Channel-optimized Vector Quantization Research Articles

PSO Algorithm Applied to Codebook Design for Channel-Optimized Vector Quantization

Vector quantization (VQ) has been used in signal compression systems. However, in the scenario of image transmission, VQ is very sensitive to channel errors. An approach to decrease such sensitivity is channel-optimized vector quantization (COVQ), which involves VQ codebook design taking into account the characteristics of the channel. In the present work, particle swarm optimization (PSO) is applied to codebook design for COVQ. Simulation results are presented for a variety of bit error rates of a binary symmetric channel (BSC) and reveal the effectiveness of the method in decreasing visual impairment by blocking artifacts in the reconstructed images, overperforming conventional COVQ codebook design in terms of peak signal to noise ratio of the reconstructed images for approximately 90% of exhaustive evaluations of image transmission over BSC.

Robust Feedback Design for Time Reversal UWB Communication Systems Under CSIT Imperfections

We propose a robust design for digital feedback of the channel impulse response in a time-reversal ultrawideband communication system. The proposed scheme employs channel optimized vector quantization to reduce distortion that occurs due to channel noise on the feedback link. Utilizing experimental channel measurements in a typical indoor environment, we indicate the robustness of the proposed strategy by showing that the scheme's performance remains resilient under channel mismatch conditions that arise due to the combined effect of quantization, feedback delay, and noise on the feedback channel.

Joint Source-Channel Vector Quantization for Compressed Sensing

We study joint source-channel coding (JSCC) of compressed sensing (CS) measurements using vector quantizer (VQ). We develop a framework for realizing optimum JSCC schemes that enable encoding and transmitting CS measurements of a sparse source over discrete memoryless channels, and decoding the sparse source signal. For this purpose, the optimal design of encoder-decoder pair of a VQ is considered, where the optimality is addressed by minimizing end-to-end mean square error (MSE). We derive a theoretical lower bound on the MSE performance and propose a practical encoder-decoder design through an iterative algorithm. The resulting coding scheme is referred to as channel-optimized VQ for CS, coined COVQ-CS. In order to address the encoding complexity issue of the COVQ-CS, we propose to use a structured quantizer, namely low-complexity multistage VQ (MSVQ). We derive new encoding and decoding conditions for the MSVQ and then propose a practical encoder-decoder design algorithm referred to as channel-optimized MSVQ for CS, coined COMSVQ-CS. Through simulation studies, we compare the proposed schemes vis-à-vis relevant quantizers.

MAP Detection and Robust Lossy Coding Over Soft-Decision Correlated Fading Channels

The joint source-channel coding (JSCC) problem for soft-decision-demodulated time-correlated fading channels is investigated without the use of channel coding and interleaving. For the purpose of system design, the recently introduced nonbinary noise discrete channel with queue-based (QB) noise (NBNDC-QB) is adopted. This analytically tractable Markovian model has been shown to represent effectively correlated fading channels that are hard to handle analytically. Optimal sequence maximum a posteriori (MAP) detection of a discrete Markov source sent over the NBNDC-QB is first studied. When the Markov source is binary and symmetric, a necessary and sufficient condition under which the MAP decoder is reduced to a simple instantaneous symbol-by-symbol decoder is established. Two robust lossy source coding schemes with a low encoding delay are next proposed for the NBNDC-QB. The first scheme consists of a scalar quantizer (SQ), a proper index assignment, and a sequence MAP decoder designed to harness the redundancy left in the indexes of the quantizer and the soft-decision output and the noise correlation of the channel. The second scheme is a classical noise-resilient vector quantizer known as the channel-optimized vector quantizer (COVQ). It is demonstrated that both systems can successfully exploit the memory and soft-decision information of the channel. Signal-to-distortion-ratio (SDR) gains of more than 1.7 dB are obtained over hard-decision demodulation by using only two bits for soft decision. Furthermore, gains as high as 4.4 dB can be achieved for a strongly correlated channel, in comparison with systems designed for the ideally interleaved (memoryless) channel. Finally, it is numerically observed that, for low coding rates, the NBNDC-QB model can accurately approximate discrete fading channels (DFCs) in terms of SDR performance.

High-Rate Vector Quantization for Noisy Channels With Applications to Wideband Speech Spectrum Compression

This paper considers the high-rate performance of source coding for noisy discrete symmetric channels with random index assignment (IA). Accurate analytical models are developed to characterize the expected distortion performance of vector quantization (VQ) for a large class of distortion measures. It is shown that when the point density is continuous, the distortion can be approximated as the sum of the source quantization distortion and the channel-error induced distortion. Expressions are also derived for the continuous point density that minimizes the expected distortion. Next, for the case of mean squared error distortion, a more accurate analytical model for the distortion is derived by allowing the point density to have a singular component. The extent of the singularity is also characterized. These results provide analytical models for the expected distortion performance of both conventional VQ as well as for channel-optimized VQ. As a practical example, compression of the linear predictive coding parameters in the wideband speech spectrum is considered, with the log spectral distortion as performance metric. The theory is able to correctly predict the channel error rate that is permissible for operation at a particular level of distortion.

Combining Beamforming and Space-Time Coding Using Noisy Quantized Feedback

The goal of combining beamforming and spacetime coding is to obtain full-diversity order and to provide additional received power (array gain) compared to conventional space-time codes. In this work, a class of code constellations is proposed, called generalized partly orthogonal designs (PODs) and both high-rate and low-rate feedback information is incorporated with possible feedback errors. A binary symmetric channel (BSC) model characterizes feedback errors. Two cases are studied: first, when the BSC bit error probability is known a priori to the transmission ends, and second, when it is not known exactly. Based on a minimum pairwise error probability (PEP) design criterion, we design a channel optimized vector quantizer (COVQ) for feedback information and a precoder matrix codebook to adjust the transmission codewords. The attractive property of our combining scheme is that it converges to conventional space-time coding with low-rate and erroneous feedback and to directional beamforming with high-rate and error-free feedback. This scheme also shows desirable robustness against feedback channel modeling mismatch.

Hybrid digital-analog coding with bandwidth compression for gaussian source-channel pairs

Three hybrid digital-analog (HDA) systems, denoted by HDA-I, HDA* and HDA-II, for the coding of a memoryless discrete-time Gaussian source over a discrete-time additive memoryless Gaussian channel under bandwidth compression are studied. The systems employ simple linear coding in their analog component and superimpose their analog and digital signals before channel transmission. Information-theoretic upper bounds on the asymptotically optimal mean squared error distortion of the systems are obtained under both matched and mismatched channel conditions. Allocation schemes for distributing the channel input power between the analog and the digital signals are also examined. It is shown that systems HDA* and HDA-II can asymptotically achieve the optimal Shannon-limit performance under matched channel conditions. Low-complexity and low-delay versions of systems HDA-I and HDA-II are next designed and implemented without the use of error correcting codes. The parameters of these HDA systems, which employ vector quantization in conjunction with binary phase-shift keying modulation in their digital part, are optimized via an iterative algorithm similar to the design algorithm for channel-optimized vector quantizers. Both systems have low complexity and low delay, and guarantee graceful performance improvements for high CSNRs. For memoryless Gaussian sources the designed HDA-II system is shown to be superior to the HDA-I designed system. When applied to a Gauss-Markov source under Karhunen-Loeve processing, the HDA-I system is shown to provide considerably better performance.

COVQ for MAP hard-decision demodulated channels

We design a channel optimized vector quantizer (COVQ) for symbol-by-symbol maximum a posteriori (MAP) hard-decision demodulated channels. The main objective is to exploit the non-uniformity of the indices representing the quantized source via the MAP decoder and iteratively optimize the overall discrete channel (at the symbol level) jointly with the quantizer. We consider memoryless Gaussian and Gauss-Markov sources transmitted over a binary phase-shift keying modulated Rayleigh fading channel. Our scheme has less encoding computational and storage complexity (particularly for noisy channel conditions) than both conventional and soft-decision COVQ systems, which use hard-decision and soft-decision maximum likelihood demodulation, respectively. Furthermore, it provides a notable signal-to-distortion ratio gain over the former system, and in some cases it matches or outperforms the latter one.

Transactions letters - Combining long-term and low-rate short-term channel state information over correlated mimo channels

A simple structure to exploit both long-term and partial short-term channel state information at the transmitter (CSIT) over a family of correlated multiple-antenna channels is proposed. Partial short-term CSIT in the form of a weighting matrix is combined with a unitary transformation based on the long-term channel statistics. The heavily quantized feedback link is directly optimized to maximize the expected achievable rate under different power constraints, using vector quantization and convex optimization techniques on a sample channel distribution. Robustness against errors in the feedback link is also pursued with tools in channel optimized vector quantization. Simulations indicate the benefits of the proposed scheme.

A COVQ-based image coder for channels with bit errors and erasures

We illustrate how channel optimized vector quantization (COVQ) can be used for channels with both bit-errors and bit-erasures. First, a memoryless channel model is presented, and the performance of COVQ's trained for this channel is evaluated for an i.i.d. Gaussian source. Then, the new method is applied in implementing an error-robust sub-band image coder, and we present image results that illustrate the resulting performance. Our experiments show that the new approach is able to outperform a traditional scheme based on separate source and channel coding.

Improved transmission of vector quantized data over noisy channels

The conventional channel-optimized vector quantization (COVQ) is very powerful in the protection of vector quantization (VQ) data over noisy channels. However, it suffers from the time consuming training process. A soft decoding self-organizing map (SOM) approach for VQ over noisy channels is presented. Compared with the COVQ approach, it does not require a long training time. For AWGN and fading channels, the distortion of the proposed approach is comparable to that of COVQ. Simulation confirmed that our proposed approach is a fast and practical method for VQ over noisy channels.

Channel-Optimized Quantization With Soft-Decision Demodulation for Space–Time Orthogonal Block-Coded Channels

We introduce three soft-decision demodulation channel-optimized vector quantizers (COVQs) to transmit analog sources over space–time orthogonal block (STOB)-coded flat Rayleigh fading channels with binary phase-shift keying (BPSK) modulation. One main objective is to judiciously utilize the soft information of the STOB-coded channel in the design of the vector quantizers while keeping a low system complexity. To meet this objective, we introduce a simple space–time decoding structure that consists of a space–time soft detector, followed by a linear combiner and a scalar uniform quantizer with resolution <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$q$</tex> . The concatenation of the space–time encoder/modulator, fading channel, and space–time receiver can be described by a binary-input, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$2^q$</tex> -output discrete memoryless channel (DMC). The scalar uniform quantizer is chosen so that the capacity of the equivalent DMC is maximized to fully exploit and capture the system's soft information by the DMC. We next determine the statistics of the DMC in closed form and use them to design three COVQ schemes with various degrees of knowledge of the channel noise power and fading coefficients at the transmitter and/or receiver. The performance of each quantization scheme is evaluated for memoryless Gaussian and Gauss–Markov sources and various STOB codes, and the benefits of each scheme is illustrated as a function of the antenna-diversity and soft-decision resolution <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$q$</tex> . Comparisons to traditional coding schemes, which perform separate source and channel coding operations, are also provided.

Concurrent genetic optimization for joint design of source and channel codes

A novel algorithm for jointly optimizing source and channel codes is presented in this paper. The algorithm uses the channel-optimized vector quantization (COVQ) for the source code, and rate-punctured convolutional coding (RCPC) for the channel code. The genetic algorithm (GA) is used for the concurrent design of both source and channel codes. The GA enhances the robustness of the rate–distortion performance of the COVQ to the selection of initial codewords. In addition, it reduces the computational time for realizing the unequal error protection scheme best matched to the COVQ. Numerical results show that the algorithm attains near optimal performance while having low computational complexity.

Iterative optimization for joint design of source and channel codes using genetic algorithms

This paper presents a novel algorithm for the joint design of source and channel codes. In the algorithm, channel‐optimized vector quantization (COVQ) and rate‐punctured convolutional coding (RCPC) are used for design of the source code and the channel code, respectively. We employ the genetic algorithm (GA) to prevent the design of COVQ from falling into a poor local optimum. We also adopt the GA to reduce the computational time needed for realizing the unequal error protection scheme best matched to the COVQ. Both the GA‐based source coding and channel coding scheme are then iteratively combined to achieve a near global optimal solution for the joint design. Numerical results show that the algorithm can be an effective alternative for applications where high rate‐distortion performance and low computational complexity are desired.

Design of Sample Adaptive Product Quantizers for Noisy Channels

Channel-optimized vector quantization (COVQ) has proven to be an effective joint source-channel coding technique that makes the underlying quantizer robust to channel noise. Unfortunately, COVQ retains the high encoding complexity of the standard vector quantizer (VQ) for medium-to-high quantization dimensions and moderate-to-good channel conditions. A technique called sample adaptive product quantization (SAPQ) was recently introduced by Kim and Shroff to reduce the complexity of the VQ while achieving comparable distortions. In this letter, we generalize the design of SAPQ for the case of memoryless noisy channels by optimizing the quantizer with respect to both source and channel statistics. Numerical results demonstrate that the channel-optimized SAPQ (COSAPQ) achieves comparable performance to the COVQ (within 0.2 dB), while maintaining considerably lower encoding complexity (up to half of that of COVQ) and storage requirements. Robustness of the COSAPQ system against channel mismatch is also examined.

Source-Optimized Channel Coding for Digital Transmission Channels

We present a new class of nonlinear block codes called source-optimized channel codes (SOCCs), which are particularly designed for parametric source encoding of speech, audio, and video. In contrast to conventional channel codes, the new codes are not optimized for minimizing residual bit-error rate, but maximizing the signal-to-noise ratio of transmitted source codec parameters. The decoding of SOCCs is not based on bit-error correction, but on parameter estimation. We compare SOCCs with other approaches to joint source/channel coding such as channel-optimized vector quantization, channel-constrained vector quantization, unequal error protection, and source-controlled channel decoding. In terms of performance, SOCCs show better robustness if under channel mismatch conditions. For real-world applications, SOCCs are attractive, since the separation of source and channel codec is preserved.

On Finite-State Vector Quantization for Noisy Channels

Finite-state vector quantization (FSVQ) over a noisy channel is studied. A major drawback of a finite-state decoder is its inability to track the encoder in the presence of channel noise. In order to overcome this problem, we propose a nontracking decoder which directly estimates the code vectors used by a finite-state encoder. The design of channel-matched finite-state vector quantizers for noisy channels, using an iterative scheme resembling the generalized Lloyd algorithm, is also investigated. Simulation results based on encoding a Gauss-Markov source over a memoryless Gaussian channel show that the proposed decoder exhibits graceful degradation of performance with increasing channel noise, as compared with a finite-state decoder. Also, the channel-matched finite-state vector quantizers are shown to outperform channel-optimized vector quantizers having the same vector dimension and rate. However, the nontracking decoder used in the channel-matched finite-state quantizer has a higher computational complexity, compared with a channel-optimized vector-quantizer decoder. Thus, if they are allowed to have the same overall complexity (encoding and decoding), the channel-optimized vector quantizer can use a longer encoding delay and achieve similar or better performance. Finally, an example of using the channel-matched finite-state quantizer as a backward-adaptive quantizer for nonstationary signals is also presented.

Genetic channel-optimized vector quantizer design for burst error channels

This paper presents a novel vector quantizer (VQ) design algorithm optimized to a burst error channel (BEC) for robust communication. The Gilbert–Elliot model is used to describe the BEC. Based on the model, the objective of this algorithm is to minimize the average distortion when the BEC is in the normal state of operation, while maintaining a minimum fidelity when the BEC is in the undesirable state. In the algorithm, an iterative design procedure is first derived for obtaining a local optimal solution to the problem. A novel genetic scheme is then proposed for attaining a near global optimal performance. Numerical results show that, when delivering information over the BEC, the algorithm significantly outperforms the VQ techniques optimizing the design only to the simple binary symmetric channels.

Joint Design of Channel-Optimized Multistage Vector Quantizer

A novel channel-optimized multistage vector quantization (COMSVQ) codec is presented in which the stage codebooks are jointly designed. The proposed codec uses a signal source and channel-dependent distortion measure to encode line spectral frequencies derived from segments of a speech signal. Simulation results are provided to demonstrate the consistent reduction in the spectral distortion obtained using the proposed codec as compared to the conventional sequentially designed channel-matched multistage vector quantizer.

Optimal Multistage Vector Quantization ofLPC Parameters Over Noisy Channels

The direct use of vector quantization (VQ) to encode LPC parameters in a communication system suffers from the following two limitations: 1) complexity of implementation for large vector dimensions and codebook sizes and 2) sensitivity to errors in the received indices due to noise in the communication channel. In the past, these issues have been simultaneously addressed by designing channel matched multistage vector quantizers (CM-MSVQ). A sub-optimal sequential design procedure has been used to train the codebooks of the CM-MSVQ. In this paper, a novel channel-optimized multistage vector quantization (CO-MSVQ) codec is presented, in which the stage codebooks are jointly designed. The proposed codec uses a source and channel-dependent distortion measure to encode line spectral frequencies derived from segments of a speech signal. Extensive simulation results are provided to demonstrate the consistent reduction in both the mean and the variance of the spectral distortion obtained using the proposed codec relative to the conventional sequentially designed CM-MSVQ. Furthermore, the perceptual quality of the reconstructed speech using the proposed codec was found to be better than that obtained using the sequentially designed CM-MSVQ.