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63
On Codes That Avoid Specified Differences
 IEEE Transactions on Information Theory
, 2001
"... Certain magnetic recording applications call for a large number of sequences whose differences do not include certain disallowed binary patterns. We show that the number of such sequences increases exponentially with their length and that the exponent, or capacity, is the logarithm of the joint spec ..."
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Cited by 21 (2 self)
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Certain magnetic recording applications call for a large number of sequences whose differences do not include certain disallowed binary patterns. We show that the number of such sequences increases exponentially with their length and that the exponent, or capacity, is the logarithm of the joint spectral radius of an appropriately defined set of matrices. We derive a new algorithm for determining the joint spectral radius of sets of nonnegative matrices and combine it with existing algorithms to determine the capacity of several sets of disallowed differences that arise in practice.
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 20 (8 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.
Constrained Coding for Binary Channels with High Intersymbol Interference
 IEEE TRANS. INFORM. THEORY
, 1999
"... Partialresponse (PR) signalling is used to model communications channels with intersymbol interference (ISI) such as the magnetic recording channel and the copper wire channel for digital subscriber lines. Coding for improving noise immunity in higherorder partial response channels, such as the "e ..."
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Cited by 17 (8 self)
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Partialresponse (PR) signalling is used to model communications channels with intersymbol interference (ISI) such as the magnetic recording channel and the copper wire channel for digital subscriber lines. Coding for improving noise immunity in higherorder partial response channels, such as the "extended" class4 channels denoted EPR4, E 2 PR4, E 3 PR4, has become an important subject as the linear densities in magnetic recording approach those at which these partialresponse channels are the best models of real channels. In this paper, we consider partialresponse channels for which ISI is so severe that the channels fail to achieve the matchedfilterbound (MFB) for symbol error rate, assuming maximum likelihood decoding. We show that their performance can be improved to the MFB by high rate codes based on constrained systems, some of which may even simplify the Viterbi detectors relative to the uncoded channels. We present several examples of highrate constrained codes for E ...
Capacity of the Trapdoor Channel with Feedback
"... We establish that the feedback capacity of the trapdoor channel is the logarithm of the golden ratio and provide a simple communication scheme that achieves capacity. As part of the analysis, we formulate a class of dynamic programs that characterize capacities of unifilar finitestate channels. The ..."
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Cited by 16 (7 self)
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We establish that the feedback capacity of the trapdoor channel is the logarithm of the golden ratio and provide a simple communication scheme that achieves capacity. As part of the analysis, we formulate a class of dynamic programs that characterize capacities of unifilar finitestate channels. The trapdoor channel is an instance that admits a simple analytic solution.
Improved BitStuffing Bounds on TwoDimensional Constraints
 IEEE Trans. Inform. Theory
, 2004
"... Abstract—We derive lower bounds on the capacity of certain twodimensional (2D) constraints by considering bounds on the entropy of measures induced by bitstuffing encoders. A more detailed analysis of a previously proposed bitstuffing encoder for ()runlengthlimited (RLL) constraints on the squ ..."
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Cited by 15 (6 self)
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Abstract—We derive lower bounds on the capacity of certain twodimensional (2D) constraints by considering bounds on the entropy of measures induced by bitstuffing encoders. A more detailed analysis of a previously proposed bitstuffing encoder for ()runlengthlimited (RLL) constraints on the square lattice yields improved lower bounds on the capacity for all 2. This encoding approach is extended to ()RLL constraints on the hexagonal lattice, and a similar analysis yields lower bounds on the capacity for 2. For the hexagonal (1)RLL constraint, the exact coding ratio of the bitstuffing encoder is calculated and is shown to be within 0.5 % of the (known) capacity. Finally, a lower bound is presented on the coding ratio of a bitstuffing encoder for the constraint on the square lattice where each bit is equal to at least one of its four closest neighbors, thereby providing a lower bound on the capacity of this constraint. Index Terms—Bitstuffing encoder, hexagonal constraint, runlengthlimited (RLL) constraints, twodimensional (2D) constraints. I.
Efficient Coding Schemes for the HardSquare Model
, 1999
"... The hardsquare model, also known as the twodimensional (1; 1)RLL constraint, consists of all binary arrays in which the 1's are isolated both horizontally and vertically. Based on a certain probability measure defined on those arrays, an efficient variableto fixed encoder scheme is presented tha ..."
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Cited by 13 (6 self)
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The hardsquare model, also known as the twodimensional (1; 1)RLL constraint, consists of all binary arrays in which the 1's are isolated both horizontally and vertically. Based on a certain probability measure defined on those arrays, an efficient variableto fixed encoder scheme is presented that maps unconstrained binary words into arrays that satisfy the hardsquare model. For sufficiently large arrays, the average rate of the encoder approaches a value which is only 0:1% below the capacity of the constraint. A second, fixedrate encoder is presented whose rate for large arrays is within 1:2% of the capacity value. Keywords: Constrained codes; Enumerative coding; Hardsquare model; Maxentropic probability measure; Permutation codes; Variabletofixed encoders; Twodimensional runlengthlimited constraints. 1 Introduction In current digital optical and magnetic recording systems, such as disks and tapes, the data is written along tracks, thus visualized as a onedimensional long ...
Parallel Constrained Coding with Application to TwoDimensional Constraints
 IEEE TRANS. INFORM. THEORY
, 2002
"... A parallel constrained coding scheme is considered where pblocks of raw data are encoded simultaneously into q tracks such that the contents of each track belong to a given constraint S. It is shown that as q increases, there are parallel block decodable encoders for S whose coding ratio, p/q, c ..."
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Cited by 10 (4 self)
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A parallel constrained coding scheme is considered where pblocks of raw data are encoded simultaneously into q tracks such that the contents of each track belong to a given constraint S. It is shown that as q increases, there are parallel block decodable encoders for S whose coding ratio, p/q, converges to the capacity of S. Examples are provided where parallel coding allows block decodable encoders, while conventional coding, at the same rate, does not. Parallel encoders are then applied as building blocks in the construction of block decodable encoders for certain families of twodimensional constraints.
PeriodicFiniteType Shift Spaces
 in IEEE Int. Symp. Information Theory
, 2001
"... We introduc e thec lass of periodic finitetype (PFT) shift spac es. They are the subc lass of shift spac es defined by a finite set of periodic ally forbidden words. Examples of PFT shifts arise naturally in thec ontext of distanc eenhanc ingc odes for partialresponsec hannels. We show that thec ..."
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Cited by 7 (2 self)
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We introduc e thec lass of periodic finitetype (PFT) shift spac es. They are the subc lass of shift spac es defined by a finite set of periodic ally forbidden words. Examples of PFT shifts arise naturally in thec ontext of distanc eenhanc ingc odes for partialresponsec hannels. We show that thec lass of PFT shifts represent a proper superset of the finitetype shift spac es and a proper subset of almostfinitetype shift spac8 . We prove several properties of labeled graphs that present PFT shifts. For a given PFT shift spac e, we identify a finite set of forbidden words  referred to as "periodic first o#enders"  that define the shift spac e and that satisfyc8 tain minimality properties. Finally, we present ane#c4k t algorithm for c onstruc ting labeled graphs that present PFT shift spac es. 1 Introducti7 Magnet i# recordi#( systems often make use ofbi#5)) codes that di# allow the appearance of certai# sequences that are problemat i# i# the data recordi#5 or retri## al process. In systems usi#6 parti# lresponse equa li#a t i# n and sequence detecti# n, socalled "di#L6 nceenhanci #( " constrai#tr codes have been proposed toi#p5( se the mi#66 umdi#6# nce at the output of the underlyi#4 i# tersymbol i# terference channel by forbi#)6p4 afini#( set ofbi#L65 patterns, e.g., [1, 2, 3]. The set of allowable code sequences are generated by paths i# a labeled, di#(L75# graph. Such sets of constra i#ra sequences are referred to as # B.E. Moision was with the MathematicA Sc0119k Researc h Center, Luc8 t Tec hnologies, Murray Hill, NJ. He is now with the Communic tions Systems and Researc h Sec18 n, Jet Propulsion Laboratory, 4800 Oak Grove Drive, Pasadena, CA 911018099 (email: bmoision@shannon.jpl.nasa.gov). P. H. Siegel is with the Center for Magnetic Rec rding Rese...
TwoDimensional Constrained Coding Based on Tiling
, 2008
"... Abstract — A new variablerate coding technique is presented for twodimensional constraints. For certain constraints, such as the (0, 2)RLL, (2, ∞)RLL, and the “no isolated bits ” (n.i.b.) constraints, the technique is shown to improve on previouslypublished lower bounds on the capacity of the co ..."
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Cited by 6 (4 self)
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Abstract — A new variablerate coding technique is presented for twodimensional constraints. For certain constraints, such as the (0, 2)RLL, (2, ∞)RLL, and the “no isolated bits ” (n.i.b.) constraints, the technique is shown to improve on previouslypublished lower bounds on the capacity of the constraint. I.