Abstract — We give a polynomial-time construction of the set of sequences that satisfy a finite-memory constraint defined by a finite list of forbidden blocks, with a specified set of bit positions unconstrained. Such a construction can be used to build modulation/error-correction codes (ECC codes) like the ones defined by the Immink-Wijngaarden scheme in which certain bit positions are reserved for ECC parity. We give a lineartime construction of a finite-state presentation of a constrained system defined by a periodic list of forbidden blocks. These systems, called periodic-finite-type systems, were introduced by Moision and Siegel. Finally, we present a linear-time algorithm for constructing the minimal periodic forbidden blocks of a finite sequence for a given period. Index Terms — Directed acyclic word graph (DAWG), finitememory systems, finite-state encoders, forbidden blocks, maximum transition run (MTR) codes, modulation codes, periodicfinite-type (PFT) systems, run-length limited (RLL) codes. I.

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A general and systematic code design methodology is proposed to efficiently combine constrained codes with PC codes for data storage channels. The proposed constrained PC code includes two component codes: the normal constrained (NC) code and the parity-related constrained (PRC) code. The NC code can be any distance-enhancing constrained code, such as the maximum transition run (MTR) code or repeated minimum transition runlength (RMTR) code. The PRC code can be any linear binary PC code. The constrained PC codes can be designed either in non-return-to-zero-inverse (NRZI) format or non-return-to-zero (NRZ) format. The rates of the designed codes are only a few tenths of a percent below the theoretical maximum. The proposed code design method enables soft information to be available to the PC decoder and facilitates soft decoding of PC codes. Furthermore, since errors are corrected equally well over the entire constrained PC codeword, error propagation due to parity bits is avoided. Efficient finite-state encoding methods are proposed to design capacity-approaching constrained codes and constrained PC codes with RMTR or MTR constraint. The generality and efficiency of the proposed code design methodology are shown by various code design examples for both magnetic and optical recording channels. Index Terms Distance-enhancing constrained codes, error correction codes (ECCs), parity-check codes, finitestate encoding method, post-processor, soft decoding. 2 I.

Several algorithms for the construction of maximum run-length limited codes are presented that are based on the sequence replacement technique. This technique effectively converts an input sequence into a constrained sequence in which a prescribed subsequence is forbidden to occur. The proposed algorithms show how all forbidden subsequences can be successively or iteratively removed to obtain a constrained sequence and how special subsequences can be inserted at predefined positions in the constrained sequence to represent the indices of the positions where the forbidden subsequences were removed. Several enhancements for providing effective error control are presented as well. The proposed algorithms prove to be very efficient and The rates of the constructed codes are close to their theoretical maximum. The proposed algorithms prove to be very efficient and are thus of practical importance for use in storage systems and data networks.

We examine the issue of scaling magnetic tape-recording to higher areal densities, focusing on the challenges of achieving 100 Gb/in 2 in the linear tape format. The current highest achieved areal density demonstrations of 6.7 Gb/in 2 in the linear tape and 23.0 Gb/in 2 in the helical scan format provide a reference for this assessment. We argue that controlling the head–tape interaction is key to achieving high linear density, whereas track-following and reel-to-reel servomechanisms as well as transverse dimensional stability are key for achieving high track density. We envision that advancements in media, data-detection techniques, reel-to-reel control, and lateral motion control will enable much higher areal densities. An achievable goal is a linear density of 800 Kb/in and a track pitch of 0.2 lm, resulting in an areal density of 100 Gb/in 2. A. J. Argumedo