In this paper an approach to joint source-channel coding (JSCC) named Shannon-Kotel’nikov (S-K) mappings is discussed. S-K mappings are continuous, or piecewise smooth direct source-to-channel mappings operating on amplitude-continuous and discrete-time signals, and they encompass several existing JSCC schemes as special cases. Many existing approaches to analog- or hybrid discrete-analog JSCC provide both excellent performance as well as robustness to variable noise level at both low and arbitrary complexity and delay. However, a general theory explaining their performance and behaviour, as well as guidelines on how to construct well-performing mappings, do not exist. Therefore, such mappings are often based on educated guesses inspired by configurations that are known in advance to produce good solutions through numerical optimization methods. The objective of this paper is to develop a theoretical framework for analysis of analog- or hybrid discrete-analog S-K mappings which enables calculation of distortion when applying them on point-to-point links, reveal more about their fundamental nature, and provide guidelines for their construction at low as well as arbitrary complexity and delay. Such guidelines will likely help constrain solutions to numerical approaches and help explain why deep learning approaches obtain the solutions they do. The overall task is difficult and we do not provide a complete framework at this stage: We focus on high SNR and memoryless sources with an arbitrary continuous unimodal density function and memoryless Gaussian channels. We also provide example mappings based on surfaces which are chosen, or constructed, based on the provided theory.

In this paper, a robust and power-efficient transmission scheme of a time-discrete signal with continuous amplitude over parallel fading channels is proposed. A block of source samples is decomposed into N layers, so-called layered source coder. Each layer is transmitted over its own fading subchannel. The end-to-end mean square error (MSE) distortion, including distortion caused by the quantization process, the lossy compression, and channel errors, is adopted as the performance metric. We derive a power allocation strategy across the layers to minimize the end-to-end MSE distortion. The proposed transmission scheme gives higher robustness over the entropy-constrained source-channel coding scheme. In addition, the proposed transmission scheme requires much lower transmission power for a given source signal to noise ratio (SNRs) than the entropy-constrained scheme in the case of bandwidth compression. This power saving is meaningful for wireless communications with battery-operated devices.

In this paper, nonlinear distributed joint source-channel coding (JSCC) schemes for transmission of multivariate Gaussian sources over a Gaussian multiple access channel are proposed and analyzed. The main contribution is a zero-delay JSCC named Distributed Quantizer Linear Coder (DQLC), which performs relatively close the information theoretical bounds, improves when the correlation among the sources increases, and does not level off as the signal-to-noise ratio (SNR) becomes large. Therefore it outperforms any linear solution for sufficiently large SNR. Further an extension of DQLC to an arbitrary code length named Vector Quantizer Linear Coder (VQLC) is analyzed. The VQLC closes in on the performance upper bound as the code length increases and can potentially achieve the bound for any number of independent sources. The VQLC leaves a gap to the bound whenever the sources are correlated, however. JSCC achieving the bound for arbitrary correlation has been found for the bivariate case, but that solution is significantly outperformed by the DQLC/VQLC when there is a low delay constraint. This indicates that different approaches are needed to perform close to the bounds when the code length is high and low. The VQLC/DQLC also apply for bandwidth compression of a multivariate Gaussian transmitted on point-to-point links.

Ultrawideband (UWB) radio technology for wireless implants has gained significant attention. UWB enables the fabrication of faster and smaller transceivers with ultralow power consumption, which may be integrated into more sophisticated implantable biomedical sensors and actuators. Nevertheless, the large path loss suffered by UWB signals propagating through inhomogeneous layers of biological tissues is a major hindering factor. For the optimal design of implantable transceivers, the accurate characterization of the UWB radio propagation in living biological tissues is indispensable. Channel measurements in phantoms and numerical simulations with digital anatomical models provide good initial insight into the expected path loss in complex propagation media like the human body, but they often fail to capture the effects of blood circulation, respiration, and temperature gradients of a living subject. Therefore, we performed UWB channel measurements within 1-6 GHz on two living porcine subjects because of the anatomical resemblance with an average human torso. We present for the first time, a path loss model derived from these in vivo measurements, which includes the frequency-dependent attenuation. The use of multiple on-body receiving antennas to combat the high propagation losses in implant radio channels was also investigated.

This paper studies the zero-delay source-channel coding problem, and specifically the problem of obtaining the vector transformations that optimally map between the m-dimensional source space and k-dimensional channel space, under a given transmission power constraint and for the mean square error distortion. The functional properties of the cost are studied and the necessary conditions for the optimality of the encoder and decoder mappings are derived. An optimization algorithm that imposes these conditions iteratively, in conjunction with the noisy channel relaxation method to mitigate poor local minima, is proposed. The numerical results show strict improvement over prior methods. The numerical approach is extended to the scenario of source-channel coding with decoder side information. The resulting encoding mappings are shown to be continuous relatives of, and in fact subsume as special case, the Wyner-Ziv mappings encountered in digital distributed source coding systems. A well-known result in information theory pertains to the linearity of optimal encoding and decoding mappings in the scalar Gaussian source and channel setting, at all channel signal-to-noise ratios (CSNRs). In this paper, the linearity of optimal coding, beyond the Gaussian source and channel, is considered and the necessary and sufficient condition for linearity of optimal mappings, given a noise (or source) distribution, and a specified a total power constraint are derived. It is shown that the Gaussian source-channel pair is unique in the sense that it is the only source-channel pair for which the optimal mappings are linear at more than one CSNR values. Moreover, the asymptotic linearity of optimal mappings is shown for low CSNR if the channel is Gaussian regardless of the source and, at the other extreme, for high CSNR if the source is Gaussian, regardless of the channel. The extension to the vector settings is also considered where besides the conditions inherited from the scalar case, additional constraints must be satisfied to ensure linearity of the optimal mappings.

This paper analyzes a multiplicative data hiding scheme, where the watermark bits are embedded within frames of a Gaussian host signal by two different, but arbitrary, embedding matrices. A closed form expression for the bit error rate (BER) of the optimal detector is derived when the frame sizes tend to infinity. Furthermore, a structure is proposed for the optimal detector which divides the detection process into two main blocks: host signal estimation and decision making. The proposed structure preserves optimality, and allows for a great deal of flexibility: The estimator can be selected according to the a priori knowledge about host signal. For example, if the host signal is an Auto-Regressive (AR) process, we argue that a Kalman filter may serve as the estimator. Compared to a direct implementation of the Neyman-Pearson detector, this approach results in significantly reduced complexity while keeping optimal performance.

In this paper, we study the zero-delay source-channel coding problem, and specifically the problem of obtaining the vector transformations that optimally map between the m-dimensional source space and the k-dimensional channel space, under a given transmission power constraint and for the mean square error distortion. We first study the functional properties of this problem and show that the objective is concave in the source and noise densities and convex in the density of the input to the channel. We then present the necessary conditions for optimality of the encoder and decoder mappings. A well known result in information theory pertains to the linearity of optimal encoding and decoding mappings in the scalar Gaussian source and channel setting, at all channel signal-to-noise ratios (CSNRs). In this paper, we study this result more generally, beyond the Gaussian source and channel, and derive the necessary and sufficient condition for linearity of optimal mappings, given a noise (or source) distribution, and a specified power constraint. We also prove that the Gaussian source-channel pair is unique in the sense that it is the only source-channel pair for which the optimal mappings are linear at more than one CSNR value. Moreover, we show the asymptotic linearity of optimal mappings for low CSNR if the channel is Gaussian regardless of the source and, at the other extreme, for high CSNR if the source is Gaussian, regardless of the channel.

In this paper we generalize an existing distributed zero-delay joint source-channel coding scheme for communication of a multivariate Gaussian on a Gaussian Multiple Access Channel named Distributed Quantization Linear Coder (DQLC) to arbitrary code length. Although the DQLC is well performing, it leaves a certain gap to the performance upper bound (or distortion lower bound) based on arbitrary code length. The purpose of this paper is to determine if the generalization of the DQLC to arbitrary code length, named Vector Quantization Linear Coder (VQLC), can close the gap to the bound when the code length is large. Our results show that the VQLC mapping has the potential to reach the upper bound for any number of Gaussian sources at high SNR when the sources are uncorrelated. We also approximately determine the VQLC performance as a function of code length for the special case of two sources.

This paper presents a power-saving communication system for the link from an in-body sensor to an on-body sensor over the abdominal channel in medical wireless body area networks. The idea of the work is to exploit the time diversity of the channel coding and the high dimensional signal constellation of M-ary pulse position modulation (M-PPM) to improve the system performance. In addition to the illustration of the significant performance improvement of the proposed communication system, the severe fading effect of the abdominal channel compared with the conventional Rayleigh channel is investigated through the theoretical capacity and bit error rate (BER) performance.

A communication system based on the joint source-channel coding principle is proposed where a fixed-rate source encoder using neither a codebook nor an entropy encoder is exploited to avoid the error propagation effect and thus gain in system robustness. An explicit expression of the mean square error (MSE) distortion of the system for a uniform source is derived. Based on the MSE distortion, the optimal design of the communication system under the total transmission rate constraint is formulated as a mixed integer nonlinear optimization problem. We provide an algorithm to achieve the optimal solution via a convex optimization solver. The numerical result shows that the overall performance of the proposed system is close to the performance of the entropy coding scalar quantizer (ECSQ) system established by A. Gyorgy and T. Linder [1] for almost all rate regions.

A communication system based on the joint source-channel coding principle is proposed, where a fixed-rate source encoder is used to avoid the error propagation effect as experienced when variable length coding is used and thus gain system robustness. An explicit expression of the mean square error (MSE) distortion of the system for a uniform source is derived. We provide an algorithm to achieve the optimal solution by investigating the Karush–Kuhn–Tucker (KKT) condition. The numerical results show that the overall performance of the proposed system is close to the performance of the entropy coded scalar quantiser (ECSQ) system established by A. György and T. Under for almost all rate region. A 0.176-bits-per-sample performance loss is found for the worst case by comparing our considered system and ECSQ system. An observation resembling the finding by V. Goya1 et al. is that in the low rate region, there exist certain regimes in which the proposed system outperforms the ECSQ system. Finally, the proposed system outperforms the equal rate system with a large margin.

In this paper, delay-free, low complexity, joint source-channel coding (JSCC) for transmission of two correlated Gaussian memoryless sources over a Gaussian Multiple Access Channel (GMAC) is considered. The main contributions of the paper are two distributed JSCC schemes: one discrete scheme based on nested scalar quantization, and one hybrid discrete-analog scheme based on a scalar quantizer and a linear continuous mapping. The proposed schemes show promising performance which improves with increasing correlation and are robust against variations in noise level. Both schemes also exhibit a constant gap to the performance upper bound when the channel signal-to-noise ratio gets large.

We study the communication problem in a sensor network which consists of multiple sensor nodes that observe memoryless Gaussian sources which are inter-correlated. The observations are transmitted over orthogonal additive white Gaussian noise channels, and all source symbols are to be recovered at the receiver. We focus on communication schemes which utilize direct source to channel mappings that operate on a symbol-by-symbol basis to ensure zero coding delay. The distortion lower bound for the network with more than two sensors case is derived. Optimal linear schemes, both distributed and cooperative, are presented. Results show that the gap to the performance upper bound is large when there is high correlation and it increases significantly when the network size is large. We then present nonlinear mappings which can be implemented distributedly and show that they can provide substantial gain when the correlation is close to one. Examples are given for networks with two and three nodes.

This paper focuses on optimal analog mappings for zero-delay, distributed source-channel coding. The objective is to obtain the optimal vector transformations that map between m-dimensional source spaces and k-dimensional channel spaces, subject to a prescribed power constraint and assuming the mean square error distortion measure. Closed-form necessary conditions for optimality of encoding and decoding mappings are derived. An iterative de- sign algorithm is proposed, which updates encoder and decoder mappings by sequentially enforcing the complementary optimality conditions at each iteration. The obtained encoding functions are shown to be a continuous relative of, and in fact subsume as a special case, the Wyner-Ziv mappings encountered in digital distributed source coding systems, by mapping multiple source intervals to the same channel interval. Example mappings and performance results are presented for Gaussian sources and channels.

The problem of lossy source channel communication under a received power constraint in a simple Gaussian sensor network is studied in this paper. A group of sensors are placed to observe a common Gaussian source. The noisy observations are then transmitted over a Gaussian multiple access channel (MAC) to the sink, where the source is estimated with a quadratic distortion criterion using all received sensor observations. We propose an analogue transmission scheme that uses noiseless causal feedback from the sink to remove correlation between the observation samples, combined with time division multiple access of the MAC. The proposed scheme offers same performance with reduced received power and sensor network size, compared with optimal transmission scheme with single channel use; and converges to the absolute performance bound with low received power level for the same use of bandwidth.

This paper proposes a limited feedback rate transmission scheme for wireless sensor networks over slowly fading channels. The design approach is based on joint source and channel coding, where source coding characteristics are taken into account to design the transmission protocol for fading channels. The transmission protocol uses an unequal protection regime for different bit groups according to their priority levels while taking into consideration of the variations within and among fading channels. Only group indices are transmitted on the feedback channel from the fusion center to the sensors. This means the feedback channel can operate at a low data rate. Furthermore, it is shown by both theoretical analysis and simulation that the proposed transmission scheme has better performances compared to the distributed beamforming counterpart in low signal-to-noise ratio (SNR) regime.

Estimating an unknown parameter using a sensor network has been considered when the fusion center receives only one bit from each sensor. The network is divided to a number of groups and all sensors in a group use a fixed and equal threshold for quantization. A combined weighted estimation structure has been proposed. At the fusion center weights are assigned to each group of sensors based on their quantized bit entropy. The results have been presented and compared to maximum likelihood estimator (MLE), which had been proposed for the same scenario. The simulation results show that the proposed method has identical performance for large number of sensors and reaches Cramer-Rao lower bound(CRLB), while it outperforms MLE for limited number of sensors and when the distance between quantization levels increases. Moreover the proposed method has very low complexity compared to MLE. It is also considerably faster than MLE, which makes it more suitable for wireless sensor networks.

To prolong the lifetime of nodes in wireless sensor networks, both transmission cost and processing power should be minimized. For this purpose, we propose a new direct source channel mapping method which utilizes large bandwidth. The system combines a closed-loop Differential Pulse Code Modulation (DPCM) source coder followed by pulse position modulation (PPM) transmission. To accommodate closed-loop prediction over a noisy channel an additional feedback channel is used. Two or more sequential samples are predicted at a time and combined before transmission, thus reducing transmission cost further. Simulations performed on both an auto regressive AR(1) source and a test image over additive white Gaussian noise (AWGN) channel show that our proposed system can achieve significant energy saving for both noiseless and noisy feedback channels without delay.

This paper deals with lossy joint source-channel coding for transmitting memoryless sources over AWGN channels. The scheme is based on the geometrical interpretation of communication by Kotel'nikov and Shannon where amplitudecontinuous, time-discrete source samples are mapped directly onto the channel using curves or planes. The source and channel spaces can have different dimensions and thereby achieving either compression or error control, depending on whether the source bandwidth is smaller or larger than the channel bandwidth. We present a general theory for 1:N and M:1 dimension changing mappings, and provide two examples for a Gaussian source and channel where we optimize both a 2:1 bandwidth-reducing and a 1:2 bandwidth-expanding mapping. Both examples show high spectral efficiency and provide both graceful degradation and improvement for imperfect channel state information at the transmitter.

In many communication applications one is interested in transmitting a time-discrete analog-valued (i.e. continuous alphabet) source over a time-discrete analog channel. We study this problem in the case of bandwidth expansion, in the sense that one source sample, X, is transmitted over N-orthogonal channels. An analog source-channel code based on orthogonal polynomials is proposed and analyzed. The code can be generated using a Gram-Schmidt procedure, to fit virtually any source distribution.

Use of wireless biomedical sensor networks in complex clinical diagnostics and treatments may provide greater flexibility for both patient and medical staff as some of the same sensors could follow the patient throughout the cycle of treatment. A typical scenario from an intensive care unit, with data from three vital sign sensors, is used as an example for both hardware and software simulations. Results show that data throughput in such biomedical networks is greatly depended on packet size while competing for channel access. A new scheduling algorithm has been proposed for multi-hop networks. Some of the hardware limitations are identified, where the trade off between hardware and software systems is demonstrated

Summary form only given. We compute the noise components in 1:N dimension expanding (error protection) and M:1 dimension reducing (lossy compression) systems for memoryless Gaussian sources transmitted over AWGN channels. A theory for dimension reducing systems was developed wherein the source- and channel coders are combined into one nonlinear operation and the parametric curves are used to map the source onto the channel. For both systems we have two types of distortion. Results show that the 2:1 system works very well and that the 1:2 system is not as close to optimum but the gain compared to a linear system is approximately the same as in the 2:1 case. The solid graphs illustrate the characteristics of the two distortion contributions. The small noise contribution and approximation noise above the optimum point (increasing CSNR), and the threshold- and channel noise below the optimum point

Summary form only given. By using nonlinear dimensional-changing mappings, a robust image transmission system for fading channels has been developed. Using robust mappings and adapting the protection of source samples results in a system that can transmit an image over a flat fading channel with a certain quality regardless of the channel variations

Summary form only given. We have earlier presented a joint source-channel coding (JSCC) method for 2:1 bandwidth reduction, a method called Shannon mappings. We extend this scheme to include a digital transport network between the point of the received JSSC symbols and the ultimate destination. Since the JSCC symbols are amplitude-continuous, some form of digitising or transcoding is necessary before transmission on the digital network. Instead of decoding the JSCC symbols and subsequently applying a digital source coder, we propose using a uniform scalar quantization directly on the received channel symbols. The quantizer can be either be applied at the receiver side or it can be applied at the transmitter with jointly optimised JSCC and quantization. We compare the performance of these two approaches with a 2D entropy-constrained vector quantizer (2D-ECVQ) applied to the decoded JSCC symbols. We see that applying the quantizer at the transmitter side and jointly optimise mapping and quantization is always better than both the 2D-ECVQ and the receiver-side quantizer. Finally, we note that with the quantizer rate equal to the channel capacity, the proposed system is only 2.8 dB away from the theoretical optimum, this without any coding at all

The Archimedes' spiral can be used as a 2:1 bandwidth reducing mapping in a joint source-channel coding (JSCC) system. The combined point of two iid Gaussian sources (the source space) is mapped, or approximated, onto a double Archimedes' spiral (the codebook), and the squared angle from the origin to the mapped point is transmitted as an analogue channel symbol (the channel space), e.g. PAM. It is shown that the total distortion of this JSCC system is minimised when the distortion contributions from the approximation noise and channel noise are equal. The given system produces a channel input distribution close to a Laplace probability density function (pdf) instead of the optimal Gaussian pdf. The loss when using this mismatched pdf is shown to be approximately equal to the relative entropy of the two pdf.

A joint source channel coding scheme for error resilient image transmission is proposed. A practical image coder was introduced in AN Kim et al, (2004) using modified differential pulse coded modulation (DPCM) codec with multi-rate processing and adaptive entropy coding. In this paper the residual redundancy of the prediction error image is exploited by using turbo codes for both data compression and error protection. In the paper we deal with robust transmission of the source over a BSC channel, but the results can be easily extended for non binary channels. Note also that simple modification of the quantizer allows for progressive transmission and successive refinement of information. With properly chosen rate and puncturing, the system is able to approach the limit theoretically attainable and to outperform the separated approach that consists on the concatenation of the system in AN Kim et al, (2004) and the best turbo codes for the same spectral efficiency.

This paper presents a scheme for scalable, error resilient coding of audio signals. The scheme is implemented here as part of a subband-based audio codec and involves the union of two interconnected ideas: tree-structured vector quantization (TSVQ) and reallocation of bits (RoB). The former ensures that the encoding procedure results in fixed-length codes while the latter is a low-complexity scaling algorithm that computes optimal bitrates for each subband when the bitstream needs to be downscaled to a lower bitrate. The functionality enabled by these two systems assumes great importance when the encoded material is to be delivered over channels and networks that have a time-varying bitrate, such as IP-based wireless networks. Such channels are often error-prone and the potentially debilitating effects of introduced errors are mitigated by the inherent fixed-length property of all codewords. We present results that highlight the performance of this system under noisy conditions and show that the degradation in quality is graceful.

The modified differential pulse coded modulation (DPCM) codec with multi-rate processing has been shown to able to efficiently code the source with monotonically decreasing spectrum at low bit rates [A.N. Kim and T.A. Ramstad]. A practical image coder is designed based on this approach. Two dimensional DPCM is used along with decimation and interpolation to reduce the number of transmitted samples. The decimation rate depends on the signal spectrum and the bit rate. Further bit rate reduction is achieved through adaptive entropy coding. Wiener filter is appended in the decoder for minimizing distortion caused by quantization noise. The decimation filter can be implemented using simple IIR filters. The necessary side information is low. Simulation results show that the coder is able to give good compression performance at low bit rates which is superior to conventional DPCM codec and JPEG. Subjective quality can be as good as JPEG2000. While at very low bit rates the proposed codec is able to retain certain image characteristics better than JPEG2000.

The paper proposes a system for combined source-channel coding for transmitting continuous amplitude source symbols on a discrete time, continuous amplitude channel. Two channel symbols are generated for each source symbol. The channel contains additive, white, Gaussian noise, and the measure of quality is the MSE of the reconstructed signal. The coder quantizes the symbols and transmits both the quantized symbol and the quantization error. The quantizer representation values and decision levels are optimized numerically. The results indicate that the use of a uniform quantizer is nearly optimal for a uniformly distributed source. Comparison to another combined source-channel coder designed for a binary channel reveals that the proposed system performs significantly better than the reference systems, more than 5 dB for every channel SNR above 15 dB.

A multi-dimensional variable-length subband coder for prestack seismic data was presented. A 2-D and 3-D separable near perfect reconstruction filter bank was optimized to maximize the coding gain, assuming that the correlation properties of pre-stack seismic data can be modeled by directional dependent autoregressive processes. Identical quantization and entropy coder allocation strategies were utilized to isolate the compression efficiency of the different high-dimensional filter bank methods. An example, with compression ratios ranging from 160:1 to 320:1, showed that 3-D subband coding of common shot gathers performed 50% better in terms of bit rate at a given signal-to-noise ratio compared to 2-D subband coding of common shot gathers.

The performance of subband image coders depends on the proper choice of filter banks. It is therefore desirable to find algorithms for optimizing the filter banks. A theory for finding jointly optimized analysis and synthesis filter banks with arbitrary filter lengths and arbitrary delay through the filter bank is proposed. Theoretical results are included. Comparisons are made against the well known 5/3, 9/7, and 10/18 wavelets. The proposed filter banks, which are both rare and source dependent, have a better distortion rate performance for all cases.

A novel way of constructing integer coefficient 2-channel filter banks is proposed. A set of relationships among the filter coefficients is established in order to satisfy linear phase, perfect reconstruction, and FIR properties. The remaining degrees of freedom are used to obtain integer coefficient values by maximizing a performance evaluation function, namely the subband coding gain. The number of bits required to represent the subband samples is kept low through efficient nonlinear implementation techniques. An octave-band frequency partitioning where the number of stages is determined according to the image size is employed. The subband samples are then classified into one out of a finite number of classes, and each class is coded by an arithmetic coder. The obtained compression ratios are encouraging compared to the "best" results reported so far in the literature.

A subband coder structure is fully optimized with respect to the minimum block mean squared error between the output and the input signals under a bit constraint. The analysis filter bank structure generates maximally decimated and equal bandwidth subbands. The subband quantizers are modeled as additive noise sources. To simplify the optimization an optimal multiple-input multiple-output system is first derived. Illustrative examples showing the system performance as well as filter transfer functions are given. The performance results are compared to the rate distortion curves.

The performance of several decorrelating transforms is evaluated in the JPEG-2000 baseline system. The transforms considered are based on uniform parallel 2-channel and 8-channel filter banks and discrete cosine transform (DCT) building blocks. Through the analysis of lossy compression results, a system employing a combination of 8- channel and 2-channel filter banks is found to perform best overall. Also, the performance of several reversible transforms is evaluated in the same coding framework. Based on lossy and lossless compression results, a reversible version of the Cohen-Daubechies-Feauveau (2,2) wavelet transform was found to be most effective.

Different algorithms are evaluated and optimizations are performed to obtain a filterbank for subband coding of images especially suited for very large scale integration (VLSI) implementation. Based on a filterbank consisting of two finite impulse response (FIR) filters combined with an 8-point discrete cosine transform (DCT), we investigate how the quantization of filter coefficients and twiddle factors in different algorithms affects the quality of the filterbank. It is found that a DCT based on a Stasinksi (1989) algorithm with twiddle factors of only 5 b together with FIR filter coefficients of 10 b gives a filterbank with high coding gain, no blocking artifacts, and limited ringing. The VLSI complexity is comparable to that of DCT transforms.

The performance of subband image coders depends on proper choice of filter banks. Although odd length filters in the filter banks produce waveform type artifacts, this can be alleviated by enforcing a smooth interpolation property to the synthesis lowpass filter. Evaluation of even, odd, and combinations of even and odd length filters in tree-structured filter banks, where the filter coefficients are obtained by optimizing for coding gain at each stage, is done for image coding purposes. Favorable results are obtained when a combination of odd and even length filters are used.

Two methods for transmission of a continuous amplitude source signal over a continuous amplitude channel with a power constraint are proposed. For both methods, bandwidth reduction is achieved by mapping from a higher dimensional source space to a lower dimensional channel space. In the first system, a source vector is quantized and mapped to a discrete set of points in a multidimensional PAM signal constellation. In the second system the source vector is approximated with a point in a continuous subset of the source space. This operation is followed by mapping the resulting vector to the channel space by a one-to-one continuous mapping resulting in continuous amplitude channel symbols. The proposed methods are evaluated for a memoryless Gaussian source with an additive white Gaussian noise channel, and offer significant gains over previously reported methods. Specifically, in the case of two-dimensional source vectors, and one-dimensional channel vectors, the gap to the optimum performance theoretically attainable is less than 1.0 dB for a wide range of channel signal-to-noise ratios.

This paper investigates a transform adaptation technique, applied to transform coding of images, as a way of exploiting the variation in local statistics within an image. The method makes use of the relationship between the Karhunen-Loeve transform (KLT) and singular value decomposition (SVD), and their energy compaction properties. We compare this approach to a standard KLT coding system. Motivated by increased coding efficiency an analysis-by-synthesis approach using switching between the KLT coding system and the hybrid KLT-SVD system is proposed. The switching is implemented using a global rate-distortion criterion. The results are encouraging and the proposed techniques provide new insights on how to use SVD in an image compression system.

The performance of subband image coders depends on the proper choice of frequency partitioning in the subband domain. It is therefore desirable to have an adaptive nonuniform filter bank to cope with the frequency characteristics of the image at hand. However, a good choice, if a nonadaptive structure is to be used, is combinations of uniform parallel and octave-band tree-structured filter banks. Uniform parallel (8-channel, 32-tap), and 3-stage and 6-stage octave-band tree-structured systems are compared using a fixed rate coder for image coding. Favorable results are obtained using the combination of a parallel filter bank and a tree-structured system. The coding results are comparable to the "best" results reported in the literature.

A new method for lossless coding of the classification table in low bit rate subband image coders with block-wise classification is proposed. The method is referred to as hierarchical enumeration and uses an algorithmic enumeration technique to associate a fixed-length unique binary codeword with each possible combination of integers defining the classification table. The resulting bit rate is less than the first order entropy of the classification table. When using hierarchical enumeration in combination with pyramid vector quantization of the subband samples, a high performance image coder using only fixed-length codewords is obtained. The proposed coder compares favorably with state-of-the art image coders using variable-length coding.

A video communication system based on combined source-channel coding is proposed. The proposed system uses a hybrid subband video coder structure in combination with power-constrained channel-optimized vector quantization (PCCOVQ) to achieve efficient and robust transmission of the video signal over a channel with multidimensional PAM signaling. The error-sensitive side information parameters are protected by using traditional channel coding and a sufficiently large minimum distance of the PAM signal constellation. This ensures error free transmission for the channel-optimized case, and graceful degradation for channel mismatch situations. For the main information, PCCOVQ with a direct mapping from the source parameter space to the channel (modulation) space is used. A traditional video communication system based on the H.263 video coder is used as a reference. The proposed system compares favorably to the reference system for high rate applications, and offers graceful degradation for channel mismatch situations.

A new motion compensation scheme for subband video coding is introduced, where both motion estimation and compensation are performed directly on the subband signals. During motion estimation, a full resolution search for the best candidate displacement vector is performed on all subband signals simultaneously, with down-sampling of each block before evaluating the error criterion. Furthermore, the proposed scheme allows for the use of a motion estimation error criterion which takes the subsequent dynamic bit allocation applied in the spatial quantization into account. In particular, it is shown that using the geometric mean of the subband signal variances instead of the arithmetic mean, results in increased performance. The proposed coder results in coding gains as high as 3.7 dB and 2.9 dB over traditional DCT and SBC schemes, respectively, for the video material tested.

A mixture distribution model is introduced to characterize the source statistics in a frequency domain image coder. More specifically, a Gaussian mixture distribution is shown to be a good statistical model of the probability density function of the composite decomposed signal. Theoretical results based on the mixture distribution model are found that quantify the obtainable entropy rate gain in the coder when using multiple entropy coders. A practical image coder using the theoretical concepts is proposed. The simulation results show close correspondence with the predicted theoretical results, thus, verifying the accuracy of the mixture distribution model.

By employing nonuniform nonunitary filter bank in an image coder increased performance in terms of both theoretical and practical (PSNR) coding gains, and subjective quality can be obtained. One possible candidate is octave-band tree-structured filter banks. An optimized perfect reconstruction octave-band three-stage tree-structured filter bank is proposed. The filter coefficients are optimized at each stage for subband coding gain. The performance of the proposed filter bank outperforms both traditional octave-band three-stage tree-structured filter banks and parallel filter banks in terms of both PSNR and visual quality.

A video transmission system based on combined source coding and multilevel modulation is proposed. For the proposed system, graceful degradation for noisy channels is obtained by finding good index maps between the quantized source coder parameters and the amplitude levels of a multilevel QAM signal constellation. The index maps are designed both for good neighbor properties and for power efficient transmission by using simulated annealing. The performance of the proposed system is comparable to a reference system based on the H.263 coder for high CSNR values, and degrades far more gracefully for low CSNR values.

A new error criterion for block based motion estimation in a hybrid video coder is proposed. Traditionally, the mean squared error between the current and the previous frames has been considered as an appropriate criterion for selecting the displacement vectors in hybrid video coders. It is shown that when the spatial domain coder is based on a DCT and dynamic bit allocation, improved performance can be achieved by using the geometric mean of the DCT coefficient variances as the error criterion. The proposed coder offers a significant gain in terms of PSNR, typically in the range of 0.2-1.0 dB, without much increase in the computational complexity.

The combination of a source coder and a digital modulator is in this article viewed as an analog-to-analog converter with signal compression ability. A reference-channel with defined available bandwidth, total received power, and noise statistics, can transmit one analog source signal. Compression is here defined as the number of such source signals that the digital system can transmit over the reference channel, and reconstruct with the same fidelity as the transmitted analog source signal. An image transmission example is provided where, for a given fidelity on a reconstructed image, the obtainable compression ratio is found for a digital compression system based on subband coding and pulse amplitude modulation.>

The construction of efficient filter bank algorithms is considered. It is shown that a proper operation grouping of a block-filtering algorithm is of great importance when its efficient use in a filter bank is analysed. Then, the construction of efficient algorithms for general and linear-phase filter banks having short polyphase filters is addressed. A set of efficient algorithms for short polyphase filters is provided, and rules for their construction described. It is also shown how to derive efficient algorithms in the case when filter bank filters have different lengths. The algorithms require less multiplications and additions than the direct filter bank realization, and are relatively simple to implement.>

An approach for compression of color images using a sorted color palette and a subband source coder is presented. When the decoded image is to be displayed on an eight bit monitor this method significantly reduces the decoder computational complexity. To avoid requantization before displaying the decoded image, the encoding and decoding are performed on a pseudo greyscale image which represents the color space defined by a sorted palette. To sort the palette, a measure for color similarity is needed. Here an l/sub 2/ distance in the RGB and luminance-chrominance color space has been studied, and a new color correlation measure is proposed. For comparison a transform source coder (JPEG) is used to encode the pseudo greyscale image. Simulation results show that the subband source coder gives better results than the transform source coder. The quality of the decoded color images is surprisingly good.>

The paper argues that the JPEG coder is based on a non-optimal entropy coding method. It is shown that for frequency domain coders using uniform quantization it is optimal to use entropy coders optimized for the entropy in each frequency component. A subband coder model with uniform quantization followed by optimal entropy coding is presented, where each subband is allocated an entropy coder based on its entropy. The theoretical coding gain limit for this model is shown to be the same as for frequency domain coders employing explicit bit allocation. However, the new model exploits the advantage associated with variable length coding. In addition, it is possible to efficiently use midtread quantizers, which have higher mean square error performance and, more important, better visual performance than midrise quantizers. Advantages for practical subband image coders are discussed in the paper.>

Consideration is given to modeling of arbitrary digital gray tone images as the fixed points of contractive transformations on the image space. The transformation is designed to exploit a form of image redundancy called piecewise self-similarity. Results from inner product space theory are used to optimize the transformation within a class of affine transformations. The resulting transformation is described by a small amount of information compared to the original image, and its piecewise self-similar fixed point, found by successively iterating the transformation from any initial image, is close to the original image. Results are improved compared to earlier results with this technique.>

The authors present a simple derivation of a parallel filterbank based on cosine-modulated versions of a model low-pass filter. With a nonuniform channel separation an efficient implementation consisting of a DFT (discrete Fourier transform) related transform and subfilters is possible. Using critical sampling of each channel and FIR (finite impulse response) filters, the conditions for perfect reconstruction are given. The computational complexity of the derived FIR filterbank is much lower than for a tree-structured FIR filterbank but cannot compete with the most efficient IIR filterbanks.>

The principle of subband coding has recently been applied for the purpose of image data compression. In this paper we present new results pertaining to our subband coder for images featuring an exact reconstruction parallel complex filter bank based on HR filters. This filter bank is characterized by its low complexity. The main advantage of subband coding is the possibility of separate coding of each subband such that the perceptually important coding noise is minimized. In this paper we exploit the nature of the complex valued subband signals of this particular coder by coding the module and phase rather than the real and imaginary parts. We determine the tolerable quantization noise levels for the module and phase signals in all subbands. These empiricaly derived data are employed in the coding simulations presented. Finally we present coding results for bit rates between 0.25 and 1.0 bits/pel.

Filter banks based on recursive filters have recently been applied with success in subband coding of still images [1, 2]. Their main feature, low computational complexity, make these filter banks extremely attractive for video coding applications. In. this paper we demonstrate the suitability of these filter banks in low bit rate image sequence coders operating in the 64 —200 Kbps range. In particular we compare the performance of two types of recursive filter banks with that of a more traditional one based on quadrature mirror FIR filters (QMF). It is shown that the performance of our hR based systems is comparable to that of the more complex FIR based systems. Also, we show that the encoding strategy of CCITT's reference model no. 7 can be adapted successfully to fit into our subband coding scheme. Finally we discuss alternative approaches to motion estimation in hybrid image sequence coders and show preliminary results in the context our video subband coder.

The paper describes methods for varying the bitrate in speech coders for minimizing the memory requirement in voice storage systems. An adaptive sub-band coder is studied in some detail, and subjective test-results are given which indicate optimal parameters for the model chosen.

The paper discusses optimization of quantization and bit-allocation in subband coders for speech signals. Time dependent subband power representation within coding frames is introduced and a "two-dimensional" bit-assignment method is employed. Furthermore, quantization of the sideinformation and its implications on the sub-band signal quantization are discussed.

Vector quantization (VQ) is examined as a technique to enhance performance in subband coding of speech at 9.6 kb/s. The set of short-term subband power levels is vector quantized, providing low-rate side information to control the coding of the subband signals. Each subband signal is then vector quantized with variable size codebooks that are dynamically assigned by the quantized side information. Two versions are described, a 7-band coder and a 14-band coder. Simulation results demonstrate that vector quantization offers a distinct perceptual improvement compared with scalar quantization of the same subband signals and side information for the same total bit rate.

The paper suggests and describes two methods for sample-rate conversion by arbitrary ratios, either between any two fixed or varying sampling frequencies. The first method is based on an impulse-invariant transform of an analog filter. A parallel form realization structure is presented, The second method combines regular IIR- or FIR-interpolators for integer or rational conversion ratios with low-order Lagrange-interpolators. An efficient realization structure is presented. Examples concerning sampling rate conversion of speech signals are given for both methods.

A sub-band coder for speech digitization with adaptive bit-allocation is studied and described. It contains a uniform filterbank of thirteen 250 Hz channels. The sub-band amplitudes are quantized by the optimal method due to Max (8). Amplitudes in bands with no bits transmitted are regenerated by noise excitation with the respective sub-band power levels. Subjective test-results for bitrates from 4.8 to 16 kbits/s are included. Experiments with background noise and transmission bit-errors are cited.

The paper discusses structures, design methods, and efficiency of digital two-rate filters for sampling rate alteration by integer or rational ratios. Four canoic filter structures are demonstrated: the direct form, the parallel form, the ladder/lattice forms, and a structure based on canonic all-pass sections. In addition, a structure exploiting numerator coefficient symmetry is presented. An extended class of filters (hybrid IIR/FIR) where the passband equalization is performed by a combination of poles and off-the-unit-circle zeros is introduced. The author also describes a design method which iteratively utilizes the Remez algorithm. This simple extension of the McClellan et al. (1973) program facilitates the design of virtually any kind of filter including hybrid filters and/or two-rate filters. Several design examples are presented to visualize the different aspects of two-rate filtering.

Direct form implementation of IIR filters for sample rate alteration has been shown (1) to be efficient when the recursive part of the filters work at the low sampling frequency. In this paper we suqgest to generalize the IIR interpolators/decimators by introducting partial zero-forming of their passband. A design method based on the Reméz exchange algorithm is proposed. The advantage of these filters is that the coefficient sensitivity as well as the quantization noise can be reduced. An illustrative design example is presented.