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36
Maximum RunlengthLimited Codes with Error Control Capabilities
 IEEE J. Select. Areas Commun
, 2001
"... New methods are presented to protect maximum runlengthlimited sequences against random and burst errors and to avoid error propagation. The methods employ parallel conversion techniques and enumerative coding algorithms that transform binary user information into constrained codewords. The new sche ..."
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Cited by 20 (5 self)
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New methods are presented to protect maximum runlengthlimited sequences against random and burst errors and to avoid error propagation. The methods employ parallel conversion techniques and enumerative coding algorithms that transform binary user information into constrained codewords. The new schemes have a low complexity and are very efficient. The approach can be used for modulation coding in recording systems and for synchronization and line coding in communication systems. The schemes enable the usage of highrate constrained codes, as error control can be provided with similar capabilities as for unconstrained sequences. Index TermsBurst correction codes, enumerative coding, forward error correction, modulation coding, ReedSolomon codes, runlength codes, synchronization. I.
Constrained systems with unconstrained positions
 IEEE Trans. Inform. Theory
, 2002
"... Abstract—We develop methods for analyzing and constructing combined modulation/errorcorrectiong codes (ECC codes), in particular codes that employ some form of reversed concatenation and whose ECC decoding scheme requires easy access to soft information (e.g., turbo codes, lowdensity paritycheck ..."
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Cited by 18 (7 self)
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Abstract—We develop methods for analyzing and constructing combined modulation/errorcorrectiong codes (ECC codes), in particular codes that employ some form of reversed concatenation and whose ECC decoding scheme requires easy access to soft information (e.g., turbo codes, lowdensity paritycheck (LDPC) codes or parity codes). We expand on earlier work of Immink and Wijngaarden and also of Fan, in which certain bit positions are reserved for ECC parity, in the sense that the bit values in these positions can be changed without violating the constraint. Earlier work has focused more on block codes for specific modulation constraints. While our treatment is completely general, we focus on finitestate codes for maximum transition run (MTR) constraints. We 1) obtain some improved constructions for MTR codes based on short block lengths, 2) specify an asymptotic lower bound for MTR constraints, which is tight in very special cases, for the maximal code rate achievable for an MTR code with a given density of unconstrained positions, and 3) show how to compute the capacity of the set of sequences that satisfy a completely arbitrary constraint with a specified set of bit positions unconstrained. Index Terms—Finitestate encoders, modulation codes, maximum transition run (MTR) codes, reversed concatenation, runlength limited (RLL) codes. I.
A Modified Concatenated Coding Scheme, with Applications to Magnetic Data Storage
 IEEE Trans. Inform. Theory
, 1997
"... When block modulation codes are concatenated with an errorcorrection code (ECC) in the standard way, the use of long block lengths results in errorpropagation. This paper analyzes the performance of modified concatenation, which involves reversing the order of modulation and ECC. This modified ..."
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Cited by 13 (3 self)
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When block modulation codes are concatenated with an errorcorrection code (ECC) in the standard way, the use of long block lengths results in errorpropagation. This paper analyzes the performance of modified concatenation, which involves reversing the order of modulation and ECC. This modified scheme reduces error propagation, provides greater flexibility in the choice of parameters, and facilitates softdecision decoding, with little or no loss in transmission rate. In particular, examples are presented which show how this technique can allow fewer interleaves per sector in hard disk drives, and permit the use of sophisticated block modulation codes which are better suited to the channel. Index terms: concatenated codes, ReedSolomon codes, modulation codes, magnetic data storage 1 Introduction This paper is concerned with the interaction between the modulation code and the errorcorrecting code (ECC). The idea of modulation is to ensure that the sequence of bits transm...
Tradeoff functions for constrained systems with unconstrained positions
 IEEE TRANS. INF. THEORY
, 2006
"... We introduce a new method for analyzing and constructing combined modulation and errorcorrecting codes (ECCs), in particular codes that utilize some form of reverse concatenation and whose ECC decoding scheme requires easy access to soft information. We expand the work of Immink and Wijngaarden an ..."
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Cited by 12 (4 self)
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We introduce a new method for analyzing and constructing combined modulation and errorcorrecting codes (ECCs), in particular codes that utilize some form of reverse concatenation and whose ECC decoding scheme requires easy access to soft information. We expand the work of Immink and Wijngaarden and also of Campello, Marcus, New, and Wilson, in which certain bit positions in the modulation code are deliberately left unconstrained for the ECC parity bits, in the sense that such positions can take on either bit value without violating the constraint. Our method of analysis involves creating a single graph that incorporates information on these unconstrained positions directly into the constraint graph without any assumptions of periodicity or sets of unconstrained positions, and is thus completely general. We establish several properties of the tradeoff function that relates the density of unconstrained positions to the maximum code rate. In particular, the tradeoff function is shown to be concave and continuous. Algorithms for computing lower and upper bounds for this function are presented. We also show how to compute the maximum possible density of unconstrained positions and give explicit values for the runlengthlimited (RLL ()) and maximumtransitionrun (MTR ()) constraints.
Constraint gain
 IEEE Trans. Inform. Theory
, 2001
"... Abstract—In digital storage systems where the input to the noisy channel is required to satisfy a modulation constraint, the constrained code and errorcontrol code (ECC) are typically designed and decoded independently. The achievable rate for this situation is evaluated as the rate of average inte ..."
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Cited by 7 (1 self)
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Abstract—In digital storage systems where the input to the noisy channel is required to satisfy a modulation constraint, the constrained code and errorcontrol code (ECC) are typically designed and decoded independently. The achievable rate for this situation is evaluated as the rate of average intersection of the constraint and the ECC. The gap from the capacity of the noisy constrained channel is called the constraint gain, which represents the potential improvement in combining the design and decoding of the constrained code and the ECC. The constraint gain is computed for various constraints over the binaryinput additive white Gaussian noise (AWGN) channel (BIAWGNC) as well as over intersymbol interference (ISI) channels. Finally, it is shown that an infinite cascade of reverse concatenation with independent decoding of constraint and ECC has a capacity equal to the rate of average intersection. Index Terms—Capacity, constrained codes, errorcontrol codes (ECCs), noisy constrained channels, reverse concatenation. I.
An enumerative coding technique for DCfree runlengthlimited sequences
 IEEE Trans. Commun
, 2000
"... ..."
VARIABLELENGTH CODES AND FINITE AUTOMATA
, 2010
"... The aim of this chapter is to present, in appropriate perspective, some selected topics in the theory of variablelength codes. One of the domains of applications is lossless data compression. The main aspects covered include optimal prefix codes and finite automata and transducers. These are a basi ..."
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Cited by 7 (1 self)
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The aim of this chapter is to present, in appropriate perspective, some selected topics in the theory of variablelength codes. One of the domains of applications is lossless data compression. The main aspects covered include optimal prefix codes and finite automata and transducers. These are a basic tool for encoding and decoding variablelength codes. Connections with codes for constrained channels and sources are developed in some detail. Generating series are used systematically for computing the parameters of encodings such as length and probability distributions. The chapter contains numerous examples and exercises with solutions.
Lossless SlidingBlock Compression of Constrained Systems
, 1999
"... A method is presented for designing lossless slidingblock compression schemes that map constrained sequences onto unconstrained ones. The new compression scheme is incorporated into a coding technique for noisy constrained channels, which has applications to magnetic and optical storage. As suggest ..."
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Cited by 4 (3 self)
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A method is presented for designing lossless slidingblock compression schemes that map constrained sequences onto unconstrained ones. The new compression scheme is incorporated into a coding technique for noisy constrained channels, which has applications to magnetic and optical storage. As suggested recently by Immink, the use of a lossless compression code can improve the performance of a modified concatenation scheme where the positions of the errorcorrecting code and constrained code are reversed (primarily in order to eliminate errorpropagation due to the constrained code). Examples are presented that demonstrate the advantage of using slidingblock compression over block compression in a noisy constrained setting. Keywords: Compression; Concatenated codes; Constrained systems; Noisy constrained channels; Slidingblock codes; Runlengthlimited codes; State splitting. 1 Introduction Constrained coding is a special kind of channel coding in which unconstrained user sequences a...
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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Cited by 3 (2 self)
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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.