Recent advances in coding theory for near error-free communications

Channel and source coding theories are discussed. The following subject areas are covered: large constraint length convolutional codes (the Galileo code); decoder design (the big Viterbi decoder); Voyager's and Galileo's data compression scheme; current research in data compression for images; neural networks for soft decoding; neural networks for source decoding; finite-state codes; and fractals for data compression

Source Coding for Quasiarithmetic Penalties

Huffman coding finds a prefix code that minimizes mean codeword length for a given probability distribution over a finite number of items. Campbell generalized the Huffman problem to a family of problems in which the goal is to minimize not mean codeword length but rather a generalized mean known as a quasiarithmetic or quasilinear mean. Such generalized means have a number of diverse applications, including applications in queueing. Several quasiarithmetic-mean problems have novel simple redundancy bounds in terms of a generalized entropy. A related property involves the existence of optimal codes: For ``well-behaved'' cost functions, optimal codes always exist for (possibly infinite-alphabet) sources having finite generalized entropy. Solving finite instances of such problems is done by generalizing an algorithm for finding length-limited binary codes to a new algorithm for finding optimal binary codes for any quasiarithmetic mean with a convex cost function. This algorithm can be performed using quadratic time and linear space, and can be extended to other penalty functions, some of which are solvable with similar space and time complexity, and others of which are solvable with slightly greater complexity. This reduces the computational complexity of a problem involving minimum delay in a queue, allows combinations of previously considered problems to be optimized, and greatly expands the space of problems solvable in quadratic time and linear space. The algorithm can be extended for purposes such as breaking ties among possibly different optimal codes, as with bottom-merge Huffman coding.Comment: 22 pages, 3 figures, submitted to IEEE Trans. Inform. Theory, revised per suggestions of reader

Constraint-based sequence mining using constraint programming

The goal of constraint-based sequence mining is to find sequences of symbols that are included in a large number of input sequences and that satisfy some constraints specified by the user. Many constraints have been proposed in the literature, but a general framework is still missing. We investigate the use of constraint programming as general framework for this task. We first identify four categories of constraints that are applicable to sequence mining. We then propose two constraint programming formulations. The first formulation introduces a new global constraint called exists-embedding. This formulation is the most efficient but does not support one type of constraint. To support such constraints, we develop a second formulation that is more general but incurs more overhead. Both formulations can use the projected database technique used in specialised algorithms. Experiments demonstrate the flexibility towards constraint-based settings and compare the approach to existing methods.Comment: In Integration of AI and OR Techniques in Constraint Programming (CPAIOR), 201

Improved quality block-based low bit rate video coding.

The aim of this research is to develop algorithms for enhancing the subjective quality and coding efficiency of standard block-based video coders. In the past few years, numerous video coding standards based on motion-compensated block-transform structure have been established where block-based motion estimation is used for reducing the correlation between consecutive images and block transform is used for coding the resulting motion-compensated residual images. Due to the use of predictive differential coding and variable length coding techniques, the output data rate exhibits extreme fluctuations. A rate control algorithm is devised for achieving a stable output data rate. This rate control algorithm, which is essentially a bit-rate estimation algorithm, is then employed in a bit-allocation algorithm for improving the visual quality of the coded images, based on some prior knowledge of the images. Block-based hybrid coders achieve high compression ratio mainly due to the employment of a motion estimation and compensation stage in the coding process. The conventional bit-allocation strategy for these coders simply assigns the bits required by the motion vectors and the rest to the residual image. However, at very low bit-rates, this bit-allocation strategy is inadequate as the motion vector bits takes up a considerable portion of the total bit-rate. A rate-constrained selection algorithm is presented where an analysis-by-synthesis approach is used for choosing the best motion vectors in term of resulting bit rate and image quality. This selection algorithm is then implemented for mode selection. A simple algorithm based on the above-mentioned bit-rate estimation algorithm is developed for the latter to reduce the computational complexity. For very low bit-rate applications, it is well-known that block-based coders suffer from blocking artifacts. A coding mode is presented for reducing these annoying artifacts by coding a down-sampled version of the residual image with a smaller quantisation step size. Its applications for adaptive source/channel coding and for coding fast changing sequences are examined

On the design of an ECOC-compliant genetic algorithm

Genetic Algorithms (GA) have been previously applied to Error-Correcting Output Codes (ECOC) in state-of-the-art works in order to find a suitable coding matrix. Nevertheless, none of the presented techniques directly take into account the properties of the ECOC matrix. As a result the considered search space is unnecessarily large. In this paper, a novel Genetic strategy to optimize the ECOC coding step is presented. This novel strategy redefines the usual crossover and mutation operators in order to take into account the theoretical properties of the ECOC framework. Thus, it reduces the search space and lets the algorithm to converge faster. In addition, a novel operator that is able to enlarge the code in a smart way is introduced. The novel methodology is tested on several UCI datasets and four challenging computer vision problems. Furthermore, the analysis of the results done in terms of performance, code length and number of Support Vectors shows that the optimization process is able to find very efficient codes, in terms of the trade-off between classification performance and the number of classifiers. Finally, classification performance per dichotomizer results shows that the novel proposal is able to obtain similar or even better results while defining a more compact number of dichotomies and SVs compared to state-of-the-art approaches

Video over DSL with LDGM Codes for Interactive Applications

Digital Subscriber Line (DSL) network access is subject to error bursts, which, for interactive video, can introduce unacceptable latencies if video packets need to be re-sent. If the video packets are protected against errors with Forward Error Correction (FEC), calculation of the application-layer channel codes themselves may also introduce additional latency. This paper proposes Low-Density Generator Matrix (LDGM) codes rather than other popular codes because they are more suitable for interactive video streaming, not only for their computational simplicity but also for their licensing advantage. The paper demonstrates that a reduction of up to 4 dB in video distortion is achievable with LDGM Application Layer (AL) FEC. In addition, an extension to the LDGM scheme is demonstrated, which works by rearranging the columns of the parity check matrix so as to make it even more resilient to burst errors. Telemedicine and video conferencing are typical target applications

Capacity -based parameter optimization of bandwidth constrained CPM

Continuous phase modulation (CPM) is an attractive modulation choice for bandwidth limited systems due to its small side lobes, fast spectral decay and the ability to be noncoherently detected. Furthermore, the constant envelope property of CPM permits highly power efficient amplification. The design of bit-interleaved coded continuous phase modulation is characterized by the code rate, modulation order, modulation index, and pulse shape. This dissertation outlines a methodology for determining the optimal values of these parameters under bandwidth and receiver complexity constraints. The cost function used to drive the optimization is the information-theoretic minimum ratio of energy-per-bit to noise-spectral density found by evaluating the constrained channel capacity. The capacity can be reliably estimated using Monte Carlo integration. A search for optimal parameters is conducted over a range of coded CPM parameters, bandwidth efficiencies, and channels. Results are presented for a system employing a trellis-based coherent detector. To constrain complexity and allow any modulation index to be considered, a soft output differential phase detector has also been developed.;Building upon the capacity results, extrinsic information transfer (EXIT) charts are used to analyze a system that iterates between demodulation and decoding. Convergence thresholds are determined for the iterative system for different outer convolutional codes, alphabet sizes, modulation indices and constellation mappings. These are used to identify the code and modulation parameters with the best energy efficiency at different spectral efficiencies for the AWGN channel. Finally, bit error rate curves are presented to corroborate the capacity and EXIT chart designs