Institute for Systems Research

We propose a new classification scheme, dubbed spectral classification, which uses the spectral characteristics of the image blocks to classify them into one of a finite number of classes. The spectral classifier is used in adaptive image coding based on the discrete wavelet transform and shown to outperform gain-based classifiers while requiring a lower computational complexity. The resulting image coding system provides one of the best available rate-distortion performances in the literature. Also, we introduce a family of multiresolution image coding systems with different constraints on the complexity. For the class of rate-scalable image coding systems, we address the problem of progressive transmission and propose a method for fast reconstruction of a subband-decomposed progressively transmitted image.

Another important problem studied in this dissertation is the transmission of images over noisy channels, especially for the wireless channels in which the characteristics of the channel is time-varying. We propose an adaptive rate allocation scheme to optimally choose the rates of the source coder and channel coder pair in a tandem source-channel coding framework. Also, we suggest two adaptive coding systems for quantization and transmission over a finite-state channel using a combined source and channel coding scheme. Finally, we develop simple table- lookup encoders to reduce the complexity of channel-optimized quantizers while providing a slightly inferior performance. We propose the use of lookup tables for transcoding in heterogeneous networks

First, several fundamental issues regarding the statistical properties of fading channels are provided. We demonstrate the constraints, that must be satisfied so that the channel can be regarded as impaired by ﲦlat (i.e., non-frequency-selective) fading with a constant fading factor over each symbol duration. Throughout this thesis these constraints are assumed to be satisfied.

We next investigate the channel capacity and cutoff rates for fading channels with DPSK-modulated input signals and perfect symbol interleaving. The impact of the channel state information (CSI), on these information-theoretic limits is also discussed. We introduce several symbol metrics for soft-decision decoding, and their performance is investigated by analytical derivation as well as by simulation. Furthermore, we define a bit metric for DQPSK modulation, and compare this bit metric to dibit (symbol) metrics.

We then consider the problem of error concealment for mobile radio, communications with a maximum-likelihood soft- decision decoder. A normalized codeword reliability is defined as the decision reliability information when CSI is not available. We employ a given, interpolation algorithm on a particular land mobile radio system and design a rule for selecting unreliable codewords. Simulation results show that error concealment can decrease the minimum operational signal-noise ratio (SNR) by 3 dB or more.

Finally, we address the problem of exploiting the residual redundancy in the source to enhance the channel decoder's performance -i.e., maximum a posteriori (MAP) decoding. We use two simple source models to demonstrate that MAP decoding can achieve significant gain over maximum-likelihood decoding. We employ a practical CELP-based land mobile radio system to show that significant residual redundancy does exist in the output of some source encoders. Simulation results show that a 2 - 3 dB gain can be achieved by MAP decoding (over ML) at low SNR.

The proposed codes are also simulated under less ideal assumptions. For instance, results for a 1 bit/sec/Hz IQ-TCM code without CSI show a significant gain over conventional coding. Finally, simulations over channels with correlated fading were undertaken; it is concluded that an interleaver span of 4v yields performance close to what is achieved with ideal interleaving.

Also included is an analysis of maximal ratio combining when the diversity branches are correlated; the cutoff rate and a tight upper bound on the pairwise error probability are derived. It is shown that, with double diversity, a branch correlation coefficient as high as 0.5 results in only slight performance degradation.

We begin by quantifying the amount of ﲲesidual redundancy inherent in the LSP's of Federal Standard 1016 CELP. This is done by modeling the LSP's as first and second-order Markov chains. Two models for LSP generation are proposed; the first model characterizes the intra-frame correlation exhibited by the LSP's, while the second model captures both intra-frame and inter-frame correlation. By comparing the entropy rates of the models thus constructed with the CELP rates, it is shown that as many as one-third of the LSP bits in every frame of speech are redundant.

We next consider methods by which this residual redundancy can be exploited by an appropriately designed channel decoder. Before transmission, the LSP's are encoded with a forward error control (FEC) code; we consider both block (Reed- Solomon) codes and convolutional codes. Soft-decision decoders that exploit the residual redundancy in the LSP's are implemented assuming additive white Gaussian noise (AWGN) and independent Rayleigh fading environments. Simulation results employing binary phaseshift keying (BPSK) indicate coding gains of 2 to 5 dB over soft-decision decoders that do not exploit the residual redundancy.

In the first part, TCM schemes that provide high coding gains over the flat, slow Rayleigh distributed fading channel are presented. It is shown that the use of two encoders in parallel used to specify the in-phase and quadrature components of the transmitted signal results in large performance improvements in bit error rates when compared with conventional TCM schemes in which a single encoder is used. Using this approach which we label ﲉ-Q TCM codes with bandwidth efficiencies of 1, 2, and 3 bits/sec/Hz are described for various constraint lengths. The performance of these codes is evaluated using tight upper bounds and simulation.

In the second part, the use of space diversity with three different combining schemes is investigated. Expressions for the cutoff rate parameter are shown for the three combining schemes over the fully interleaved Rayleigh-distributed flat fading channel. Also, tight upper bounds on the pairwise error probability are derived for the three combining schemes. Examples of I-Q TCM schemes with diversity combining are shown. The cutoff rate and a tight upper bound on the pairwise error probability are also derived for maximal ration combining with correlated branches.

In the last part the problem of reliably transmitting trellis coded signals over very noisy channels is considered. Sequence maximum a posteriori (MAP) decoding of correlated signals transmitted over very noisy AWGN and Rayleigh channels is presented. A variety of different systems with different sources, modulation schemes, encoder rates and complexities are simulated. Sequence MAP decoding proves to substantially improve the performance at very noisy channel conditions especially for systems with moderate redundancies and encoder rates. A practical example for coding the CELP line spectral parameters (LSPs) is also considered. Two source models are used. Coding gains of as much as 4 dB are achieved.

By combining trellis codes (that achieve a significant granular gain) with SVQ, ECSQ, and AECQ, we obtain Trellis-Based Scalar- Vector Quantizer (TB-SVQ), Entropy-Constrained Trellis- Coded Quantizer (ECTCQ), and Pathwise-Adaptive ECTCQ (PA-ECTCQ), respectively. With an 8-state underlying trellis code, these trellis-coded quantization schemes perform about 1.0 dB better than their naive counterparts. There are two approaches that can extend the quantizers (TB-SVQ, ECTCQ, and PA-ECTCQ) for quantizing sources with memory. The first is to combine the predictive coding operation of the Differential Pulse Code Modulation scheme with various quantizers, yielding Predictive TB-SVQ, Predictive ECTCQ, and Predictive PA-ECTCQ, respectively. There is a duality between quantizing sources with memory and transmitting data over channels with memory. Laroia, Tretter, and Farvardin have recently introduced a precoding idea that helps transmitting data efficiently over channels with memory. By exploiting this duality, the second approach combines the precoder with TB-SVQ and ECTCQ to arrive at Precoded TB-SVQ and Precoded ECTCQ, respectively. Simulation results indicate that the porformance of these quantizers are also close to the rate- distortion limit.

The PA-ECTCQ performance has been shown to be robust, in the presence of source scale and, to a lesser extent, shape mismatch conditions. We also considered adjusting the underlying entropy encoder based on the quantized output (which provide some approximate information on the source statistics). The performance of the resulting Shape-Adjusting PA-ECTCQ has been shown to be robust to a rather wide range of source shape mismatch conditions. are also close to the rate-distortion limit.