Trellis-coded Vector Quantization Research Articles

A Trellis-Coded Quantization Approach to Transmitting Correlated Gaussian Sources Over a Fading MAC Without Transmitter-CSI

It is known that source-channel separation is sub-optimal for communicating correlated Gaussian sources over a Gaussian multiple access channel (GMAC). Considering a two-to-one GMAC which undergoes Rayleigh block-fading, we present a novel approach to practical joint source-channel coding for the scenario in which the common receiver has instantaneous CSI but only the CSI distribution is available to the individual transmitters. This approach, referred to as source-channel trellis-coded vector quantization (SC-TCVQ), simply relies on using TCVQs as fixed-rate source-channel encoders. One key issue is the optimization of the TCVQ codebooks to the mean channel signal-to-noise ratio (CSNR), and to this end, we present an analytical method to obtain the rates required for codebook design. Another key issue is the joint estimation of the sources at the receiver, for which we present a detector-estimator based on the Cartesian product of the two encoder-trellises. Simulation results show that the proposed SC-TCVQ codes, in some cases, can even beat the asymptotic performance bound for a separate source-channel code consisting of a distributed vector quantizer and capacity achieving channel codes. SC-TCVQ appears to be the best known practical code design to date for the given communication problem.

Wyner-Ziv coding based on TCQ and LDPC codes

This paper considers trellis coded quantization (TCQ) and low-density parity-check (LDPC) codes for the quadratic Gaussian Wyner-Ziv coding problem. After TCQ of the source X, LDPC codes are used to implement Slepian-Wolf coding of the quantized source Q(X) with side information Y at the decoder. Assuming 256-state TCQ and ideal Slepian-Wolf coding in the sense of achieving the theoretical limit H(Q(X)|Y ), we experimentally show that Slepian-Wolf coded TCQ performs 0.2 dB away from the Wyner-Ziv distortion-rate function DWZ(R) at high rate. This result mirrors that of entropy-constrained TCQ in classic source coding of Gaussian sources. Furthermore, using 8,192-state TCQ and assuming ideal Slepian-Wolf coding, our simulations show that Slepian-Wolf coded TCQ performs only 0.1 dB away from DWZ(R) at high rate. These results establish the practical performance limit of Slepian-Wolf coded TCQ for quadratic Gaussian Wyner-Ziv coding. Practical designs give performance very close to the theoretical limit. For example, with 8,192-state TCQ, irregular LDPC codes for Slepian-Wolf coding and optimal non-linear estimation at the decoder, our performance gap to DWZ(R) is 0.20 dB, 0.22 dB, 0.30 dB, and 0.93 dB at 3.83 bit per sample (b/s), 1.83 b/s, 1.53 b/s, and 1.05 b/s, respectively. When 256-state 4-D trellis-coded vector quantization instead of TCQ is employed, the performance gap to DWZ(R) is 0.51 dB, 0.51 dB, 0.54 dB, and 0.80 dB at 2.04 b/s, 1.38 b/s, 1.0 b/s, and 0.5 b/s, respectively.

Low-Complexity Wideband LSF Quantization Using Algebraic Trellis VQ

In this paper an algebraic trellis vector quantization (ATVQ) that introduces algebraic codebooks into trellis coded vector quantization (TCVQ) structure is presented. Low encoding complexity and minimum memory storage requirements are achieved using the proposed approach. It exploits advantages of both the TCVQ and the algebraic codebooks to know the delayed decision, the codebook widening, the low computational complexity and the no storage of codebook. This novel vector quantization scheme is used to encode the wideband speech line spectral frequencies (LSF) parameters. Experimental results on wideband speech have shown that ATVQ yields the same performance as the traditional split vector quantization (SVQ) and the TCVQ in terms of spectral distortion (SD). It can achieve a transparent quality at 47bits/frame with a considerable reduction of memory storage and computation complexity when compared to SVQ and TCVQ.

Block Constrained Trellis Coded Vector Quantization of LSF Parameters for Wideband Speech Codecs

In this paper, block constrained trellis coded vector quantization (BC-TCVQ) is presented for quantizing the line spectrum frequency parameters of the wideband speech codec. Both a predictive structure and a safety-net concept are combined into BC-TCVQ to develop the predictive BC-TCVQ. The performance of this quantization is compared with that of the linear predictive coding vector quantizer used in the AMR-WB codec, demonstrating reductions in spectral distortion.

Optimized trellis coded vector quantization of LSF parameters, application to the 4.8 kbps FS1016 speech coder

Speech coders operating at low bit rates necessitate efficient encoding of the linear predictive coding (LPC) coefficients. Line spectral frequencies (LSF) parameters are currently one of the most efficient choices of transmission parameters for the LPC coefficients. In this paper, an optimized trellis coded vector quantization (TCVQ) scheme for encoding the LSF parameters is developed. When the selection of a proper distortion measure is the most important issue in the design and operation of the encoder, an appropriate weighted distance measure has been used during the TCVQ construction process. Using this distance, we will show that the LSF TCVQ encoder performs better than the encoder conceived with the unweighted distance and a reduction of about 1–2 bits/frame is obtained while maintaining the same performance. We further applied the TCVQ encoder system for encoding the LSF parameters of the US federal standard (FS1016) 4.8 kbps code excited linear prediction (CELP) speech coder. At lower bit rates, our objective and subjective evaluation results show that the incorporated LSF TCVQ encoder performs better than the 34 bits/frame LSF scalar quantizer used originally in the FS1016 coder. The subjective tests reveal also that the 27 bits/frame scheme produces equivalent perceptual quality to that when the LSF parameters are unquantized.

Self-organizing codebooks for trellis-coded VQ

Because of its computational complexity, vector quantization (VQ) can work only on relatively small vectors, which severely limits its encoding performance. Trellis-coded VQ (TCVQ) circumvents this problem by using VQ in combination with a trellis encoding strategy, thus treating very large blocks of data at once. TCVQ is based on a size-N VQ codebook which is recursively partitioned to form two (possibly nearly optimal) codebooks of size N/2, four of size N/4, etc. Here we show that such a tree of codebooks can be easily designed, without the need of any postprocessing, by means of the Kohonen algorithm. Numerical experiments show the effectiveness of the proposed approach.

Fast Trellis-Coded Color Quantization of Images

We examine color quantization of images using trellis-coded quantization (TCQ) in both the RGB domain and YUV domain. Together with a simple dithering scheme, an eight-bit trellis-coded color quantizer reproduces images that are visually indistinguishable from the 24-bit originals. It can be viewed as a predictive trellis-coded color quantization scheme. We also study trellis-coded vector quantization (TCVQ) for color quantization. Our proposed TCQ-based color quantization schemes are universal in the sense that no training or look-up table is needed. The complexity of TCQ is linear with respect to image size, making trellis-coded color quantization suitable for color printing, real-time interactive graphics and window-based display environment.

Jointly optimized trellis-coded residual vector quantization

The union of residual vector quantization (RVQ) and trellis-coded vector quantization (TCVQ) was considered by various authors where the emphasis was on the sequential design. We consider a new jointly optimized combination of RVQ and TCVQ with advantages in all categories. Necessary conditions for optimality of the jointly optimized trellis-coded residual vector quantizers (TCRVQ) are derived. A constrained direct sum tree structure is introduced that facilitates RVQ codebook partitioning. Simulation results for jointly optimized TCRVQ are presented for memoryless Gaussian, Laplacian, and uniform sources. The rate-distortion performance is shown to be better than RVQ and sequentially designed TCRVQ.

Compression of SAR raw data through range focusing and variable-rate trellis-coded quantization

There is an ever-growing interest in the compression of SAR data because of the huge resources required for storage and transmission. This is especially true for spaceborne sensors, given the limited capacity of the downlink channel. Unfortunately, SAR data lack the useful properties on which compression algorithms rely; indeed, these are present in the focused images, but focusing is too complex for on-board implementation at this time. Poggi et al. (2000) proposed to perform on the satellite only the low-complexity range focusing, which increases the data correlation and better concentrates their energy. These properties were then exploited by adopting a variable-rate vector quantizer, with a clear performance improvement with respect to reference techniques. However, vector quantization (VQ) is too complex for actual on-board implementation, and therefore, here we replace VQ with trellis-coded VQ. To limit complexity, only small vectors are used, which reduces VQ's ability to exploit data dependencies; on the other hand, trellis coding allows one to encode large blocks of data at once, and to obtain a better partition of the input space. Experiments on real SAR data show that the overall performance is comparable to that of Poggi et al., but the complexity is much lower, making on-board implementation possible.

Conditional entropy-constrained trellis-coded RVQ with application to image coding

This paper introduces an extension of conditional entropy-constrained RVQ (CEC-RVQ) that embodies trellis-coded quantization. The method, which we call conditional entropy-constrained trellis-coded residual vector quantization (CEC-TCRVQ), quantizes a supervector (made from a large number of neighboring vectors) to better extract the two-dimensional (2-D) correlation present in real images. Simulation results indicate that CEC-TCRVQ provides 0.3-0.4 dB improvement over CEC-RVQ for the 4/spl times/4 vector case and 1.3 dB improvement for the 8/spl times/8 case.

Compression of synthetic aperture radar video phase history data using trellis-coded quantization techniques

Synthetic aperture radar (SAR) is a remote-sensing technology that uses the motion of the radar transmitter to synthesize an antenna aperture much larger than the actual antenna aperture to yield high-spatial resolution radar images. In this paper, trellis-coded quantization (TCQ) techniques are shown to provide a high-performance, low bit-error sensitivity solution to the problem of downlink data rate reduction for SAR systems. Trellis-coded vector quantization (TCVQ) and universal TCQ coding systems are discussed, implemented, and compared with other data compression schemes [block adaptive quantization (BAQ) and VQ] that can be used to compress SAR phase history data.

Vector quantization of speech line spectrum pair parameters and reflection coefficients

Methods are presented for intraframe encoding of line spectrum pairs. A two-stage vector quantizer-lattice vector quantizer (VQ-LVQ) has a 2-3 b/vector performance advantage over the split vector quantizer, and can save 1-3 b/vector, compared to multistage vector quantization, depending on the number of stages and the number of survivors retained at each stage. The vector quantizer-lattice vector quantizer has a moderate computational complexity. Among three trellis codes considered, trellis-coded vector quantization with nonlinear prediction provides line spectrum pair encoding performance similar to the split vector quantizer. Hybrid transformations are developed for encoding the reflection coefficients using vector quantization, and offer a small encoding advantage over the commonly used arcsine transformation and log area ratios.

Design, performance, and complexity analysis of residual trellis-coded vector quantizers

Multistage trellis-coded vector quantization (MS-TCVQ) is developed as a constrained trellis source-coding technique. The performance of the two-stage TCVQ is studied for Gaussian sources. Issues of stage-by-stage design, output alphabet selection, and complexity are addressed with emphasis on selecting and partitioning the stage codebooks. For a given rate, MS-TCVQ achieves low encoding and storage complexity compared to TCVQ, and comparisons with same-dimensional multistage vector quantization indicate a 0.5-3-dB improvement in signal-to-quantization-noise ratio.

Symmetric trellis-coded vector quantization

We present here design techniques for trellis-coded vector quantizers with symmetric codebooks that facilitate low-complexity quantization as well as partitioning into equiprobable sets for trellis coding. The quantization performance of this coder on the independently identically distributed (i.i.d.) Laplacian source matches the performance of trellis-based scalar-vector quantization (TB-SVQ), but requires less computational complexity.

CELP coding using trellis-coded vector quantization of the excitation

We analyze the performance of a CELP coder where the vector quantization (VQ) of the excitation is replaced with trellis-coded vector quantization (TCVQ). Our results show that TCVQ performs significantly better than VQ, with reasonable complexity. This makes TCVQ a fair choice for trading quality against complexity and/or delay. We describe a systematic procedure to replace VQ with TCVQ for existing CELP coders. We propose an optimization algorithm to appropriately populate the trellis. We show how pseudo-Gray coding can be applied to the TCVQ codebook to improve intrinsic coder robustness to channel errors. Finally, we evaluate the complexity and performance of the method.

Trellis excitation speech coding at low bit rates

Trellis coded vector quantization (TCVQ) and code-excited linear prediction (CELP) coding are combined to form an efficient low-bit rate speech coding system. The resulting system uses a trellis search to select the synthesis filter excitation sequence, and is referred to as trellis excitation coding (TEC). Simulations are performed for encoding rates of 6.4 and 8 kbps. Informal listening tests indicate that the 8 kbps TEC system has quality roughly between that of 6-bit and 7-bit /spl mu/-law PCM with /spl mu/=255. The 6.4 kbps TEC system provides speech quality between 5-bit and 6-bit /spl mu/-law PCM. A subjective comparison with vector sum excited linear prediction (VSELP) indicates that the 8 kbps TEC and the VSELP reconstructed speech is about equally preferable.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Trellis-searched adaptive predictive coding of speech

Trellis coded vector quantization (TCVQ) and forward adaptive predictive coding (APC) are used to form an efficient speech coding system operating at bit rates of 16 and 9.6 kb/s. The effectiveness of the system is studied for a variety of system parameters and utterances. Simulation results indicate that segmental signal-to-noise ratios as high as 23.8 and 15.4 dB are obtainable at 16 and 9.6 kb/s respectively. The quality of the reconstructed speech is deemed to be excellent at 16 kb/s and very good at 9.6 kb/s. An algorithm for optimizing the residual codebooks is presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Trellis coded vector quantization

A vector generalization of trellis coded quantization (TCQ), called trellis coded vector quantization (TCVQ), and experimental results showing its performance for an i.i.d. Gaussian source are presented. For a given rate, TCVQ yields a lower distortion that TCQ at the cost of an increase in implementation complexity. In addition, TCVQ allows fractional rates, which TCQ does not.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Trellis-coded vector quantization

Trellis-coded quantization is generalized to allow a vector reproduction alphabet. Three encoding structures are described, several encoder design rules are presented, and two design algorithms are developed. It is shown that for a stationary ergodic vector source, if the optimized trellis-coded vector quantization reproduction process is jointly stationary and ergodic with the source, then the quantization noise is zero-mean and of a variance equal to the difference between the source variance and the variance of the reproduction sequence. Several examples illustrate the encoder design procedure and performance. >