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Combinatorial Representation of Generalized Fibonacci Numbers
, 1991
"... New formulae are presented which express various generalizations of Fibonacci numbers as simple sums of binomial and multinomial coefficients. The equalities are inferred from the special properties of the representations of the integers in certain numeration systems. ..."
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New formulae are presented which express various generalizations of Fibonacci numbers as simple sums of binomial and multinomial coefficients. The equalities are inferred from the special properties of the representations of the integers in certain numeration systems.
Online multiplication in real and complex base
 In Proceedings of the 16th IEEE Symposium on Computer Arithmetic (ARITH 16
, 2003
"... Multiplication of two numbers represented in base is shown to be computable by an online algorithm when is a negative integer, a positive noninteger real number, or a complex number of the form�, where is a positive integer. 1 ..."
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Multiplication of two numbers represented in base is shown to be computable by an online algorithm when is a negative integer, a positive noninteger real number, or a complex number of the form�, where is a positive integer. 1
HighRate Maximum Runlength Constrained Coding Schemes Using Nibble Replacement
"... Summary We will present coding techniques for the characterconstrained channel, where information is conveyed using qbit characters (nibbles), where w prescribed characters are disallowed. Using codes for the characterconstrained channel, we present simple and systematic constructions of highrat ..."
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Summary We will present coding techniques for the characterconstrained channel, where information is conveyed using qbit characters (nibbles), where w prescribed characters are disallowed. Using codes for the characterconstrained channel, we present simple and systematic constructions of highrate binary maximum runlength constrained codes. The new constructions have the virtue that large lookup tables for encoding and decoding are not required. We will compare the error propagation performance of codes based on the new construction with that of prior art codes. I.
FMKZ: an even simpler alphabetindependent FMindex
 Czech Technical University, Prague
, 2006
"... Abstract. In an earlier work [6] we presented a simple FMindex variant, based on the idea of Huffmancompressing the text and then applying the BurrowsWheeler transform over it. The main drawback of using Huffman was its lack of synchronizing properties, forcing us to supply another bit stream ind ..."
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Abstract. In an earlier work [6] we presented a simple FMindex variant, based on the idea of Huffmancompressing the text and then applying the BurrowsWheeler transform over it. The main drawback of using Huffman was its lack of synchronizing properties, forcing us to supply another bit stream indicating the Huffman codeword boundaries. In this way, the resulting index needed O(n(H0 +1)) bits of space but with the constant 2 (concerning the main term). There are several options aiming to mitigate the overhead in space, with various effects on the query handling speed. In this work we propose KautzZeckendorf coding as a both simple and practical replacement for Huffman. We dub the new index FMKZ. We also present an efficient implementation of the rank operation, which is the main building brick of the FMKZ. Experimental results show that our index provides an attractive space/time tradeoff in comparison with existing succinct data structures, and in the DNA test it even wins both in search time and space use. An additional asset of our solution is its relative simplicity. 1
Data Synchronization with Timing
 IEEE TRANS. INFORM. THEORY
, 1999
"... This paper proposes and analyzes data synchronization techniques that not only resynchronize after encoded bits are corrupted by insertion, deletion or substitution errors, but also produce estimates of the time indices of the decoded data symbols, in order to determine their positions in the origin ..."
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This paper proposes and analyzes data synchronization techniques that not only resynchronize after encoded bits are corrupted by insertion, deletion or substitution errors, but also produce estimates of the time indices of the decoded data symbols, in order to determine their positions in the original source sequence. The techniques are based on block codes, and the estimates are of the time indices modulo some integer T , called the timing span, which is desired to be large. Several types of block codes that encode binary data are analyzed on the basis of the maximum attainable timing span for a given coding rate R (or, equivalently, redundancy ae = 1 \Gamma R) and permissible resynchronization delay D. It is found that relatively simple codes can asymptotically attain the maximum timing span among such block codes, which grows exponentially with delay, with exponent D(1 \Gamma R) + o(D). Thus large timing span can be attained with little redundancy and only moderate values of delay.
Error Propagation Assessment of Enumerative Coding Schemes
 Proc. IEEE International Conference on Communications 2
, 1999
"... Introduction The technique of enumerative coding [1] makes it possible to translate source words into codewords and vice versa by invoking an algorithmic procedure rather than performing the translation with a lookup table. The usage of long codewords makes it possible to approach a code rate whic ..."
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Introduction The technique of enumerative coding [1] makes it possible to translate source words into codewords and vice versa by invoking an algorithmic procedure rather than performing the translation with a lookup table. The usage of long codewords makes it possible to approach a code rate which is arbitrarily close to Shannon's noiseless capacity of the constrained channel. The risk of extreme error propagation precluded its usage in practical systems. Single channel bit errors may result in error propagation that could corrupt the entire data in the decoded word, and, of course, the longer the codeword the greater the number of data symbols affected. This article will evaluate the effects of error propagation of enumerative coding, where it is assumed that the constrained code is used in the conventional code configuration. It will be shown that when certain measures are taken, the average error propagation can be controlled to a level which is quite acceptable for many
On the Capacity of the PrecisionResolution System
"... Abstract—Arguably, the most prominent constrained system in storage applications is the runlength limited (RLL) system, where every binary sequence obeys the constraint that every two adjacent 1’s are separated by at least consecutive ’s and at most consecutive ’s, namely, runs of ’s are lengt ..."
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Abstract—Arguably, the most prominent constrained system in storage applications is the runlength limited (RLL) system, where every binary sequence obeys the constraint that every two adjacent 1’s are separated by at least consecutive ’s and at most consecutive ’s, namely, runs of ’s are length limited. The motivation for the RLL constraint arises mainly from the physical limitations of the read and write technologies in magnetic and optical storage systems. We revisit the rationale for the RLL system, reevaluate its relationship to the constraints of the physical media and propose a new framework that we call the PrecisionResolution (PR) system. Specifically, in the PR system there is a separation between the encoder constraints (which relate to the precision of writing information into the physical media) and the decoder constraints (which relate to its resolution, namely, the ability to distinguish between two different signals received by reading the physical media). We compute the capacity of a general PR system and compare it to the traditional RLL system. Index Terms—Runlength limited (RLL), constrained coding, capacity of constrained channels. I.
Codes for SelfClocking, ACCoupled Transmission: Aspects of Synthesis and Analysis
 IBM J. Res. Develop
, 1975
"... Abstract: We consider NRZI waveform codes that satisfy a given set of runlength constraints and the upper bound on the accumulated dc charge of the waveform. These constraints enable the codeword to be selfclocking, accoupled, and suitable for data processing tape and communication applications. ..."
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Abstract: We consider NRZI waveform codes that satisfy a given set of runlength constraints and the upper bound on the accumulated dc charge of the waveform. These constraints enable the codeword to be selfclocking, accoupled, and suitable for data processing tape and communication applications. Various aspects of synthesis and analysis of such codes, called (d, k, C) codes, are illustrated by means of several examples. The choice of the initial state of the encoder is shown to influence the length of the data sequence over which the encoder must lookahead.
New Bounds on the Capacity of Multidimensional RunLength Constraints
, 2011
"... We examine the wellknown problem of determining the capacity of multidimensional runlengthlimited constrained systems. By recasting the problem, which is essentially a combinatorial counting problem, into a probabilistic setting, we are able to derive new lower and upper bounds on the capacity o ..."
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We examine the wellknown problem of determining the capacity of multidimensional runlengthlimited constrained systems. By recasting the problem, which is essentially a combinatorial counting problem, into a probabilistic setting, we are able to derive new lower and upper bounds on the capacity of RLL systems. These bounds are better than all previouslyknown analytical bounds for , and are tight asymptotically. Thus, we settle the open question: what is the rate at which the capacity of RLL systems converges to 1 as ? We also provide the first nontrivial upper bound on the capacity of general RLL systems.
FMKZ: An Even Simpler AlphabetIndependent FMIndex
"... Abstract. In an earlier work [6] we presented a simple FMindex variant, based on the idea of Huffmancompressing the text and then applying the BurrowsWheeler transform over it. The main drawback of using Huffman was its lack of synchronizing properties, forcing us to supply another bit stream ind ..."
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Abstract. In an earlier work [6] we presented a simple FMindex variant, based on the idea of Huffmancompressing the text and then applying the BurrowsWheeler transform over it. The main drawback of using Huffman was its lack of synchronizing properties, forcing us to supply another bit stream indicating the Huffman codeword boundaries. In this way, the resulting index needed O(n(H0+1)) bits of space but with the constant 2 (concerning the main term). There are several options aiming to mitigate the overhead in space, with various effects on the query handling speed. In this work we propose KautzZeckendorf coding as a both simple and practical replacement for Huffman. We dub the new index FMKZ. We also present an efficient implementation of the rank operation, which is the main building brick of the FMKZ. Experimental results show that our index provides an attractive space/time tradeoff in comparison with existing succinct data structures, and in the DNA test it even wins both in search time and space use. An additional asset of our solution is its relative simplicity. 1