Joint design of a channel-optimized quantizer and multicarriermodulation

We present an algorithm for design of a joint source-channel coder using a channel-optimized quantizer and multicarrier modulation. By changing the power of each subchannel in the multicarrier modulation system, different degrees of error protection can be provided for different bits according to their importance. The algorithm converges to a locally optimum system design. Compared to a Lloyd-Max scalar quantizer or a LBG vector quantizer using single-channel transmission, our optimized code can yield substantial performance improvements. The performance improvements are most pronounced at low channel signal-to-noise ratios     

Very low bit-rate video coding using variable block-sizeentropy-constrained residual vector quantizers

We present a practical video coding algorithm for use at very low bit rates. For efficient coding at very low bit rates, it is important to intelligently allocate bits within a frame, and so a powerful variable-rate algorithm is required. We use vector quantization to encode the motion-compensated residue signal in an H.263-like framework. For a given complexity, it is well understood that structured vector quantizers perform better than unstructured and unconstrained vector quantizers. A combination of structured vector quantizers is used in our work to encode the video sequences. The proposed codec is a multistage residual vector quantizer, with transform vector quantizers in the initial stages. The transform-VQ captures the low-frequency information, using only a small portion of the bit budget, while the later stage residual VQ captures the high-frequency information, using the remaining bits. We used a strategy to adaptively refine only areas of high activity, using recursive decomposition and selective refinement in the later stages. An entropy constraint was used to modify the codebooks to allow better entropy coding of the indexes. We evaluate the performance of the proposed codec, and compare this data with the performance of the H.263-based codec. Experimental results show that the proposed codec delivered significantly better perceptual quality along with better quantitative performance     

An algorithm for uniform vector quantizer design

A vector quantizer maps ak-dimensional vector into one of a finite set of output vectors or "points". Although certain lattices have been shown to have desirable properties for vector quantization applications, there are as yet no algorithms available in the quantization literature for building quantizers based on these lattices. An algorithm for designing vector quantizers based on the root latticesA_{n}, D_{n}, andE_{n}and their duals is presented. Also, a coding scheme that has general applicability to all vector quantizers is presented. A four-dimensional uniform vector quantizer is used to encode Laplacian and gamma-distributed sources at entropy rates of one and two bits/sample and is demonstrated to achieve performance that compares favorably with the rate distortion bound and other scalar and vector quantizers. Finally, an application using uniform four- and eight-dimensional vector quantizers for encoding the discrete cosine transform coefficients of an image at0.5bit/pel is presented, which visibly illustrates the performance advantage of vector quantization over scalar quantization.     

Transmit power allocation for BER performance improvement in multicarrier systems

In a multicarrier system, transmit power allocation over different subchannels is an effective means of improving the performance. We develop the optimal transmit power allocation scheme to improve bit-error rate (BER) performance in a multicarrier system with diversity reception. A simple suboptimal scheme is also derived from the optimal one, and an asymptotic case referred to as the equal-signal-to-noise ratio scheme is discussed. Numerical results show that the optimal and suboptimal power allocation schemes significantly outperform the equal power allocation scheme. The effects of the modulation level, the number of receiving antennas, and the number of subchannels on the BER performance are also investigated.     

Quantization based on a novel sample-adaptive product quantizer(SAPQ)

In this paper, we propose a novel feedforward adaptive quantization scheme called the sample-adaptive product quantizer (SAPQ). This is a structurally constrained vector quantizer that uses unions of product codebooks. SAPQ is based on a concept of adaptive quantization to the varying samples of the source and is very different from traditional adaptation techniques for nonstationary sources. SAPQ quantizes each source sample using a sequence of quantizers. Even when using scalar quantization in SAPQ, we can achieve performance comparable to vector quantization (with the complexity still close to that of scalar quantization). We also show that important lattice-based vector quantizers can be constructed using scalar quantization in SAPQ. We mathematically analyze SAPQ and propose a algorithm to implement it. We numerically study SAPQ for independent and identically distributed Gaussian and Laplacian sources. Through our numerical study, we find that SAPQ using scalar quantizers achieves typical gains of 13 dB in distortion over the Lloyd-Max quantizer. We also show that SAPQ can he used in conjunction with vector quantizers to further improve the gains     

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$q$. The concatenation of the space–time encoder/modulator, fading channel, and space–time receiver can be described by a binary-input,$2^q$-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$q$. Comparisons to traditional coding schemes, which perform separate source and channel coding operations, are also provided.     

Vector Quantizer Design for Memoryless Gaussian, Gamma, and Laplacian Sources

Locally optimum vector quantizer (VQ) designs are presented for memoryless Gaussian, gamma, and Laplacian sources. For Gaussian sources, low (2-6) dimensional vector quantization provides relatively little improvement in mean-squared error (MSE) compared to the minimum mean-squared error (MMSE) scalar quantizer. For Laplacian or gamma sources, however, significant improvement in MSE is available with vector quantization. The Laplacian and gamma 6 bit, sixdimensional vector quantizers achieve, respectively, improvements of 2 and 4.5 dB over the corresponding scalar MMSE quantizer distortions.     

Encoding of Speech Spectral Parameters Using Adaptive Quantization Range Method

Efficient quantization methods of the line spectrum pairs (LSP) which have good performances, low complexity and memory are proposed. The adaptive quantization range method utilizing the ordering property of LSP parameters is used in a scalar quantizer and a vector‐scalar hybrid quantizer. As the maximum quantization range of each LSP parameter is varied adaptively on the quantized value of the previous order's LSP parameter, efficient quantization methods can be obtained. The proposed scalar quantization algorithm needs 31 bits/frame, which is 3 bits less per frame than in the conventional scalar quantization method with interframe prediction to maintain the transparent quality of speech. The improved vector‐scalar quantizer achieves an average spectral distortion of 1 dB using 26 bits/frame. The performances of proposed quantization methods are also evaluated in the transmission errors.     

Power allocation and control for multicarrier systems with softdecoding

We consider the application of multicarrier modulation in a wireless cellular network in order to enable high-data rate communication and alleviate the multipath induced intersymbol interference (ISI). In this scenario, power control becomes crucial in enhancing the spectral and power efficiency. A conventional approach of maintaining the same link quality for all the subchannels, in other words, disregarding any possible post-demodulation processing, is considered first. This approach appears to have increasing power consumption as the number of subchannels increases. It also deteriorates the power control stability and convergence properties in a multicell network. We attribute this phenomenon to lack of frequency diversity exploitation, and thus, we propose to use channel coding and soft decoding as vehicles to profit from the (frequency) diversity advantage in addition to the coding advantage. Based on the soft decoding performance bound, a power allocation and control algorithm is proposed. It is shown through simulations that the proposed algorithm improves the power efficiency as the number of subchannels increases. It also provides a better convergence property and is able to “detect” and eliminate ill-conditioned subchannels. The advantages of using multicarrier modulation are thus reassured. Besides these enhancements, the proposed algorithm is simple and feasible in that it consists of only the traditional closed-loop power control algorithm and a target signal-to-interference ratio (SIR) reassignment at the receiver. Detailed channel information feedback from receiver to transmitter is not required     

Scalar-vector quantization of medical images

A new coding scheme based on the scalar-vector quantizer (SVQ) is developed for compression of medical images. The SVQ is a fixed rate encoder and its rate-distortion performance is close to that of optimal entropy-constrained scalar quantizers (ECSQs) for memoryless sources. The use of a fixed-rate quantizer is expected to eliminate some of the complexity of using variable-length scalar quantizers. When transmission of images over noisy channels is considered, our coding scheme does not suffer from error propagation that is typical of coding schemes using variable-length codes. For a set of magnetic resonance (MR) images, coding results obtained from SVQ and ECSQ at low bit rates are indistinguishable. Furthermore, our encoded images are perceptually indistinguishable from the original when displayed on a monitor. This makes our SVQ-based coder an attractive compression scheme for picture archiving and communication systems (PACS). PACS are currently under study for use in an all-digital radiology environment in hospitals, where reliable transmission, storage, and high fidelity reconstruction of images are desired     

Error-resilient pyramid vector quantization for image compression

Pyramid vector quantization (PVQ) uses the lattice points of a pyramidal shape in multidimensional space as the quantizer codebook. It is a fixed-rate quantization technique that can be used for the compression of Laplacian-like sources arising from transform and subband image coding, where its performance approaches the optimal entropy-coded scalar quantizer without the necessity of variable length codes. In this paper, we investigate the use of PVQ for compressed image transmission over noisy channels, where the fixed-rate quantization reduces the susceptibility to bit-error corruption. We propose a new method of deriving the indices of the lattice points of the multidimensional pyramid and describe how these techniques can also improve the channel noise immunity of general symmetric lattice quantizers. Our new indexing scheme improves channel robustness by up to 3 dB over previous indexing methods, and can be performed with similar computational cost. The final fixed-rate coding algorithm surpasses the performance of typical Joint Photographic Experts Group (JPEG) implementations and exhibits much greater error resilience.     

Asymptotic Capacity of Multicarrier Transmission With Frequency-Selective Fading and Limited Feedback

We study the capacity of multicarrier transmission through a slow frequency-selective fading channel with limited feedback, which specifies channel state information. Our results are asymptotic in the number of subchannels . We first assume independent and identically distributed (i.i.d.) subchannel gains, and show that, for a large class of fading distributions, a uniform power distribution over an optimized subset of subchannels, or on-off power allocation, gives the same asymptotic growth in capacity as optimal water filling, e.g., with Rayleigh fading. Furthermore, the growth in data rate can be achieved with a feedback rate as . If the number of active subchannels is bounded, the capacity grows only as with the feedback rate of . We then consider correlated subchannels modeled as a Markov process, and study the savings in feedback. Assuming a fixed ratio of coherence bandwidth to the total bandwidth, the ratio between minimum feedback rates with correlated and i.i.d. subchannels converges to zero with , e.g., as for Rayleigh-fading subchannels satisfying a first-order autoregressive process. We also show that adaptive modulation, or rate control schemes, in which the rate on each subchannel is selected from a quantized set, achieves the same asymptotic growth rates in capacity and required feedback. Finally, our results are extended to cellular uplink and downlink channel models.     

A vector quantization approach to universal noiseless coding andquantization

A two-stage code is a block code in which each block of data is coded in two stages: the first stage codes the identity of a block code among a collection of codes, and the second stage codes the data using the identified code. The collection of codes may be noiseless codes, fixed-rate quantizers, or variable-rate quantizers. We take a vector quantization approach to two-stage coding, in which the first stage code can be regarded as a vector quantizer that “quantizes” the input data of length n to one of a fixed collection of block codes. We apply the generalized Lloyd algorithm to the first-stage quantizer, using induced measures of rate and distortion, to design locally optimal two-stage codes. On a source of medical images, two-stage variable-rate vector quantizers designed in this way outperform standard (one-stage) fixed-rate vector quantizers by over 9 dB. The tail of the operational distortion-rate function of the first-stage quantizer determines the optimal rate of convergence of the redundancy of a universal sequence of two-stage codes. We show that there exist two-stage universal noiseless codes, fixed-rate quantizers, and variable-rate quantizers whose per-letter rate and distortion redundancies converge to zero as (k/2)n ^-1 log n, when the universe of sources has finite dimension k. This extends the achievability part of Rissanen's theorem from universal noiseless codes to universal quantizers. Further, we show that the redundancies converge as O(n^-1) when the universe of sources is countable, and as O(n^-1+ϵ) when the universe of sources is infinite-dimensional, under appropriate conditions     

Soft-decoding vector quantizer using reliability information fromturbo-codes

The optimum soft-decoding vector quantizer using the reliability information from turbo-codes is derived for combined source-channel coding. The encoder and decoder of the quantizer are optimized iteratively. For a four-dimensional vector quantizer having a rate of 1 bit/sample transmitted through a noisy channel, the soft-decoding channel-optimized quantizer can achieve about 3-3.7 dB performance improvement over conventional source-optimized quantizer     

On entropy-constrained vector quantization using gaussian mixture models

A flexible and low-complexity entropy-constrained vector quantizer (ECVQ) scheme based on Gaussian mixture models (GMMs), lattice quantization, and arithmetic coding is presented. The source is assumed to have a probability density function of a GMM. An input vector is first classified to one of the mixture components, and the Karhunen-Lo`eve transform of the selected mixture component is applied to the vector, followed by quantization using a lattice structured codebook. Finally, the scalar elements of the quantized vector are entropy coded sequentially using a specially designed arithmetic coder. The computational complexity of the proposed scheme is low, and independent of the coding rate in both the encoder and the decoder. Therefore, the proposed scheme serves as a lower complexity alternative to the GMM based ECVQ proposed by Gardner, Subramaniam and Rao [1]. The performance of the proposed scheme is analyzed under a high-rate assumption, and quantified for a given GMM. The practical performance of the scheme was evaluated through simulations on both synthetic and speech line spectral frequency (LSF) vectors. For LSF quantization, the proposed scheme has a comparable performance to [1] at rates relevant for speech coding (20-28 bits per vector) with lower computational complexity.     

Adaptive channel error protection of subband encoded images

Protection of images that are encoded using subband coding from channel error is addressed. In this scheme the low-pass subband is encoded using DPCM (differential pulse-code modulation), and the other subbands are encoded using a scalar quantizer. The quantizers are all Lloyd-Max quantizers, from which the representation levels have fixed length codewords. First, considering only single errors in each codeword, a channel error distortion measure is derived for each quantizer, that is, for each subband. Codewords are assigned to the quantizer representation levels, yielding a low value of the distortion measure. Next, sets S_ij consisting of the jth bit from subband i are formed. Each set S _ij is assigned a particular BCH code C_ij. An algorithm that optimally assigns BCH codes C_ij to each set S_ij, based on a channel error distortion measure for the entire image, is derived. The protection scheme is adaptive, because each set of bits within each subband can be assigned a different error protection code. Examples show that this approach is preferable to assigning equal error protection codes to each set of bits. It is shown that in the case of a channel error probability of 10 ^-3, only 5% to 10% extra bits are needed for adequate channel error protection     

Quantization loss in convolutional decoding

The loss in quantizing coded symbols in the additive white Gaussian noise (AWGN) channel with binary phase-shift keying (BPSK) or quadrature phase-shift keying (QPSK) modulation is discussed. A quantization scheme and branch metric calculation method are presented. For the uniformly quantized AWGN channel, cutoff rate is used to determine the step size and the smallest number of quantization bits needed for a given bit-signal-to-noise ratio (E_b/N₀) loss. A nine-level quantizer is presented, along with 3-b branch metrics for a rate-1/2 code, which causes an E_b/N₀ loss of only 0.14 dB. These results also apply to soft-decision decoding of block codes. A tight upper bound is derived for the range of path metrics in a Viterbi decoder. The calculations are verified by simulations of several convolutional codes, including the memory-14, rate-1/4 or -1/6 codes used by the big Viterbi decoders at JPL     

Nonlinear quantization and the design of coded and uncoded signalconstellations

The author analyzes the effects of nonlinear quantizers, used in T1 carrier systems, on the performance of QAM (quadrature amplitude modulation) and TCM (trellis coded modulation) voiceband data communication modems, and introduces a method to counteract the effects of these nonlinearities. The effect of nonlinear quantizers is modeled as a source of multiplicative noise whose variance is proportional to the amplitude of the quantized signal. The relation between variance of the multiplicative noise, characteristics of the nonlinear quantizer, and impulse response of the pulse shaping filters used in the modems is derived. Effects of multiplicative noise on the performance of QAM and TCM modems are analyzed. A method for the design of QAM and TCM signal constellations is introduced which counteracts the harmful effects of nonlinear quantizers. The new constellations provide 2-3 dB performance improvements in multiplicative noise channels while losing less than 0.5 dB in additive noise channels     

Suboptimality of the Karhunen-Loeve transform for transform coding

We examine the performance of the Karhunen-Loeve transform (KLT) for transform coding applications. The KLT has long been viewed as the best available block transform for a system that orthogonally transforms a vector source, scalar quantizes the components of the transformed vector using optimal bit allocation, and then inverse transforms the vector. This paper treats fixed-rate and variable-rate transform codes of non-Gaussian sources. The fixed-rate approach uses an optimal fixed-rate scalar quantizer to describe the transform coefficients; the variable-rate approach uses a uniform scalar quantizer followed by an optimal entropy code, and each quantized component is encoded separately. Earlier work shows that for the variable-rate case there exist sources on which the KLT is not unique and the optimal quantization and coding stage matched to a "worst" KLT yields performance as much as 1.5 dB worse than the optimal quantization and coding stage matched to a "best" KLT. In this paper, we strengthen that result to show that in both the fixed-rate and the variable-rate coding frameworks there exist sources for which the performance penalty for using a "worst" KLT can be made arbitrarily large. Further, we demonstrate in both frameworks that there exist sources for which even a best KLT gives suboptimal performance. Finally, we show that even for vector sources where the KLT yields independent coefficients, the KLT can be suboptimal for fixed-rate coding.