We discuss representations of prefix codes and the corresponding storage space and decoding time requirements. We assume that a dictionary of words to be encoded has been defined and that a prefix code appropriate to the dictionary has been constructed. The encoding operation becomes simple given these assumptions and given an appropriate parsing strategy, therefore we concentrate on decoding. The application which led us to this work constrains the use of internal memory during the decode operation. As a result, we seek a method of decoding which has a small memory requirement. Introduction Data compression is an important and much-studied problem. Compressing data to be stored or transmitted can result in significant improvements in the use of computing resources. The degree of improvement that can be achieved depends not only on the selection of a data compression method, but also on the characteristics of the particular application. That is, no single data compression algorithm wi...

: A new data structure is investigated, which allows fast decoding of texts encoded by canonical Huffman codes. The storage requirements are much lower than for conventional Huffman trees, O(log 2 n) for trees of depth O(log n), and decoding is faster, because a part of the bit-comparisons necessary for the decoding may be saved. Empirical results on large real-life distributions show a reduction of up to 50% and more in the number of bit operations. The basic idea is then generalized, yielding further savings. This is an extended version of a paper which has been presented at the 8th Annual Symposium on Combinatorial Pattern Matching (CPM'97), and appeared in its proceedings, pp. 65--75. -- 1 -- 1.

my family-- especially my father, Donald. iv Abstract Many important data analysis tasks can be addressed by formulating them as probability estimation problems. For example, a popular general approach to automatic classification problems is to learn a probabilistic model of each class from data in which the classes are known, and then use Bayes's rule with these models to predict the correct classes of other data for which they are not known. Anomaly detection and scientific discovery tasks can often be addressed by learning probability models over possible events and then looking for events to which these models assign low probabilities. Many data compression algorithms such as Huffman coding and arithmetic coding rely on probabilistic models of the data stream in order achieve high compression rates.

This thesis addresses low-complexity algorithms in digital receivers. This includes algorithms for estimation, detection, and source coding.

Implementation of variable-length code (VLC) decoders can involve a tradeoff between number of decoding steps and memory usage. In this paper, we proposed a novel scheme for optimizing this tradeoff using a machine model abstracted from general purpose processors with hierarchical memories. We formulate the VLC decode problem as an optimization problem where the objective is to minimize the average decoding time. After showing that the problem is NP-complete, we present a Lagrangian algorithm that finds an approximate solution with bounded error. An implementation is automatically synthesized by a code generator. To demonstrate the efficacy of our approach, we conducted experiments of decoding codebooks for pruned tree-structured vector quantizer and H.263 motion vector that show a performance gain of our proposed algorithm over single table lookup implementation and logic implementation.

In this paper, an algorithm for the fast decoding of binary variable-length codes is analysed, both regaxding the decoding speed, relative to a traditional tree-search decoder, artd with regaxd to the memory spce. The algorithm is based on a lookup table, which will allow blocks of compressed data to be decoded in one cycle.

this paper depends on the word size and the number of different symbols. For example, for bytes and 256 symbols, the node transition table for every node has 256 entries, and each entry consists of a field for the next node (one byte) and an array for the output symbols, often not more than two or three per transition, which depends on the shape of the binary code tree. If on the average using 10 bytes for an entry, including the symbol array and a pointer to it, the data structure consumes less than 1MB of main memory (255 * 256 * 10 0.6MB). The additional fields for the symbol endings and the number of symbols encoded in one word would account for another 2 bytes per entry in our example, thus not significantly enlarging the overall data structure. Note that the tables do not have to be transmitted in case of a network communication because they can efficiently be reconstructed by sender and receiver if necessary from the binary code tree, which requires only 2 bits per node for encoding it.

As large main memory becomes more and more available at reasonable prices, processing speed of large data sets becomes more important than reducing main memory usage of internal data structures which are small compared to the available main memory capacity. In this paper we describe the use of a finite state machine for fast processing of prefix codes that significantly improves decoding performance in practice, and that is easy to implement. We present an intuitive explanation of this method, an extension to discover symbol boundaries in compressed data, implementation details, and we also provide experimental performance results.

Recent publications advocate the use of various variable length codes for which each codeword consists of an integral number of bytes in compression applications using large alphabets. This paper shows that another tradeoff with similar properties can be obtained by Fibonacci codes. These are fixed codeword sets, using binary representations of integers based on Fibonacci numbers of order m ≥ 2. Fibonacci codes have been used before, and this paper extends previous work presenting several novel features. In particular, the compression efficiency is analyzed and compared to that of dense codes, and various table-driven decoding routines are suggested.