Several measures are defined and investigated, which allow the comparison of codes as to their robustness against errors. Then new universal and complete sequences of variable-length codewords are proposed, based on representing the integers in a binary Fibonacci numeration system. Each sequence is constant and need not be generated for every probability distribution. These codes can be used as alternatives to Huffman codes when the optimal compression of the latter is not required, and simplicity, faster processing and robustness are preferred. The codes are compared on several "real-life" examples. 1. Motivation and Introduction Let A = fA 1 ; A 2 ; \Delta \Delta \Delta ; An g be a finite set of elements, called cleartext elements, to be encoded by a static uniquely decipherable (UD) code. For notational ease, we use the term `code' as abbreviation for `set of codewords'; the corresponding encoding and decoding algorithms are always either given or clear from the context. A code i...

Under what conditions can Huffman codes be efficiently decoded in both directions? The usual decoding procedure works also for backward decoding only if the code has the affix property, i.e., both prefix and suffix properties. Some affix Huffman codes are exhibited, and necessary conditions for the existence of such codes are given. An algorithm is presented which, for a given set of codeword lengths, constructs an affix code, if there exists one. Since for many distributions there is no affix code giving the same compression as the Huffman code, a new algorithm for backward decoding of non-affix Huffman codes is presented, and its worst case complexity is proved to be linear in the length of the encoded text. 1. Introduction For a given sequence of n weights w 1 ; : : : ; wn , with w i ? 0, Huffman's wellknown algorithm [9] constructs an optimum prefix code. We use throughout the term `code' as abbreviation for `set of codewords'. In a prefix code no codeword is the prefix of any o...

A new general scheme is introduced that allows bidirectional decoding of variable length coded bitstreams from either end. Except for a small fixed number of extra bits appended to a sequence of code words, the scheme is as efficient as Huffman coding. The extra operations required at coder and decoder are code word reversal and one EXOR for each bit.

We consider the problem of constructing statistically synchronizable codes over arbitrary alphabets and for any finite source. We show how to efficiently construct a statistically synchronizable code whose average codeword length is whithin the least likely codeword probability from that of the Huffman code for the same source. Moreover, we give a method for constructing codes having a synchronizing codeword. The codes we construct present high synchronizing capability and low redundancy. 3 Part of this work was done while visiting IBM T. J. Watson Research Center, P.O. Box 218, Yorktown Heights, New York, 10598. This work was partially supported by the Italian Ministry of the University and Scientific Research, within the framework of the Project: Progetto ed Analisi di Algoritmi. Part of this work has been presented at the 1990 IEEE International Symposium on Information Theory, San Diego, CA, Jan. 1990. 1 1 Introduction A basic problem in information transmission is to mai...

I hereby declare that I am the sole author of this thesis. I authorize the University of Waterloo to lend this thesis to other institutions or individuals for the purpose of scholarly research. I further authorize the University of Waterloo to reproduce this thesis by pho-tocopying or by other means, in total or in part, at the request of other institutions or individuals for the purpose of scholarly research. ii The University of Waterloo requires the signatures of all persons using or pho-tocopying this thesis. Please sign below, and give address and date. iii The fixed-rate entropy-constrained vector quantizer draws its motivation from the large gap in the performance of the optimal entropy-constrained scalar quantizer (ESCQ) and the fixed-rate LMQ for most non-uniform sources and tries to bridge this gap while maintaining a fixed-rate output. Having a fixed-rate output avoids

The probability that a complete binary prefix code has a self-synchronizing string approaches one, as the number of codewords tends to infinity.

Variable length binary codes have been frequently used for communications since Huffman’s important paper on constructing minimum average length codes. One drawback of variable length codes is the potential loss of synchronization in the presence of channel errors. However, many variable length codes seem to possess a “self-synchronization” property that lets them recover from bit errors. In particular, for some variable length codes there exists a certain binary string (not necessarily a codeword) which automatically resynchronizes the code. That is, if a transmitted sequence of bits is corrupted by one or more bit errors, then as soon as the receiver by random chance correctly detects a self-synchronizing string, the receiver can continue properly parsing the bit sequence into codewords. Most commonly used binary prefix codes, including Huffman codes, are “complete”, in the sense that the vertices in their decoding trees are either leaves or have two children. An open question has been

This paper addresses the issue of robust transmission of Variable Length Codes (VLCs) encoded sources over error-prone channels. A new class of codes, called self-multiplexed codes, is introduced. Their performance in terms of compression is the same as the one of classical VLCs (e.g. Huffman codes). Their property in terms of energy distribution on respective transitions of the codetree allows to confine error propagation to transitions bearing low reconstruction energy. Simulation results reveal high performances in terms of signal to noise ratio.

It is paradoxical that, as the technology for stor-

This paper investigates the design and analysis of data synchronization codes whose decoders have the property that, in addition to reestablishing correct decoding after encoded data is lost or afflicted with errors, they produce the original time index of each decoded data symbol modulo some integer T . The motivation for such data synchronization with timing is that in many situations where data must be encoded, it is not sufficient for the decoder to present a sequence of correct data symbols. Instead, the user also needs to know the position in the original source sequence of the symbols being presented. With this goal in mind, periodic prefix-synchronized (PPS) codes are introduced and analyzed on the basis of their synchronization delay D, rate R, and timing span T . Introduced are two specific PPS designs called natural marker and cascaded codes. A principal result is that when coding binary data with rate R, the largest possible timing span attainable with PPS codes...