We present advanced combinatorial techniques for constructing maximum runlength-limited (RLL) block codes and maximum transition run (MTR) codes. These codes find widespread application in recording systems. The propo...
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We present advanced combinatorial techniques for constructing maximum runlength-limited (RLL) block codes and maximum transition run (MTR) codes. These codes find widespread application in recording systems. The proposed techniques are used to construct a high-rate multipurpose modulation code for recording systems. The code, a rate 16/17, (0, 3, 2, 2) MTR code, that also fulfills (0, 15, 9, 9) RLL constraints is a high-rate distance-enhancing code with additional constraints for improving timing and gain control. The encoder and decoder have a particularly efficient architecture and allow an instantaneous translation of 16-bit source words into 17-bit codewords and vice versa. The code has been implemented in Lucent read-channel chips and has excellent performance.
During the past few years, significant progress has been made in defining high capacity constraints which prohibit specified differences between constrained sequences, thus ensuring that the minimum distance between t...
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During the past few years, significant progress has been made in defining high capacity constraints which prohibit specified differences between constrained sequences, thus ensuring that the minimum distance between them is larger than for the uncoded system. However, different constraints which avoid the same prescribed set of differences may have different capacities, and codes into such constraints may have different complexity of encoder/decoder architecture and different performance on more realistic channel models. These issues, which have to be considered in application of distance enhancing codes, are discussed here. We define several distance enhancing constraints which support design of high rate codes. We also define weak constraints for which the minimum distance between sequences may be the same as for the uncoded system but the number of pairs of sequences at the minimum distance is smaller. These constraints support design of even higher rate codes. We discuss the implementation issues of both types of constraints as well as their performance on the ideal channel and channels with colored noise and intertrack interference.
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 ...
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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 growth rate, 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.
A new twins constraint for maximum transition run (MTR) codes is introduced to eliminate quasi-catastrophic error propagation in sequence detectors for generalized partial response channels with spectral nulls both at...
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A new twins constraint for maximum transition run (MTR) codes is introduced to eliminate quasi-catastrophic error propagation in sequence detectors for generalized partial response channels with spectral nulls both at de and at the Nyquist frequency. Two variants of the twins constraint that depend on whether the generalized partial response detector trellis is unconstrained or j -constrained are studied. Deterministic finite-state transition diagrams that present the twins constraint are specified, and the capacity of the new class of MTR constraints is computed. The connection between (G, I) constraints and MTR(j)) constraints is clarified. Code design methodologies that are based on look-ahead coding in combination with violation detection/substitution as well as on state splitting are used to obtain several specific constructions of high-rate MTR codes.
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