In this paper, we study multiple description (MD) coding and transport for real-time video using multiple asymmetric paths in a packetized network. In particular, we construct the motion- compensated (MC) MD codes using MC-FGS video coder, based on the statistical characteristics and the asymmetry of the multiple routing paths. The MCMDs are the optimally allocated to the multiple paths to minimize the end-to-end video distortion. Simulation results demonstrate that the proposed video transport system can achieve improved performance in both end user quality-of-service and error resilience.

In this correspondence, we investigate the accuracy of low-complexity discrete-time Markov chain models in characterizing the packet-loss process associated with a transport network whose behavior can be described in terms of a single bottleneck node, modeled by a single multiplexer. The results are useful since network behavior is often characterized in terms of a single bottleneck node and it is of some interest to establish the accuracy of Markov chain models in predicting the packet-loss process on even such a simplified network model. We demonstrate that, although higher order Markov chain models can achieve increasingly more accurate descriptions, the Gilbert model has some serious deficiencies in predicting the packet-loss statistics of the single-multiplexer model for a variety of packet arrival processes. We show that this has some serious consequences for the performance evaluation of forward error correction (FEC) coding schemes using Markov chain models compared to that predicted by an exact queueing analysis of the single-multiplexer model.

We investigate an embedded multicast/broadcast approach for transport of digital video over spread-spectrum code-division multiple access (CDMA) cellular networks. Previous work has shown that the incorporation of a scalable source coding scheme with multiresolution modulation provides a promising design paradigm for the practical realization of the information-theoretic performance predictions originally developed by Cover, which demonstrated that optimal multicast/broadcast performance could be achieved by an embedded transmission scheme. Hence, the major technical challenge associated with the design of an end-to-end embedded multicast/broadcast system is how to match an embedded modulation constellation with a scalable source coding scheme. In this work, taking into consideration both the interference-limited and bandwidth-limited characteristics of a CDMA system, we provide a cross-layer approach incorporating adaptive power allocation and channel coding strategies and effectively match a discrete cosine transform based scalable motion-compensated video encoder to an embedded multiresolution modulation scheme to simultaneously deliver a basic quality-of-service (QoS) to less capable receivers while maximizing both the QoS for more capable receivers and the system capacity. We demonstrate the efficacy of this approach using the ITU-T H.263+ video scalable hybrid coder, although the approach is generally extensible to other scalable coding schemes as well

This paper describes a novel approach to represent the rate-distortion characteristics of an encoded media. This work is distinguished by three key contributions. The first is the introduction of the concept of data-rate PSNR information table (DRPIT), which facilitates for very fast packet scheduling during video streaming. Rate-distortion characteristic of the compressed video is extracted during preprocessing and is stored as DRPIT. The second contribution is an efficient algorithm to compute DRPIT during preprocessing, which decreases the computation time drastically. The algorithm exploits the acyclic dependency of the independently decodable units of the compressed packetized media. The third contribution consists of the application of DRPIT in variable rate video streaming systems. Two different types of systems are explained using two specific implementations which are also used for performance validation of the proposed approach. Experimental results demonstrate that the systems using DRPIT provide 6-10 dB gain, relative to the systems that do not distinguish between individual packets and treat them equally.

We propose an analytical model to study the overall effectiveness of packet-level FEC in improving delay-constrained video transport over wired networks subject to random loss and delay. In particular, we provide an exact analysis for the effect of the additional delay resulting from FEC coding/ decoding on end-to-end video transmission quality. The effects of several key system parameters on the effectiveness of FEC are investigated and the tradeoffs associated with choice of these parameters are demonstrated by some specific numerical examples.

We propose a joint source-coding power-control approach combined with joint source-channel coding employing the class of rate-compatible codes for video transport over code-division multiple-access networks. We show that this cross-layer approach can provide improved spectral efficiency and network use while exhibiting graceful degradation characteristics with an increasing number of users.

In this work, we consider the delivery of digital video over future 3G wireless IP networks and we propose a low-complexity adaptive motion-based unequal error protection (UEP) video coding and transmission system which efficiently combines three existing error-resilience techniques by exploiting knowledge of the source material as well as the channel operating conditions. Given this information, the proposed system can adaptively adjust the operating parameters of the video source encoder and the forward error correction (FEC) channel encoder to maximize the delivered video quality based upon both application-layer video motion estimates and link-layer channel estimates. We demonstrate the efficacy of this approach using the ITU-T H.264 video source coder. The results indicate that a significant performance improvement can be achieved with enhanced resilience to inaccurate channel feedback information and with substantially reduced computational complexity compared to competing approaches

In wireless networks, channel state information is hard to obtain in a reliable and timely manner due to the rapid change of wireless environments. In this paper we propose instead the use of source information, which is always available at the encoder and can be easily and accurately obtained from video sequences, to achieve error-resilience. With use of exponential weighted moving average (EWMA) estimation for the motion-level information associated with video frames, a source-adaptive intra-coding rate selection scheme is described to provide error-resilience to N successive video frames. Based on our proposed cross-layer packetization scheme, a novel intra-frame packet interleaving scheme is implemented together with a fixed FEC coding strategy at the application-layer to combat the severe bursty losses over wireless channels, and the performance of the combined approach is investigated. Our objective and subjective results demonstrate the effectiveness of our approach in dealing with the bursty packet losses on both wireless single-hop and multi-hop networks without any additional system complexity or delay.

For video communications over wireless ad-hoc networks, there are fundamentally two different kinds of packet losses: packet losses due to channel over-pumping, where the operating transmission rate is higher than the prevailing channel capacity, and packet losses due to transmission errors. To eliminate the first kind of packet losses, rate-control is necessary in order to adapt to the time-varying channel capacity. For the second kind of packet losses, error-resilient coding techniques should be used. In this paper, we propose a cross-layer rate-control scheme based on an analytical study of how the effective video transmission rate is affected by the prevailing operating parameters. Furthermore, in order to provide error-resilient real-time video delivery over such wireless ad-hoc networks, a cross-layer delay-constrained joint source-channel coding (JSCC) approach, to be used in conjunction with rate-control, is proposed and investigated. Simulation results demonstrate the effectiveness of this combination of cross-layer rate-control and delay-constrained JSCC for supporting error-resilient video delivery over wireless ad-hoc networks operating under a delay constraint.

Packet video transport over networks is expected to experience packet losses due to congestion, link failures and timeouts. Packet-level FEC is often proposed to combat these packet losses and thus improve received video quality. However, the redundant packets associated with the FEC coding will increase the effective network load and, as a result, further exacerbate the network packet-loss rates. In this work, we propose a model framework to describe FEC-protected packet video network transport systems and analytically investigate the overall efficacy of packet-level FEC in improving the end-to-end video quality. We consider a simplified network scenario, where the network congestion performance can be described in terms of a single bottleneck node, modeled as a multiplexer. Our results show that packet-level FEC can significantly improve the end-to-end video quality provided that the coding block size is large enough and the coding rate is appropriately chosen, assuming other system parameters are likewise appropriately chosen. We also demonstrate that, when multiple sources share the multiplexer, FEC coding can achieve significant multiplexing gain in terms of the number of video sources that can be supported for a given end-to-end performance.

The Gilbert model (1-st order Markov chain model) and the single-multiplexer model are two frequently used models in the study of packet-loss processes in communication networks. In this paper we investigate the accuracy of the Gilbert model, and higher-order Markov chain extended Gilbert models, in characterizing the packet-loss process associated with a transport network modeled in terms of a single-multiplexer. More specifically, we quantitatively compare the packet-loss statistics predicted by the Gilbert models with those predicted by an exact queueing analysis of the single-multiplexer model. This topic is important since low-complexity Gilbert models are frequently used to characterize end-to-end network packet-loss behavior. On the other hand, network congestion behavior is often characterized in terms of a single bottleneck node modeled as a multiplexer. It is of some interest then to establish the relative accuracy of Gilbert models in predicting the packet-loss behavior on even such a simplified network model. We demonstrate that the Gilbert models have some serious deficiencies in accurately predicting the packet-loss statistics of the single-multiplexer model. The results are shown to have some serious consequences for the performance evaluation of forward error correction (FEC) coding schemes used to combat the effects of packet losses due to network buffer overflows.

In this paper, we investigate the effect of path correlation on video communications when path-diversity routing techniques are employed together with forward error correction (FEC). We study the statistical properties of packet losses when correlation between paths exists and demonstrate that the effects of path correlation on received video quality depend on various factors, such as the effectiveness of error control strategies (passive error concealment, FEC, etc.) and the existing channel conditions. We demonstrate that, contrary to common belief, path correlation need not be detrimental to the system performance. The results are expected to have some impact on the development of explicit multi-path routing strategies.

Packet video transmission over wireless networks is expected to experience packet losses due to noise, interference, multipath and the motion of mobile hosts. Such packet losses often occur in bursts which may cause substantial degradation to the transmitted video quality. In this paper, we propose the use of a cross-layer unequal error protection (UEP) approach which is achieved by assigning an unequal amount of forward error correction (FEC) to each group of link-layer packets according to the corresponding motion level of the slice acquired at the application layer. Also, a novel packetization scheme and an intraframe packet interleaving scheme are proposed to be used together with FEC/UEP in order to combat the bursty packet losses in 3G wireless environments. Our results demonstrate that the proposed approach is very effective in dealing with the packet losses occurring on wireless networks without incurring any additional implementation complexity or delay.

We study a problem in cross-layer optimization for video delivery over CDMA networks. By considering the resource requirements as the aggregate of the products of source coding rates and the energy per information bit to noise ratio, we propose a joint source coding-power control (JSCPC) strategy combined with joint source-channel coding (JSCC) employing the class of rate-compatible punctured turbo (RCPT) codes to provide forward error correction with unequal error protection (FEC/UEP). We show that this cross-layer approach can simultaneously maximize the quality of the delivered video while minimizing the total resource consumption, thereby providing improved spectral efficiency and network utilization. We demonstrate the efficacy of this approach using the ITU-T H.263+ video source coder.

In this paper, we address the problem of enabling robust interactive video coding and transmission over heterogeneous wired-to-wireless IP networks. We propose the use of an FEC coding scheme employing Reed-Solomon (RS) codes and rate-compatible punctured convolutional (RCPC) codes to protect the video data from packet loss and bit errors, respectively. Furthermore, we apply an end-to-end architecture using an edge proxy in a mobile support station to implement differential error protection for the corresponding channel impairments expected on the two networks. Results indicate that with an appropriate joint source-channel coding approach and the use of an edge proxy, FEC-based error-control techniques together with passive error-recovery techniques can significantly improve the effective video throughput and lead to acceptable video delivery quality over time-varying heterogeneous wired-to-wireless IP networks.

We consider future generation wireless code-division multiple-access (CDMA) cellular networks supporting heterogeneous compressed video traffic and investigate transport schemes for maximizing the number of users that can be supported in a single cell while simultaneously maximizing the reconstructed video quality of individual users. More specifically, we demonstrate that the network resources consumed by an individual user in a spread-spectrum CDMA network can be taken as the product of the allocated source-coding rate R/sub s/ and the energy per bit normalized to the multiple-access interference noise density /spl gamma/b. We propose a joint source coding and power control (JSCPC) approach for allocating these two quantities to an individual user, subject to a constraint on the total available bandwidth, to simultaneously maximize the per-cell capacity while maximizing the quality of the delivered video to individual users. We demonstrate the efficacy of this approach using the ITU-T H.263+ video source coder, although the approach is generally applicable to other source-coding schemes as well. The results indicate a significant improvement in delivered quality-of-service (QoS), measured in terms of the end-user average peak signal-to-noise ratio, that can be achieved at a given level of network loading. Furthermore, we demonstrate that without an appropriate JSCPC strategy the traditional soft-capacity limit associated with CDMA networks is no longer present. Indeed, a precipitous decrease in performance can be expected with increasing load. We show that this behavior can be avoided with the proposed JSCPC approach, thereby significantly extending the useful capacity of the CDMA network while exhibiting a more graceful degradation pattern under increasing load.

We consider real-time video coding and transmission over packet-switched wireless IP networks using RCPT codes in a joint source and channel coding (JSCC) approach. In particular, we study performance of this JSCC approach employing RCPT coding schemes for real-time transport protocol (RTP) H.263+ packet video transmission over slow fading Rician channels. Results indicate that an RCPT-JSCC approach is attractive for real-time video applications and leads to increased system capacity together with more acceptable delivered video quality over time-varying wireless networks.

We investigate the transport of scalable digital video over future third-generation (3G) wireless CDMA cellular systems By considering the resource requirements as the aggregate of the products of source coding rates and the energy per information bit to noise ratio, we propose a joint source coding and power control (JSCPC) scheme which simultaneously maximizes the quality of the delivered video while minimizing the total resource consumption. We demonstrate the efficacy of this approach using the ITU-T H.263+ video source coder, although the approach is generally applicable to other source coding schemes as well.

In this paper we describe a multi-layered video transport scheme for wireless channels capable of adapting to channel conditions in order to maximize end-to-end quality of service (QoS). This scheme combines a scalable H.263+ video source coder with unequal error protection (UEP) across layers. The UEP is achieved by employing different channel codes together with a multiresolution modulation approach to transport the different priority layers. Adaptivity to channel conditions is provided through use of joint source-channel coding (JSCC) which attempts to jointly optimize the source and channel coding rates together with the modulation parameters to obtain the maximum achievable end-to-end QoS for the prevailing channel conditions. Results indicate that this adaptive JSCC scheme employing scalable video encoding together with a multiresolution modulation/coding approach leads to significant improvements in delivered video quality for specified channel conditions. In particular, the approach results in considerably improved graceful degradation properties for decreasing channel SNR.

Typically, spectral efficiency, the throughput in bits/second/hertz, has been evaluated for fixed values of the bit error probability. We introduce a cutoff-rate-based approach to evaluation of the spectral efficiency of direct-sequence spread-spectrum schemes so that the results are independent of specific bit error rates or channel codes. Results are shown for M-ary phase-shift keyed modulation on the slow-fading Rician channel.

A joint source-channel coding (JSCC) approach for ATM-based network transport of scalable variable bit rate (VBR) digital video is described. We provide a new methodology for finding the optimum source and channel coding rates, together with the optimum data-partitioning ratio, to maximize the statistical multiplexing gain while maximizing the end-to-end video quality. The results provide a quantitative demonstration of the effectiveness of a scalable delivery approach over the single-layer JSCC.

The use of forward error-control (FEC) coding, possibly in conjunction with passive-error recovery techniques, has emerged as a promising approach for real-time video transport over ATM networks for cell loss recovery and/or bit error correction, such as might be required for wireless links. Although FEC provides cell-loss recovery, through its erasure correcting capabilities, it also introduces transmission overhead which can possibly cause additional cell losses. A joint source-channel coding methodology is described to maximize the number of video sources multiplexed at a given quality of service (QoS), measured in terms of overall reproduced video quality. The transport channel is modeled as a block interference channel (BIC) and the multiplexer as a single server, deterministic service, finite buffer supporting N users. Based upon an information-theoretic characterization of the BIC and large deviation bounds on the buffer overflow probability, we describe a methodology that provides theoretically achievable upper limits on the number of sources multiplexed at a given level of performance. Performance of a specific coding technique using an MPEG-2 source encoder and interlaced non-binary Reed-Solomon (RS) channel codes is illustrated and shown to approach the information-theoretic predictions with increasing levels of complexity.

There has been an increased interest in the transmission of digital video over real-world transmission media, such as the direct broadcast satellite (DBS) channel. Video transmitted over such a channel is subject to degradation due, in part, to additive white Gaussian noise (AWGN). Some form of forward error-control (FEC) coding may be applied in order to reduce the effect of the noise on the transmitted bitstream; however, determination of the appropriate level of FEC coding is generally an unwieldy and computationally intensive problem, as it may depend upon a variety of parameters such as the type of video, the available bandwidth, and the channel SNR. More specifically, a combined source-channel coding approach is necessary in optimally allocating rate between source and channel coding subject to a fixed constraint on overall transmission bandwidth. In this paper we develop a method of optimal bit allocation under the assumption that the distortion is additive and independent on a frame-by-frame basis. A set of universal operational distortion-rate characteristics is developed which balances the tradeoff between source coding accuracy and channel error protection for a fixed overall transmission rate and provides the basis for the optimal bit allocation approach. The results for specific source and channel coding schemes show marked improvement over suboptimum choices of channel error protection. In addition, we show that our results approach information-theoretic performance bounds which are developed in this work.

In the original paper (see ibid., vol.9, no.6, p.868-81, Sept. 1999) some of the figures did not appear as intended by the authors. The correct versions of the figures are given here.

Two hybrid error concealment schemes based on application of forward error control (FEC) coding in combination with passive error concealment techniques to different layers of coded data in a video transmission system are evaluated. It is shown that use of passive error concealment schemes alone generally does not provide sufficient protection against channel errors, especially in the case of video sequences with significant motion or scene changes. Motivated by these observations, a third hybrid scheme is introduced; this scheme involves adaptive application of FEC codes to high-priority information depending on the level of motion in a sequence. It is shown that through application of this adaptive motion-based scheme, significant savings in bandwidth may be obtained at the expense of only a negligible decrease in reconstructed image quality. Implementation of adaptive motion-based FEC coding in a multiresolution asynchronous transfer mode framework is discussed, and metrics for computing motion in both a subband and an MPEG-2 coding system are introduced.

The development of broadband networks has led to the possibility of a wide variety of new and improved service offerings. Packetized video is likely to be one of the most significant high-bandwidth users of such networks. The transmission of variable bit-rate (VBR) video offers the potential promise of constant video quality but is generally accompanied by packet loss which significantly diminishes this potential. We study a class of error recovery schemes employing forward error-control (FEC) coding to recover from such losses. In particular, we show that a hybrid error recovery strategy involving the use of active FEC in tandem with simple passive error concealment schemes offers very robust performance even under high packet losses. We discuss two different methods of applying FEC to alleviate the problem of packet loss. The conventional method of applying FEC generally allocates additional bandwidth for channel coding while maintaining a specified average video coding rate. Such an approach suffers performance degradations at high loads since the bandwidth expansion associated with the use of FEC creates additional congestion that negates the potential benefit in using FEC. In contrast, we study a more efficient FEC application technique in our hybrid approach, which allocates bandwidth for channel coding by throttling the source coder rate (i.e., performing higher compression) while maintaining a fixed overall transmission rate. More specifically, we consider the performance of the hybrid approach where the bandwidth to accommodate the FEC overhead is made available by throttling the source coder rate sufficiently so that the overall rate after application of FEC is identical to that of the original unprotected system. We obtain the operational rate-distortion characteristics of such a scheme employing selected FEC codes. In doing so, we demonstrate the robust performance achieved by appropriate use of FEC under moderate-to-high packet losses in comparison to the unprotected system.

This paper describes a methodology for evaluating the operational rate-distortion behavior of combined source and channel coding schemes with particular application to images. In particular, we demonstrate use of the operational rate-distortion function to obtain the optimum tradeoff between source coding accuracy and channel error protection under the constraint of a fixed transmission bandwidth for the investigated transmission schemes. Furthermore, we develop information-theoretic bounds on performance for specific source and channel coding systems and demonstrate that our combined source-channel coding methodology applied to different schemes results in operational rate-distortion performance which closely approach these theoretical limits. We concentrate specifically on a wavelet-based subband source coding scheme and the use of binary rate-compatible punctured convolutional (RCPC) codes for transmission over the additive white Gaussian noise (AWGN) channel. Explicit results for real-world images demonstrate the efficacy of this approach.

In this work we consider the problem of combined source-channel coding for H.263 coded video transmitted over a wireless channel which is modeled as a slow-fading Rician channel. As wireless channels are generally bandwidth limited, the specific channel coding scheme employed here is non-binary bandwidth-efficient trellis-coded modulation (TCM) employing appropriate phase-shift keyed modulation. We describe a methodology for determining the optimal tradeoff between source and channel coding as a function of channel characteristics. In particular, if feedback on channel parameters is available, the video information can be optimally coded. In the case where feedback is not available, we illustrate the effects of using mismatched codes designed for other than the existing channel conditions.

Image segmentation is an important and early processing stage in many image analysis problems. Often, this must be done in an unsupervised fashion in that training data is not available and the class-conditioned feature vectors must be estimated directly from the data. A major problem in such applications is the determination of the number of classes actually present in an image. This problem, called the cluster validation problem, remains essentially unsolved. We investigate the cluster validation problem associated with the use of a previously developed unsupervised segmentation algorithm based upon the expectation-maximization (EM) algorithm. More specifically, we consider several well-known information-theoretic criteria (ICs) as candidate solutions to the validation problem when used in conjunction with this EM-based segmentation scheme. We show that these criteria generally provide inappropriate solutions due to the domination of the penalty term by the associated log-likelihood function. As an alternative we propose a model-fitting technique in which the complete data log-likelihood functional is modeled as an exponential function in the number of classes acting. The estimated number of classes are then determined in a manner similar to finding the rise time of the exponential function. This new validation technique is shown to be robust and outperform the ICs in our experiments. Experimental results for both synthetic and real world imagery are detailed.

In this paper, we explore the design of forward error control (FEC)-based error concealment schemes for digital video transmission on ATM networks. In particular, we study the impact of code selection on the overall performance and provide a judicious code selection strategy. The use of FEC provides an active and powerful means of recovery from packet loss which is particularly useful when the encoded video material has high motion and scene changes. The best technique for applying FEC is to throttle the source coding rate so that the overall transmission rate after FEC application equals the original unprotected rate. However, the resulting performance then depends on the particular code selected. A well-chosen code provides good protection while allowing little sacrifice in quality and at the same time satisfies specified delay constraints. Our results show that a single code is generally insufficient to provide good performance under all operating conditions. However, a small group of codes can be preselected, using the efficient code-selection strategy described here, which will provide efficient and robust performance over a wide range of channel conditions. We show that this simple code selection strategy is sufficient to select codes judiciously for a wide range of operating conditions and constraints. Employing this selection strategy, we demonstrate that moderate length codes are sufficient to provide good performance while meeting the imposed delay constraint.

This paper describes a methodology for evaluating the rate-distortion behavior of combined source and channel coding schemes with particular application to images. We demonstrate use of the operational rate-distortion function to obtain the optimum tradeoff between source coding accuracy and channel error protection under the constraint of a fixed transmission bandwidth. Furthermore, we develop information-theoretic bounds on performance and demonstrate that our combined source-channel coding methodology results in rate-distortion performance which closely approaches these theoretical limits. We concentrate specifically on a wavelet-based subband source coding scheme and the use of binary rate-compatible punctured convolutional (RCPC) codes for transmission over the additive white Gaussian noise (AWGN) channel.

This paper describes a second-generation region-based coding scheme operating in a subband environment. Specifically, this is a compression technique based on approximating the lowest-frequency subband of an image with a 2-D spline model. Following a segmentation procedure, parametric polynomials are fitted to the resulting regions of the lowest-frequency subband. This subband is then represented by the spline coefficients, the region boundary description and the residual error. The residual error plus the higher-frequency subbands are encoded using conventional pixel-based quantization schemes while we describe an efficient encoding scheme for the 2-D spline representation. An entropy-constrained design procedure is developed for designing these individual encoders to minimize the overall mean-square distortion subject to a constraint on the output entropy. A comprehensive study of the operational rate-distortion performance of the resulting scheme is presented, which indicates the superiority of this approach to the more traditional pixel-based entropy-constrained schemes.>

Image segmentation is an important processing stage in many image analysis problems. Often this must be done in an unsupervised fashion in that training data is not available. A major obstacle in such applications is the determination of the number of distinct regions present in an image. This problem, called the cluster validation problem, remains essentially unsolved. We investigate the cluster validation problem associated with the use of a previously developed unsupervised segmentation algorithm based upon the expectation-maximization (EM) algorithm. We consider several well-known information-theoretic criteria (ICs) as candidate solutions. We show that these criteria generally provide inappropriate results. As an alternative we propose a model-fitting technique in which the complete data log-likelihood functional is modeled as an exponential function in the number of classes acting, and the class estimate is related to the rise time. This new validation technique is shown to be robust and outperform the ICs in our experiments.>

An unsupervised stochastic model-based approach to image segmentation is described, and some of its properties investigated. In this approach, the problem of model parameter estimation is formulated as a problem of parameter estimation from incomplete data, and the expectation-maximization (EM) algorithm is used to determine a maximum-likelihood (ML) estimate. Previously, the use of the EM algorithm in this application has encountered difficulties since an analytical expression for the conditional expectations required in the EM procedure is generally unavailable, except for the simplest models. In this paper, two solutions are proposed to solve this problem: a Monte Carlo scheme and a scheme related to Besag's (1986) iterated conditional mode (ICM) method. Both schemes make use of Markov random-field modeling assumptions. Examples are provided to illustrate the implementation of the EM algorithm for several general classes of image models. Experimental results on both synthetic and real images are provided.

Simpler versions of a previously introduced adaptive entropy-coded predictive vector quantization (PVQ) scheme where the embedded entropy constrained vector quantizer (ECVQ) is replaced by a pruned tree-structured VQ (PTSVQ) are described. The resulting encoding scheme is shown to result in drastically reduced complexity at only a small cost in performance. Coding results for selected real-world images are given.>

A new approach to image sequence coding based on variable-rate entropy-constrained subband coding (ECSBC) is described. The corresponding practical implementation of the ECSBC scheme for fixed-rate channels is developed by extending recent adaptive entropy-coded (AEC) quantization techniques. Although the entropy-constrained design of subband coding systems provides improve coding efficiency compared to level-constrained design approaches, the resulting coding system generates variable-rate outputs which must be buffered before fixed-rate transmissions. In this case, the finite buffer, however large, that interfaces the encoder and the channel will eventually overflow or underflow, resulting in a catastrophic loss of encoder-decoder synchronism with an associated large amount of distortion. A buffer-adaptive arithmetic-coded implementation of the ECSBC scheme, called adaptive entropy-coded subband coding (ECSBC/AEC), is described to completely eliminate the associated encoder buffer overflow/underflow problems, even with a very small encoder buffer.>

The application of a Markov random field (MRF) state model in an expectation-maximization (EM)-based approach to unsupervised image segmentation is investigated. In the calculation of the marginal distribution of the state field, it is shown that the use of the expected state values for interacting pixel sites in the computation of the MRF energy function may be interpreted as a mean-field approximation. The implications of calculating a self-consistent expectation of the state field are considered. EM convergence criteria are considered, and a criterion based upon divergence is proposed. Experimental results based on synthetic data illustrate the performance advantage of the mean-field approximation and the computational advantage of using self-consistent expectations.>

An image is segmented into a collection of disjoint regions that form the nodes of an adjacency graph, and image interpretation is achieved through assigning object labels (or interpretations) to the segmented regions (or nodes) using domain knowledge, extracted feature measurements, and spatial relationships between the various regions. The interpretation labels are modeled as a Markov random field (MRF) on the corresponding adjacency graph, and the image interpretation problem is then formulated as a maximum a posteriori (MAP) estimation rule, given domain knowledge and region-based measurements. Simulated annealing is used to find this best realization or optimal MAP interpretation. This approach also provides a systematic method for organizing and representing domain knowledge through appropriate design of the clique functions describing the Gibbs distribution representing the pdf of the underlying MRF. A general methodology is provided for the design of the clique functions. Results of image interpretation experiments on synthetic and real-world images are described.>

The authors describe a design approach, called 2-D entropy-constrained subband coding (ECSBC), based upon recently developed 2-D entropy-constrained vector quantization (ECVQ) schemes. The output indexes of the embedded quantizers are further compressed by use of noiseless entropy coding schemes, such as Huffman or arithmetic codes, resulting in variable-rate outputs. Depending upon the specific configurations of the ECVQ and the ECPVQ over the subbands, many different types of SBC schemes can be derived within the generic 2-D ECSBC framework. Among these, the authors concentrate on three representative types of 2-D ECSBC schemes and provide relative performance evaluations. They also describe an adaptive buffer instrumented version of 2-D ECSBC, called 2-D ECSBC/AEC, for use with fixed-rate channels which completely eliminates buffer overflow/underflow problems. This adaptive scheme achieves performance quite close to the corresponding ideal 2-D ECSBC system.

A clustering scheme is used for model parameter estimation. Most of the existing clustering procedures require prior knowledge of the number of classes, which is often, as in unsupervised image segmentation, unavailable and must be estimated. This problem is known as the cluster validation problem. For unsupervised image segmentation the solution of this problem directly affects the quality of the segmentation. A model-fitting approach to the cluster validation problem based on Akaike's information criterion is proposed, and its efficacy and robustness are demonstrated through experimental results for synthetic mixture data and image data.>

An investigation is conducted of the effects of various source statistics and buffer management algorithms for a buffer of fixed size, and an algorithm that provides particularly robust rate-distortion performance for a wide range of stationary sources is described. The performance of this scheme, which is referred to as the adaptive entropy-coded quantizer (AECQ), is compared to that of conventional adaptive pulse code modulation (APCM) operating at the same fixed channel transmission rate. Experimental results indicate that the AECQ can provide considerably improved performance and more robust operation than APCM. The relative sensitivity of the AECQ to scale mismatch is directly related to the rather simple memoryless feedback control strategy employed. This might be remedied by alternative choices of the memoryless feedback control function or by introducing memory. The former is much easier to implement and/or analyze than the latter.>

The issue addressed is how closely ideal performance can be approached using a practical erasure declaration mechanism. A description is given of a specific practical erasure declaration mechanism, and the resulting coded system performance is investigated on the digital subscriber loop. Results indicate that, by appropriate choice of system parameters, it is possible to closely approach the ideal performance.>

Buffer underflow and overflow problems associated with entropy coding are completely eliminated by effectively imposing reflecting walls at the buffer endpoints. Synchronous operation of the AECQ (adaptive entropy-coded quantizer) encoder and decoder is examined in detail, and it is shown that synchronous operation is easily achieved without side information. A method is developed to explicitly solve for the buffer-state probability distribution and the resulting average distortion when memoryless buffer-state feedback is used as well as when the source is stationary and memoryless. This method is then used as a tool in the design of low-distortion AECQ systems, with particular attention given to developing source scale-invariant distortion performance. It is shown that the introduction of reflecting buffer walls in a properly designed AECQ system results in a very small rate-distortion performance penalty and that the resulting AECQ system can be an extremely simple and effective solution to the stationary memoryless source-coding problem for a wide range of source types. Operation with nonstationary sources is also examined.>

A Markov random field (MRF) model-based approach to automated image interpretation is described and demonstrated as a region-based scheme. In this approach, an image is first segmented into a collection of disjoint regions which form the nodes of an adjacency graph. Image interpretation is then achieved through assigning object labels, or interpretations, to the segmented regions, or nodes, using domain knowledge, extracted feature measurements, and spatial relationships between the various regions. The interpretation labels are modeled as a MRF on the corresponding adjacency graph, and the image interpretation problem are formulated as a maximum a posteriori estimation rule. Simulated annealing is used to find the best realization, or optimal interpretation. Through the MRF model, this approach also provides a systematic method for organizing and representing domain knowledge through the clique functions of the probability density function underlying MRF. Results of image interpretation experiments performed on synthetic and real-world images using this approach are described.>

The authors describe the theory and performance of a particular adaptive entropy-coded quantization (AECQ) scheme used in conjunction with 2-D DPCM (differential pulse code modulation) and operating on real-world image sources. The resulting system, called 2-D DPCM/AECQ, is described in detail and its performance illustrated on a typical real-world image. The system makes use of an adaptive buffer-control strategy to modify the DPCM quantizer characteristics on the basis of the buffer occupancy state. This adaptive buffer-state feedback is used to control the average rate of the variable-length entropy-coded quantizer code words at the input to the buffer, to allow interfacing to a fixed-rate transmission or storage channel. Image coding results demonstrate, both objectively and subjectively, that achievable performance is close to that predicted on the basis of rate-distortion considerations even for reasonably small buffer sizes.>

A model-fitting approach to the cluster validation problem based upon Akaike's information criterion (AIC) is proposed. The explicit evaluation of the AIC for the image segmentation problem is achieved through an approximate maximum-likelihood-estimation algorithm. The efficacy of the proposed approach is demonstrated through experimental results for both synthetic mixture data, where the number of clusters is known, and stochastic model-based image segmentation operating on real-world images, for which the number of clusters is unknown. This approach is shown to correctly identify the known number of clusters in the synthetically generated data and to result in good subjective segmentations in aerial photographs.>

The design, operation, and capabilities of a workstation-communications-simulation software system (WCS) for interactive simulation of point-to-point digital communication links is described. The system is based on Fortran-77 and is hosted on an IBM PC/AT or compatible microcomputer. At the heart of the system is a single-board floating-point array processor that provide approximately three orders of magnitude increase in computational throughput over operations performed in the AT alone. A description is given of how a unique method of interfacing to a PC host allows considerable flexibility in partitioning a simulation problem for execution on an attached processor. The WCS system is a highly graphics-oriented system using the latest advances in interactive color workstation technology.>

The authors describe an approach to combatting impulse noise (IN) on digital subscriber loops using short-constraint length convolutional codes and Viterbi decoding operating in hard-decision-and-erasure mode. Attention is restricted to time-compression-multiplexing transmission schemes using bipolar, or alternate-mark inversion (AMI), line coding, and a rather idealized IN model, although the approach and general conclusions are more broadly applicable. They discuss the tradeoffs in choosing the channel encoding rate to yield an optimum compromise between error-control protection and the combined effects of intersymbol interference and crosstalk. Numerical results are demonstrated for selected typical line configurations.>

We consider the convergence and tracking properties of an adaptive multielement integrated receiver structure operating in the presence of impulsive or burst noise. The receiver structure is integrated in the sense that it incorporates both the spatial/temporal predetection processing and demodulation functions in a single entity. This integrated receiver structure has been developed in previous work to approximate maximum-likelihood (ML) reception in the presence of both intersymbol interference (ISI) and spatially distributed interference (SDI) when the latter is modeled as zero-mean Gaussian noise. The present paper is devoted to a simulation study of the convergence properties of this receiver structure when the SDI is replaced by non-Gaussian impulsive or burst noise. Results indicate that the convergence characteristics are relatively insensitive to the statistics of the SDI provided that secondorder properties are held fixed, at least for moderate deviations from Gaussian behavior. For highly impulsive SDI environments, however, the adaptive system exhibits a complete failure to converge.

We describe a methodology for the characterization of the 2-wire twisted-pair subscriber loop plant for high-speed digital communications typical of evolving integrated service digital networks (ISDN's). Through use of this analytical/numerical approach it is possible to predict the resulting error probability performance as a function of signal-to-noise ratio for a given set of input parameters representing a particular subscriber loop and its noise environment, including such effects as intersymbol interference, crosstalk and impulse noise. The results are useful in penetration assessment studies of the loop plant population at a fixed grade of service measured objectively in terms of operating bit error probability. This approach is in contrast to simulation-based methodologies leading to subjective performance assessment criteria, such as eye opening measurements. In the present paper we describe the modeling assumptions together with the analytical/numerical techniques underlying this approach. Attention is restricted to time-compression multiplexing (TCM) schemes with bipolar line coding, although the approach is much more general. Numerical results are illustrated through sample graphical output of an extensive computer program implementing this approach. Finally, we illustrate the application of this approach to objective penetration assessment of the GTE subscriber loop plant utilizing data collected as part of an extensive recent survey.

Variable-length codes can be used in entropy coding the outputs of an optimum entropy-constrained quantizer. Transmitting these codes over a synchronous channel; however, requires a buffer connecting the entropy coder to the channel. In a practical application, this buffer is of finite size and hence might overflow or undertow. To alleviate this difficulty, we use an adaptive scheme in which the quantizer parameters are changed successively according to the state of the buffer. Rate-distortion performance of optimum entropy-constrained quantizers in conjunction with this adaptive scheme is studied for the class of generalized Gaussian sources. It is demonstrated through simulations that the overflow/ undertow problem can be practically eliminated at the cost of a negligible increase in average distortion. Furthermore, it is shown that the efficiency of this system is more pronounced at high rates and for more broadtailed source densities. Easily computable upper and lower bounds on the average distortion of the adaptive system are developed.

It is well-known that variable-length coding schemes can be employed in entropy encoding of finite-alphabet sources. To transmit these codes over a synchronous channel, however, requires a buffer. Since in practice this buffer is of finite size, it is subject to both overflow and undertow. The buffer behavior is studied with particular application to Huffman coding of the outputs of an optimum uniform-threshold quantizer driven by a memoryless Gaussian source. Fairly general upper and lower bounds on the average terminal time are developed. Under certain conditions, the tightness of these bounds is verified, and asymptotic formulas are developed. As an example, an encoding scheme employing Huffman codes in conjunction with uniform quantization of memoryless Gaussian sources is considered, and the buffer behavior as a function of the buffer size and output rate is studied.

The structure and performance of a maximum likelihood (ML) receiver for reception in spatially distributed interference channels when a multielement array capability is available are described. Under the assumption of Gaussian interference, the receiver consists of an optimum ML array processor followed by a sequence estimator implemented using the Viterbi Algorithm. Numerical results are provided to illustrate the symbol error probability performance of this optimum ML receiver. A completely adaptive realization of this scheme is described with performance illustrated through simulation.

Quantizers for block transform image coding systems are typically designed under the assumption of Gaussian statistics for the transform coefficients. While convincing arguments can be provided in support of this approach, empirical evidence is presented demonstrating that, except possibly for the dc term, wide departures from Gaussian behavior can be expected for real-world imagery at typical block sizes. In this paper we describe the performance of a block cosine image coding system with an adaptive quantizer matched to the statistics of the transform coefficients. The adaptive quantizer is based upon a recently developed algorithm which employs a training sequence in the design procedure. At encoding rates of approximately 1 bit/pixel and above, this approach results in significant improvement in reconstructed image quality compared to fixed quantization schemes designed under the Gaussian assumption. For rates much below 1 bit/pixel the relative improvement is negligible.

An analysis of the rate-distortion performance of differential pulse code modulation (DPCM) schemes operating on discrete-time auto-regressive processes is presented. The approach uses an iterative algorithm for the design of the predictive quantizer subject to an entropy constraint on the output sequence. At each stage the iterative algorithm optimizes the quantizer structure, given the probability distribution of the prediction error, while simultaneously updating the distribution of the resulting prediction error. Different orthogonal expansions specifically matched to the source are used to express the prediction error density. A complete description of the algorithm, including convergence and uniqueness properties, is given. Results are presented for rate-distortion performance of the optimum DPCM scheme for first-order Gauss-Markov and Laplace-Markov sources, including comparisons with the corresponding rate-distortion bounds. Furthermore, asymptotic formulas indicating the high-rate performance of these schemes are developed for both first-order Gaussian and Laplacian autoregressive sources.

We consider the performance and complexity of optimum quantization schemes subject to an entropy constraint for discrete-time memoryless sources. In particular we describe the performance of optimum zero-memory quantizers for a generalized Gaussian source distribution, Specific implementation of these schemes generally requires variable-length coding of the quantizer output. For transmission over a synchronous fixed-rate channel some form of buffering is required which is subject to overflow or underflow. To alleviate this problem we describe an adaptive scheme in which the quantizer parameters are controlled by the state of the buffer in an effort to avoid overflow/underflow.

In this paper we describe efforts to develop a comprehensive tool for the digital simulation of a wide variety of point-to-point digital communication systems. These efforts have resulted in the interactive communications simulator (ICS); a flexible, graphics-oriented, and highly interactive hardware/software system consisting of a typical minicomputer acting as host to a fast peripheral array processor. This system is presently being employed both to evaluate existing modem performance and to explore new modulation/coding concepts appropriate for military, commercial, and space applications. A detailed functional description of the ICS is provided together with pertinent software considerations. An outline of existing ICS capabilities is presented and illustrated through typical, graphical output. A thorough discussion of channel modeling considerations is provided. The use of the ICS in the overall design of receiver structures for impulsive noise channels will be illustrated.

An adaptive approach to two-dimensional tree encoding of images is presented based upon the use of spatial masking concepts. Specifically, we make use of an adaptive encoding filter of the smoothing variety whose smoothing action is controlled by the local visibility of the encoding noise. The approach is an attempt to obtain an optimum compromise between slope overload and granular noise characteristics associated with existing two-dimensional tree encoding schemes. We demonstrate that this adaptive approach can provide improved overall image coding performance, both objectively and subjectively, compared to existing tree encoding schemes at a reduced order of complexity. The subjective improvements are clear and striking to the eye.

The performance of optimum quantizers subject to an entropy constraint is studied for a wide class of memoryless sources. For a general distortion criterion, necessary conditions are developed for optimality and a recursive algorithm is described for obtaining the optimum quantizer. Under a mean-square error criterion, the performance of entropy encoded uniform quantization of memoryless Gaussian sources is well-known to be within0.255bits/sample of the rate-distortion bound at relatively high rates. Despite claims to the contrary, it is demonstrated that similar performance can be expected for a wide range of memoryless sources. Indeed, for the cases considered, the worst case performance is observed to be less than0.3bits/sample from the rate-distortion bound, and in most cases this disparity is less at Iow rates.

A combined source-channel coding approach is described for the encoding, transmission, and remote reconstruction of image data. The transmission medium considered is that of a fading dispersive communications channel. Both the Rician fading and Rayleigh fading channel models are considered. The image source encoder employs two-dimensional (2-D) differential pulse code modulation (DPCM). This is a relatively efficient encoding scheme in the absence of channel errors. In the presence of fading, however, the performance degrades rapidly. By providing error control protection to those encoded bits which contribute most significantly to image reconstruction, it is possible to minimize this degradation without sacrificing transmission bandwidth. Several modulation techniques are employed in evaluation of system performance including noncoherent multiple frequency shift-keyed (MFSK) modulation. Analytical results are provided for assumed 2-D autoregressive image models, while simulation results are described for real-world images.

A new approach to texture classification is described which is based on measurements of the spatial gray-level co-occurrence probability matrix. This approach can make use of assumed stochastic models for texture in imagery and is an approximation to the statistically optimum maximum likelihood classifier. The efficacy of the approach is demonstrated through experimental results obtained with real-world texture data.

New short constraint length convolutional code constructions are tabulated for ratesR=(n-k)/n, k=1,2, \cdots ,n-1withn=2, 3,\cdots ,8, and for constraint lengthsK=3,4, \cdots,8. These codes have been determined by iterative search based upon a criterion of optimizing the free distance profile. Specifically, these codes maximize the free distanced_{f}while minimizing the number of adversaries in the distance, or weight, spectrum. In several instances we demonstrate the superiority of these codes over previously published code constructions at the same rate and constraint length. These codes are expected to have a number of applications, including combined source-channel coding schemes as well as coding for burst or impulsive noise channels.

Algorithms for the soft-decision decoding of linear block codes are presented. These algorithms perform a reduced complexity search through a trellis derived from the parity check matrix of an(n, k)linear block code. The computational complexity of the algorithms is considerably reduced from that of a full maximum-likelihood algorithm. We demonstrate the trade-off between complexity and efficiency of the algorithms through computer simulation.

A new approach to texture discrimination is described. This approach is based upon an assumed stochastic model for texture in imagery and is an approximation to the statistically optimum maximum likelihood classifier. The construction and properties of the stochastic texture model are described and a digital filtering implementation of the resulting maximum likelihood texture discriminant is provided. The efficacy of this approach is demonstrated through experimental results obtained with simulated texture data. A comparison is provided with more conventional texture discriminants under identical conditions. The implications to texture discrimination in realworld imagery are discussed.

A new approach to the design of the feedback predictor in a two-dimensional (2-D) DPCM encoder is presented. This approach is based upon an assumed stochastic image model which exhibits the predominant and pronounced edge structure typical of real-world imagery and is in distinction from the conventional approach based upon 2-D autoregressive (AR) modeling assumptions. The performance of the resulting DPCM encoder is shown to offer significant performance advantages over existing DPCM design approaches at transmission rates of 2 bits/pixel or less. Furthermore, this new approach results in improved ability to cope with channel errors.

A class of robust two-dimensional (2-D) tree coding procedures are described for efficient encoding of monochrome images. The encoding filter is designed on the basis of ensemble properties of a particular class of stochastic random fields which have been shown to provide a useful model for typical imagery data. We make use of the (M; K', L') algorithm in instrumenting the 2-D tree search. Results are demonstrated for both synthetic images and a number of head-and-shoulders images. These results demonstrate the effectiveness of 2-D tree encoding using fairly moderate search intensities and the inherent robustness of 2-D tree encoding more generally. In particular, it is demonstrated that, by logical design of the encoding filter under an appropriate stochastic modeling assumption, the 2-D tree encoder provides relatively efficient performance for a rather wide range of real-world imagery.

An approach is described for exploiting the tradeoffs between source and channel coding in the context of image transmission. The source encoder employs two-dimensional (2-D) block transform coding using the discrete cosine transform (DCT). This technique has proven to be an efficient and readily implementable source coding technique in the absence of channel errors. In the presence of channel errors, however, the performance degrades rapidly, requiring some form of error-control protection if high quality image reconstruction is to be achieved. This channel coding can be extremely wasteful of channel bandwidth if not applied judiciously. The approach described here provides a rationale for combined source-channel coding which provides improved quality image reconstruction without sacrificing transmission bandwidth. This approach is shown to result in a relatively robust design which is reasonably insensitive to channel errors and yet provides performance approaching theoretical performance limits. Analytical results are provided for assumed 2-D autoregressive image models, while simulation results are provided for real-world images.

The performance and complexity of tree encoding of images in the presence of channel errors is considered. We demonstrate that a variation of the(M, L)algorithm yields performance close to the rate-distortion bound in the absence of channel errors for synthetic images modeled as two-dimensional autoregressive random fields. Trade-offs in optimizing the choice of tree search parameters are described, and experimental results on real-world images are presented. Simple tree search procedures are shown to provide signal-to-noise improvements in excess of 5 dB over conventional two-dimensional DPCM at the important rate of one bit/pixel; the effect is clear and striking to the eye. Channel error effects are treated by computer simulation and demonstrate signal-to-noise ratio improvement as high as 8 dB using tree encoding. Finally, a combined source-channel coding approach is described that exploits the significant trade-offs between source quantization accuracy and vulnerability to channel errors.

A two-dimensional homogeneous and isotropic random field is described which is generated by a polygonal partition process on the plane. In particular, the plane is divided into elementary disjoint polygonal regions by a Poisson line process. Gray levels within these elementary polygonal regions are assigned to have specified correlation wilh gray levels in contiguous regions. Explicit evaluation of the resulting autocorrelation function and power spectral density is provided. Several applications are described.

The problem of image enhancement by nonlinear two-dimensional (2-D) homomorphic filtering is approached using stochastic models of the signal and degradations. Homomorphic filtering has been used previously for image enhancement but the linear filtering operation has generally been chosen heuristically. In this paper stochastic image models described and analyzed previously by the authors are used to model the true image and interferring components (shadows and salt-and-pepper noise). The problem of designing the linear operation can then be formulated as one of linear least mean-squared error (Wiener) filtering. Examples of processing on typical real-world images are included to indicate the results obtainable.

A combined source-channel coding approach is described for the encoding, transmission and remote reconstruction of image data. The source encoder employs two-dimensional (2-D) differential pulse code modulation (DPCM). This is a relatively efficient encoding scheme in the absence of channel errors. In the presence of channel errors, however, the performance degrades rapidly. By providing error control protection to those encoded bits which contribute most significantly to image reconstruction, it is possible to minimize this degradation without sacrificing transmission bandwidth. The result is a relatively robust design which is reasonably insensitive to channel errors and yet provides performance approaching the rate-distortion bound. Analytical results are provided for assumed 2-D autoregressive image models while simulation results are described for real-world images.

A class of nonlinear receiver structures is described for the detection of weak signals in non-Gaussian narrowband noise. In particular, the concept of a locally optimum receiver structure is extended to the ease of narrowband signal and noise models. A useful class of non-Gaussian narrowband noise models is developed for which the locally optimum receiver implementation is explicitly determined. These structures are shown to provide considerable improvement over conventional linear receiver structures. The basis of comparison is taken as the asymptotic relative efficiency (ARE). Unfortunately, the locally optimum receiver requires explicit{sl a priori}knowledge of the underlying noise distribution. To circumvent this difficulty a rather simple adaptive nonlinear receiver structure is described which attempts to adapt to the unknown prevailing noise environment. This adaptive receiver is shown to provide fairly efficient and robust performance in a wide variety of non-Gaussian narrowband noise environments.

A detector structure and an adaptive algorithm are proposed for the reception of signals in noise backgrounds possessing broad-tailed probability distributions typical of impulsive noise. The adaptive detector combines the best features of linear matched filtering and hard-limiting receiver structures resulting in a small-signal SNR performance which is an improvement over either of these detectors alone. Furthermore, the adaptive detector is relatively easy to implement and is shown to provide efficient and robust performance for a wide range of underlying noise distributions.

The bit error probability performance of a differentiallycoherent phase-shift keyed (DPSK) modem with convolutional encoding and Viterbi decoding on time-varying fading channels is examined. We consider both the Rician and the lognormal channels. Bit error probability upper bounds on fully-interleaved (zero-memory) fading channels are derived and substantiated by computer simulation. It is shown that the resulting coded system performance is a relatively insensitive function of the choice of channel model provided that the channel parameters are related according to the correspondence developed as part of this paper. Finally, a comparison of DPSK with a number of other modulation strategies is provided.

The performance of short constraint length convolutional codes in conjunction with binary phase-shift keyed (BPSK) modulation and Viterbi maximum likelihood decoding on the classical Rician fading channel is examined in detail. Primary interest is in the bit error probability performance as a function ofE_{b}/N_{0}parameterized by the fading channel parameters. Fairly general upper bounds on bit error probability performance in the presence of fading are obtained and compared with simulation results in the two extremes of zero channel memory and infinite channel memory. The efficacy of simple block interleaving in combating the memory of the channel is thoroughly explored. Results include the effects of fading on tracking loop performance and the subsequent impact on overall coded system performance. The approach is analytical where possible; otherwise resort is made to digital computer simulation.

This paper investigates the effects of dependence on rank tests, in particular on a class of recently defined nonparametric tests called "mixed" statistical tests. It is shown that the mixed test statistic is asymptotically normal for Gaussian processes with mild regularity properties justifying the use of asymptotic relative efficiency (ARE) as a figure of merit. Results are presented in terms of variations on three well-known statistics--the one-sample Wilcoxon, the two-sample Mann-Whitney, and the Kendall\tau. It is found that the effects of dependence on ARE with respect to a parametric test can be offset to some extent by appropriately grouping sample values. If, however, a constant false-alarm rate is to be attained, either the form of the dependence must be known or some learning scheme must be applied.