Conference Paper

Distance-Enhancing Constrained Codes for Optical Recording Channels

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This paper proposes distance-enhancing constrained codes for optical recording channels. The repeated minimum transition runlength (RMTR) constraints are first investigated, based on error event analysis and capacity calculation. A new RMTR constrained code is then proposed. Compared with the codes used in standard systems, it imposes the minimum achievable RMTR constraint on the channel bit stream with the least decoding window length, without introducing additional code rate loss. A systematic method is further proposed, which can efficiently combine the RMTR code with the parity-check (PC) codes. Simulation results show that the new RMTR constrained PC code performs 1.1 dB better than the 17PP code, at BER = 10<sup>-5</sup> and high recording density.

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Preface to the Second Edition About five years after the publication of the first edition, it was felt that an update of this text would be inescapable as so many relevant publications, including patents and survey papers, have been published. The author's principal aim in writing the second edition is to add the newly published coding methods, and discuss them in the context of the prior art. As a result about 150 new references, including many patents and patent applications, most of them younger than five years old, have been added to the former list of references. Fortunately, the US Patent Office now follows the European Patent Office in publishing a patent application after eighteen months of its first application, and this policy clearly adds to the rapid access to this important part of the technical literature. I am grateful to many readers who have helped me to correct (clerical) errors in the first edition and also to those who brought new and exciting material to my attention. I have tried to correct every error that I found or was brought to my attention by attentive readers, and seriously tried to avoid introducing new errors in the Second Edition. China is becoming a major player in the art of constructing, designing, and basic research of electronic storage systems. A Chinese translation of the first edition has been published early 2004. The author is indebted to prof. Xu, Tsinghua University, Beijing, for taking the initiative for this Chinese version, and also to Mr. Zhijun Lei, Tsinghua University, for undertaking the arduous task of translating this book from English to Chinese. Clearly, this translation makes it possible that a billion more people will now have access to it. Kees A. Schouhamer Immink Rotterdam, November 2004
Conference Paper
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For the optical recording channel, a new runlength-limited (RLL) code is proposed, called the 1102PC code, which is a d = 1 RLL code with a compact 2-to-3 PCWA-mapping for DC-control that offers a significant performance benefit over traditional soft-decodable d = 1, k = 7 codes thanks to the reduced frequency of occurrence of the shortest 2T-runs as realized via an r = 2 RMTR-constraint; in addition, it still offers a low k-constraint (k = 10) and a SISO-complexity much lower than that of 17PP. The 1102PC code has also been evaluated experimentally for near-field optical recording.
We have developed a new error correction method (Picket: a combination of a long distance code (LDC) and a burst indicator subcode (BIS)), a new channel modulation scheme (17PP, or (1, 7) RLL parity preserve (PP)-prohibit repeated minimum transition runlength (RMTR) in full), and a new address format (zoned constant angular velocity (ZCAV) with headers and wobble, and practically constant linear density) for a digital video recording system (DVR) using a phase change disc with 9.2 GB capacity with the use of a red (lambda=650 nm) laser and an objective lens with a numerical aperture (\mathit{NA}) of 0.85 in combination with a thin cover layer. Despite its high density, this new format is highly reliable and efficient. When extended for use with blue-violet (lambda&ap; 405 nm) diode lasers, the format is well suited to be the basis of a third-generation optical recording system with over 22 GB capacity on a single layer of a 12-cm-diameter disc.
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Conference Paper
This paper presents a generalized Braat-Hopkins model for read-only and re-writable optical channels. The objective is to expose the effect of code rate and recording density on the various parameters of the channel model, so that this model can be used to assess the receiver performance for various code rates and recording densities.
Conference Paper
We derive performance bounds on bit error rates and error event probabilities for optical recording channels with d = 1 constraint. The bounds account for the use of various parity codes. They serve as benchmarks for the development of parity codes and post-processing schemes. Computer simulations have been carried out to demonstrate the accuracy of the proposed bounds and to evaluate the performance of various parity codes.
A low-density parity-check code is a code specified by a parity-check matrix with the following properties: each column contains a small fixed number j geq 3 of l's and each row contains a small fixed number k > j of l's. The typical minimum distance of these codes increases linearly with block length for a fixed rate and fixed j . When used with maximum likelihood decoding on a sufficiently quiet binary-input symmetric channel, the typical probability of decoding error decreases exponentially with block length for a fixed rate and fixed j . A simple but nonoptimum decoding scheme operating directly from the channel a posteriori probabilities is described. Both the equipment complexity and the data-handling capacity in bits per second of this decoder increase approximately linearly with block length. For j > 3 and a sufficiently low rate, the probability of error using this decoder on a binary symmetric channel is shown to decrease at least exponentially with a root of the block length. Some experimental results show that the actual probability of decoding error is much smaller than this theoretical bound.
The performance of single-parity codes used in conjunction with the Reed-Solomon error-correcting code (ECC) is investigated. Specifically, the tradeoff between simply increasing ECC power instead of using a parity code is explored.
The performance of magnetic recording systems that include conventional modulation codes combined with multiple parity bits is studied. Various performance measures, including bit error rate at the output of time inverse precoder, byte error probability at the input of the Reed-Solomon (RS) decoder and sector error rate, are used to evaluate the performance of various coding/detection schemes. Suboptimum detection/decoding schemes consisting of a 16-state noise-predictive maximum-likelihood (NPML) detector followed by parity-based noise-predictive post-processing, and maximum-likelihood sequence detection/decoding on the combined channel/parity trellis are considered. For conventional modulation codes, it is shown that although the dual-parity post-processor gains 0.5 dB over the single-parity post-processor in terms of bit- and byte-error-rate performance, the sector-error-rate performance of both schemes is almost the same. Furthermore, the sector-error-rate performance of optimum 64-state combined channel/parity detection for the dual-parity code is shown to be approximately 0.1 dB better than that of optimum 32-state combined channel/parity detection for the single-parity code. These performance gains can be even more substantial if appropriate coding techniques that eliminate certain error events and minimize error burst length or multiparity codes in conjunction with combined parity/channel detection are used
Codes for mass data storage systems, Shannon Founda-tion Publishers, The Netherlands
  • K A S Immink
K.A.S. Immink, Codes for mass data storage systems, Shannon Founda-tion Publishers, The Netherlands, 1999.
Low-Density Parity-Check Codes This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE
  • R G Gallager
R.G. Gallager, Low-Density Parity-Check Codes. Cambridge, MA: MIT Press, 1963. This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2008 proceedings. 978-1-4244-2324-8/08/$25.00 © 2008 IEEE.