, mostly for JPEG compressed images. In this paper, we present a CNN-based post-processing algorithm for High Efficiency Video Coding (HEVC), the state-of-the-art video coding standard. We redesign a Variable-filter-size Residue-learning CNN (VRCNN) to improve the performance and to accelerate network training. Experimental results show that using our VRCNN as post-processing leads to on average 4.6% bit-rate reduction compared to HEVC baseline. The VRCNN outperforms previously studied networks in achieving higher bit-rate reduction, lower memory cost, and multiplied computational speedup.

Whenever size, power, or other constraints preclude the use of multiple-input multiple-output (MIMO) systems, wireless systems cannot benefit from the well- known advantages of space-time coding (STC) methods. Also the complexity (multiple radio-frequency (RF) front ends at both the transmitter and the receiver), channel estimation, and spatial correlation in centralized MIMO systems degrade the performance. In situations like these, the alternative would be to resort to cooperative communications via multiple relay nodes. When these nodes work cooperatively, they form a virtual MIMO system. The destination receives multiple versions of the same message from the source and one or more relays, and combines these to create diversity.

An error probability analysis of a communications link employing convolutional coding with soft decision viterbi decoding implemented on a fast frequency hopped, binary frequency shift keying (FFH(BFSK) spread spectrum system is performed. The signal is transmitted through a Rician fading channel with partial band noise interference. The receiver structures examined are the conventional receiver with no diversity, the conventional receiver with diversity and the assumption of perfect side information, and the self normalized combining receiver with diversity. The self normalized receiver minimizes the effects of hostile partial band interference, while diversity alleviates the effects of fading. It is found that with the implementation of soft decision viterbi decoding the performance of the self normalized receiver is improved dramatically for moderate coded bit energy to partialband noise power spectral density ratio (EbNI). Coding drives the jammer to a full band jamming strategy for worst case performance. Nearly worst case jamming occurs when barrage jamming is employed and there is no diversity even in cases where there is very strong direct signal. Performance improves as the constraint length of the convolutional code is increased. For the most powerful convolutional codes, performance is seen to degrade slightly with increasing diversity except in instances of a very weak direct signal. Also, soft decision decoding is found to be superior to hard decision decoding by approximately 4 dB at moderate Eb/NI.

Random network coding recently attracts attention as a technique to disseminate information in a network. This paper considers a non-coherent multi-shot network, where the unknown and time-variant network is used several times. In order to create dependencies between the different shots, particular convolutional codes in rank metric are used. These codes are so-called (partial) unit memory ((P)UM) codes, i.e., convolutional codes with memory one. First, distance measures for convolutional codes in rank metric are shown and two constructions of (P)UM codes in rank metric based on the generator matrices of maximum rank distance codes are presented. Second, an efficient error-erasure decoding algorithm for these codes is presented. Its guaranteed decoding radius is derived and its complexity is bounded. Finally, it is shown how to apply these codes for error correction in random linear and affine network coding.

In this paper, convolutional network coding is formulated by means of matrix power series representation of the local encoding kernel (LEK) matrices and global encoding kernel (GEK) matrices to establish its theoretical fundamentals for practical implementations. From the encoding perspective, the GEKs of a convolutional network code (CNC) are shown to be uniquely determined by its LEK matrix $K(z)$ if $K_0$, the constant coefficient matrix of $K(z)$, is nilpotent. This will simplify the CNC design because a nilpotent $K_0$ suffices to guarantee a unique set of GEKs. Besides, the relation between coding topology and $K(z)$ is also discussed. From the decoding perspective, the main theme is to justify that the first $L+1$ terms of the GEK matrix $F(z)$ at a sink $r$ suffice to check whether the code is decodable at $r$ with delay $L$ and to start decoding if so. The concomitant decoding scheme avoids dealing with $F(z)$, which may contain infinite terms, as a whole and hence reduces the complexity of decodability check. It potentially makes CNCs applicable to wireless networks.

An analysis of the performance of a binary phase shift keying (BPSK) communication system employing fast frequency hopped (FFH) spread spectrum modulation under conditions of hostile partial band noise interference is performed in this thesis. The data are assumed to be encoded using convolutional coding and the receivers are assumed to use soft decision Viterbi decoding. The receiver structures to be examined are the conventional FFH/BPSK receiver with diversity the conventional FFH/BPSK receiver with diversity and the assumption of perfect side information and the noise normalized FFH/BPSK combining receiver with diversity. The FFH/BPSK noise normalized receiver with diversity minimizes the effects of hostile partial band noise interference and alleviates the effects of fading. The effect of inaccurate measurement of the noise power present in each hop is also examined and it is found that noise measurement error does not significantly degrade receiver performance. For the conventional FFH/BPSK receiver with perfect side information the effect of a Ricean fading channel is also examined.

This paper presents a variable-length decision-feedback scheme that uses tail-biting convolutional codes and the tail-biting Reliability-Output Viterbi Algoritm (ROVA). Comparing with recent results in finite-blocklength information theory, simulation results for both the BSC and the AWGN channel show that the decision-feedback scheme using ROVA can surpass the random-coding lower bound on throughput for feedback codes at average blocklengths less than 100 symbols. This paper explores ROVA-based decision feedback both with decoding after every symbol and with decoding limited to a small number of increments. The performance of the reliability-based stopping rule with the ROVA is compared to retransmission decisions based on CRCs. For short blocklengths where the latency overhead of the CRC bits is severe, the ROVA-based approach delivers superior rates.

The performance of coherent and noncoherent RAKE receivers over a fading channel in the presence of pulse-noise interference and additive white Gaussian noise is analyzed. Coherent RAKE receivers require a pilot tone for coherent demodulation. Using a first order phase-lock-loop to recover a pilot tone with additive white Gaussian noise causes phase distortions at the phase-lock-loop output, which produce an irreducible phase noise error floor for soft decision Viterbi decoding. Both coherent and noncoherent RAKE receivers optimized for additive white Gaussian noise perform poorly when pulse-noise interference is present. When soft decision convolutional coding is considered, the performance degrades as the duty cycle of the pulse-noise interference signal decreases. The reverse is true for hard decision Viterbi decoding, since fewer bits experience interference and bit errors with high noise variance cannot dominate the decision statistics. Soft decision RAKE receiver optimized for pulse-noise interference and additive white Gaussian noise performed the best for both the coherent and noncoherent RAKE receivers. This receiver scales the received signal by the inverse of the variance on a bit-by-bit basis to minimize the effect of pulse-noise interference. The efficacy is demonstrated by analytical results, which reveal that this receiver reduces the probability of bit error down to the irreducible phase noise error floor when pulse-noise interference is present. This demonstrates how important it is to design the receiver for the intended operational environment.

An error probability analysis of a communications link employing convolutional coding with soft decision viterbi decoding implemented on a fast frequency hopped, binary frequency shift keying (FFH(BFSK) spread spectrum system is performed. The signal is transmitted through a Rician fading channel with partial band noise interference. The receiver structures examined are the conventional receiver with no diversity, the conventional receiver with diversity and the assumption of perfect side information, and the self normalized combining receiver with diversity. The self normalized receiver minimizes the effects of hostile partial band interference, while diversity alleviates the effects of fading. It is found that with the implementation of soft decision viterbi decoding the performance of the self normalized receiver is improved dramatically for moderate coded bit energy to partialband noise power spectral density ratio (EbNI). Coding drives the jammer to a full band jamming strategy for worst case performance. Nearly worst case jamming occurs when barrage jamming is employed and there is no diversity even in cases where there is very strong direct signal. Performance improves as the constraint length of the convolutional code is increased. For the most powerful convolutional codes, performance is seen to degrade slightly with increasing diversity except in instances of a very weak direct signal. Also, soft decision decoding is found to be superior to hard decision decoding by approximately 4 dB at moderate Eb/NI.

The performance analysis of a differential phase shift keyed (DPSK) communications system, operating in a Rayleigh fading environment, employing convolutional coding and diversity processing is presented. The receiver is the conventional square-law DPSK receiver using soft-decision convolutional decoding. The computationally efficient union bound technique is utilized to evaluate the system performance. The coded and uncoded system performances of various diversity combining techniques are evaluated and compared. The combining techniques considered include equal gain combining (EGC), selection combining (SC), and a generalization of SC, whereby two or three signals with the two or three largest amplitudes are noncoherently combined. This generalized method is called second or third order SC and denoted as SC2 or SC3, respectively. Numerical results indicate that coded systems with SC2 and SC3 techniques significantly enhance the bit-error rate (BER) performance relative to that achievable with SC.

Concatenated coding systems utilizing a convolutional code as the inner code and a Reed-Solomon code as the outer code are considered. In order to obtain very reliable communications over a very noisy channel with relatively small coding complexity, it is proposed to concatenate a byte oriented unit memory convolutional code with an RS outer code whose symbol size is one byte. It is further proposed to utilize a real time minimal byte error probability decoding algorithm, together with feedback from the outer decoder, in the decoder for the inner convolutional code. The performance of the proposed concatenated coding system is studied, and the improvement over conventional concatenated systems due to each additional feature is isolated.

Convolutional coding, used to upgrade digital data transmission under adverse signal conditions, has been improved by a method which ensures data transitions, permitting bit synchronizer operation at lower signal levels. Method also increases decoding ability by removing ambiguous condition.

Convolutional coding offers substantial improvement in the bit error probability performance of MFSK/FH modulation when applied to Rayleigh fading or partial band Gaussian interference channels. Using a 4-ary modulation with rate-1/2 codes as a special example, several convolutional coding options are considered, including binary, dual-2, and triple-2 codes. Union-Chernoff upper bounds reveal that improvements of up to 35 dB in (in Eb/N sub o reduction) are achievable at a .00001 bit error probability in comparison to an uncoded system. (Author)

Results of research on the use of convolutional codes in data communications are presented. Convolutional coding fundamentals are discussed along with modulation and coding interaction. Concatenated coding systems and data compression with convolutional codes are described.