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28
On the Channel Capacity of Read/Write Isolated Memory
 Discrete Applied Math
, 1994
"... We apply graph theory to find upper and lower bounds on the channel capacity of a serial, binary, rewritable medium in which consecutive locations may not store 1's, and consecutive locations may not be altered during a single rewriting pass. If the true capacity is close to the upper bound, then a ..."
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We apply graph theory to find upper and lower bounds on the channel capacity of a serial, binary, rewritable medium in which consecutive locations may not store 1's, and consecutive locations may not be altered during a single rewriting pass. If the true capacity is close to the upper bound, then a trivial code is nearly optimal. 1 Introduction A serial, binary (0,1) memory is said to be read isolated if no two consecutive positions may store 1's; it is said to be write isolated if no two consecutive positions may be changed during rewriting. A read/write isolated memory (RWIM) is a binary, linearly ordered, rewritable storage medium obeying both restrictions. 1.1 Origin of the Problem The first restriction alone, no consecutive 1's, is typical of magnetic recording and has recurred in optical recording. The problem was first studied by Freiman and Wyner [1], and a subcase by Kautz [2]; they showed that the capacity was 0:694 . . . = log 2 OE bits per symbol, where OE is the larger...
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.
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
Online multiplication in real and complex base
 Proc. IEEE ARITH 16, I.E.E.E. Computer Society Press
, 2003
"... Multiplication of two numbers represented in base 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 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.
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
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.
Data Synchronization with Timing
 IEEE Trans. Inform. Theory
"... 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. Keywords cascaded codes, commafree codes, embeddedindex codes, natural marker codes, periodic prefixsynchronized (PPS) codes, prefixsynchronized codes, synchronization delay, synctiming codes, timing span This work was supported by NSF Grants NCR9415754 and CCR9815006. Portions were published in the proceedings of the Data Compression Conference, Snowbird Utah, Mar. 1999, and of the 1999 IEEE Information Theory Workshop, Kruger National Park, South Africa, June 1999. 1 I.
Error Popagation Assessment of Enumerative Coding Schemes
, 1999
"... Enumerative coding is an attractive algorithmic procedure for translating long source words into codewords and vice versa. The usage of long codewords makes it possible to approach a code rate which is as close as desired to Shannon's noiseless capacity of the constrained channel. Enumerative encodi ..."
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Enumerative coding is an attractive algorithmic procedure for translating long source words into codewords and vice versa. The usage of long codewords makes it possible to approach a code rate which is as close as desired to Shannon's noiseless capacity of the constrained channel. Enumerative encoding is prone to massive error propagation as a single bit error could ruin entire decoded words. This contribution will evaluate the effects of error propagation of the enumerative coding of runlengthlimited sequences. Index TermsEnumerative coding, error propagation, RLL. I.
consisting of two fourstate trellises. To this point, though, no new codes comparable to, for example, the rate
"... Enumerative coding is an attractive algorithmic procedure for translating long source words into codewords and vice versa. The usage of long codewords makes it possible to approach a code rate which is as close as desired to Shannon's noiseless capacity of the constrained channel. Enumerative encodi ..."
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Enumerative coding is an attractive algorithmic procedure for translating long source words into codewords and vice versa. The usage of long codewords makes it possible to approach a code rate which is as close as desired to Shannon's noiseless capacity of the constrained channel. Enumerative encoding is prone to massive error propagation as a single bit error could ruin entire decoded words. This contribution will evaluate the effects of error propagation of the enumerative coding of runlengthlimited sequences. Index TermsEnumerative coding, error propagation, RLL. I.