A prefix encoding for a constructed language

This work focuses in the formal and technical analysis of some aspects of a constructed language. As a first part of the work, a possible coding for the language will be studied, emphasizing the pre x coding, for which an extension of the Hu man algorithm from binary to n-ary will be implemented. Because of that in the language we can't know a priori the frequency of use of the words, a study will be done and several strategies will be proposed for an open words system, analyzing previously the existing number of words in current natural languages. As a possible upgrade of the coding, we'll take also a look to the synchronization loss problem, as well as to its solution: the self-synchronization, a t-codes study with the number of possible words for the language, as well as other alternatives. Finally, and from a less formal approach, several applications for the language have been developed: A voice synthesizer, a speech recognition system and a system font for the use of the language in text processors. For each of these applications, the process used for its construction, as well as the problems encountered and still to solve in each will be detailed

Algebraic synchronization criterion and computing reset words

We refine a uniform algebraic approach for deriving upper bounds on reset thresholds of synchronizing automata. We express the condition that an automaton is synchronizing in terms of linear algebra, and obtain upper bounds for the reset thresholds of automata with a short word of a small rank. The results are applied to make several improvements in the area. We improve the best general upper bound for reset thresholds of finite prefix codes (Huffman codes): we show that an $n$-state synchronizing decoder has a reset word of length at most $O(n \log^3 n)$. In addition to that, we prove that the expected reset threshold of a uniformly random synchronizing binary $n$-state decoder is at most $O(n \log n)$. We also show that for any non-unary alphabet there exist decoders whose reset threshold is in $\varTheta(n)$. We prove the \v{C}ern\'{y} conjecture for $n$-state automata with a letter of rank at most $\sqrt[3]{6n-6}$. In another corollary, based on the recent results of Nicaud, we show that the probability that the \v{C}ern\'y conjecture does not hold for a random synchronizing binary automaton is exponentially small in terms of the number of states, and also that the expected value of the reset threshold of an $n$-state random synchronizing binary automaton is at most $n^{3/2+o(1)}$. Moreover, reset words of lengths within all of our bounds are computable in polynomial time. We present suitable algorithms for this task for various classes of automata, such as (quasi-)one-cluster and (quasi-)Eulerian automata, for which our results can be applied.Comment: 18 pages, 2 figure

On palimpsests in neural memory: an information theory viewpoint

The finite capacity of neural memory and the reconsolidation phenomenon suggest it is important to be able to update stored information as in a palimpsest, where new information overwrites old information. Moreover, changing information in memory is metabolically costly. In this paper, we suggest that information-theoretic approaches may inform the fundamental limits in constructing such a memory system. In particular, we define malleable coding, that considers not only representation length but also ease of representation update, thereby encouraging some form of recycling to convert an old codeword into a new one. Malleability cost is the difficulty of synchronizing compressed versions, and malleable codes are of particular interest when representing information and modifying the representation are both expensive. We examine the tradeoff between compression efficiency and malleability cost, under a malleability metric defined with respect to a string edit distance. This introduces a metric topology to the compressed domain. We characterize the exact set of achievable rates and malleability as the solution of a subgraph isomorphism problem. This is all done within the optimization approach to biology framework.Accepted manuscrip

Application of symbol avoidance in reed-solomon codes to improve their synchronization

Abstract: In our previous work we introduced a method for avoiding/excluding some symbols in Reed-Solomon (RS) codes, called symbol avoidance. In this paper, we apply the symbol avoidance method to make synchronization of RS encoded data more effective. We avoid symbols in a RS code and then perform conventional frame synchronization on RS encoded data by appending sync-words on the data. The symbols in the RS code are avoided according to the sync-word used, such that the sync-word has very low probability of being found in the RS codewords, where it was not inserted. Therefore, for different sync-words, different symbols need to be avoided in the RS code. The goal here is to reduce the probability of mistaking data for the sync-word in the RS encoded framed data. Hence, the probability of successful synchronization is improved. Not only does our symbol avoidance code improve probability of successful synchronization, it also reduces the overall amount of redundancy required when the channel is very noisy

Synchronization with permutation codes and Reed-Solomon codes

D.Ing. (Electrical And Electronic Engineering)We address the issue of synchronization, using sync-words (or markers), for encoded data. We focus on data that is encoded using permutation codes or Reed-Solomon codes. For each type of code (permutation code and Reed-Solomon code) we give a synchronization procedure or algorithm such that synchronization is improved compared to when the procedure is not employed. The gure of merit for judging the performance is probability of synchronization (acquisition). The word acquisition is used to indicate that a sync-word is acquired or found in the right place in a frame. A new synchronization procedure for permutation codes is presented. This procedure is about nding sync-words that can be used speci cally with permutation codes, such that acceptable synchronization performance is possible even under channels with frequency selective fading/jamming, such as the power line communication channel. Our new procedure is tested with permutation codes known as distance-preserving mappings (DPMs). DPMs were chosen because they have de ned encoding and decoding procedures. Another new procedure for avoiding symbols in Reed-Solomon codes is presented. We call the procedure symbol avoidance. The symbol avoidance procedure is then used to improve the synchronization performance of Reed-Solomon codes, where known binary sync-words are used for synchronization. We give performance comparison results, in terms of probability of synchronization, where we compare Reed-Solomon with and without symbol avoidance applied

Design of tch-type sequences for communications

This thesis deals with the design of a class of cyclic codes inspired by TCH codewords. Since TCH codes are linked to finite fields the fundamental concepts and facts about abstract algebra, namely group theory and number theory, constitute the first part of the thesis. By exploring group geometric properties and identifying an equivalence between some operations on codes and the symmetries of the dihedral group we were able to simplify the generation of codewords thus saving on the necessary number of computations. Moreover, we also presented an algebraic method to obtain binary generalized TCH codewords of length N = 2k, k = 1,2, . . . , 16. By exploring Zech logarithm’s properties as well as a group theoretic isomorphism we developed a method that is both faster and less complex than what was proposed before. In addition, it is valid for all relevant cases relating the codeword length N and not only those resulting from N = p

Algebraic synchronization criterion and computing reset words

We refine a uniform algebraic approach for deriving upper bounds on reset thresholds of synchronizing automata. We express the condition that an automaton is synchronizing in terms of linear algebra, and obtain new upper bounds for automata with a short word of small rank. The results are applied to make several improvements in the area. In particular, we improve the upper bound for reset thresholds of finite prefix codes (Huffman codes): we show that an n-state synchronizing decoder has a reset word of length at most O(nlog3n). In addition to that, we prove that the expected reset threshold of a uniformly random synchronizing binary n-state decoder is at most O(nlog n). We prove the Černý conjecture for n-state automata with a letter of rank ≤6n−63. In another corollary, we show that the probability that the Černý conjecture does not hold for a random synchronizing binary automaton is exponentially small in terms of the number of states, and that the expected value of the reset threshold is at most n3/2+o(1). Moreover, all of our bounds are constructible. We present suitable polynomial algorithms for the task of finding a reset word of length within our bounds. © 201

Algebraic synchronization criterion and computing reset words

We refine results about relations between Markov chains and synchronizing automata. We express the condition that an automaton is synchronizing in terms of linear algebra, and obtain upper bounds for the reset thresholds of automata with a short word of a small rank. The results are applied to make several improvements in the area. We improve the best general upper bound for reset thresholds of finite prefix codes (Huffman codes): we show that an n-state synchronizing decoder has a reset word of length at most O(n log3 n). Also, we prove the Černý conjecture for n-state automata with a letter of rank at most 3√6n-6. In another corollary, based on the recent results of Nicaud, we show that the probability that the Čern conjecture does not hold for a random synchronizing binary automaton is exponentially small in terms of the number of states. It follows that the expected value of the reset threshold of an n-state random synchronizing binary automaton is at most n7/4+o(1). Moreover, reset words of the lengths within our bounds are computable in polynomial time. We present suitable algorithms for this task for various classes of automata for which our results can be applied. These include (quasi-)one-cluster and (quasi-)Eulerian automata. © Springer-Verlag Berlin Heidelberg 2015

Some basic properties of fix-free codes.

by Chunxuan Ye.Thesis (M.Phil.)--Chinese University of Hong Kong, 2000.Includes bibliographical references (leaves 74-[78]).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Information Theory --- p.1Chapter 1.2 --- Source Coding --- p.2Chapter 1.3 --- Fixed Length Codes and Variable Length Codes --- p.4Chapter 1.4 --- Prefix Codes --- p.5Chapter 1.4.1 --- Kraft Inequality --- p.7Chapter 1.4.2 --- Huffman Coding --- p.9Chapter 2 --- Existence of Fix-Free Codes --- p.13Chapter 2.1 --- Introduction --- p.13Chapter 2.2 --- Previous Results --- p.14Chapter 2.2.1 --- Complete Fix-Free Codes --- p.14Chapter 2.2.2 --- Ahlswede's Results --- p.16Chapter 2.3 --- Two Properties of Fix-Free Codes --- p.17Chapter 2.4 --- A Sufficient Condition --- p.20Chapter 2.5 --- Other Sufficient Conditions --- p.33Chapter 2.6 --- A Necessary Condition --- p.37Chapter 2.7 --- A Necessary and Sufficient Condition --- p.42Chapter 3 --- Redundancy of Optimal Fix-Free Codes --- p.44Chapter 3.1 --- Introduction --- p.44Chapter 3.2 --- An Upper Bound in Terms of q --- p.46Chapter 3.3 --- An Upper Bound in Terms of p1 --- p.48Chapter 3.4 --- An Upper Bound in Terms of pn --- p.51Chapter 4 --- Two Applications of the Probabilistic Method --- p.54Chapter 4.1 --- An Alternative Proof for the Kraft Inequality --- p.54Chapter 4.2 --- A Characteristic Inequality for ´ب1´ة-ended Codes --- p.59Chapter 5 --- Summary and Future Work --- p.69Appendix --- p.71A Length Assignment for Upper Bounding the Redundancy of Fix-Free Codes --- p.71Bibliography --- p.7