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Abstract

The relationship between the number of encoder states and the probable size of certain runlength-limited (RLL) codes is derived analytically. By associating the number of encoder states with (generalized) Fibonacci numbers, the minimum number of encoder states is obtained, which maximizes the rate of the designed code, irrespective of the codeword length.

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... Note that the above inequalities are equivalent to the approximate eigenvector equation [1], and they are necessary conditions for code construction. Following these criteria, and by using either computer search or analytical approaches proposed in [18], we can determine the optimum number of encoder states to maximize the rate of the PRC code. The corresponding code rate ...
... First of all, a new (1,18) constrained single-bit even PC code is designed. The rate 9/13 (1,18) code with 5 states (i.e. r = 5, r 1 = 3, r 2 = 2) FSM proposed in [7] is used as the NC code, since its rate is 3.85% higher than that of the rate 2/3 d = 1 codes used in BD and HD-DVD systems. ...
... r = 5, r 1 = 3, r 2 = 2) FSM proposed in [7] is used as the NC code, since its rate is 3.85% higher than that of the rate 2/3 d = 1 codes used in BD and HD-DVD systems. A new rate 12/19 (1,18) code with 5 states is designed as the PRC code, which requires only 1 channel bit per parity bit with respect to the rate 2/3 d = 1 codes. Table I (ii), which also shows that 12-bit user data words can be supported. ...
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This paper proposes a general and systematic code design method to efficiently combine constrained codes with parity-check (PC) codes for optical recording. The proposed constrained PC code includes two component codes: the normal constrained (NC) code and the parity-related constrained (PRC) code. They are designed based on the same finite state machine (FSM). The rates of the designed codes are only a few tenths below the theoretical maximum. The PC constraint is defined by the generator matrix (or generator polynomial) of a linear binary PC code, which can detect any type of dominant error events or error event combinations of the system. Error propagation due to parity bits is avoided, since both component codes are protected by PCs. Two approaches are proposed to design the code in the non-return-to-zero-inverse (NRZI) format and the non-return-to-zero (NRZ) format, respectively. Designing the codes in NRZ format may reduce the number of parity bits required for error detection and simplify post-processing for error correction. Examples of several newly designed codes are illustrated. Simulation results with the Blu-Ray disc (BD) systems show that the new d = 1 constrained 4-bit PC code significantly outperforms the rate 2/3 code without parity, at both nominal density and high density.
... It is much harder to define coding schemas when the coding rate is close to the capacity of the given (d,k) channel. An interesting study on successful allocation of codewords to the encoder states to maximise the code rate is given in Cai and Immink's (2006). The study shows that the number of encoder states, for the certain RLL codes, can always be associated with generalised Fibonacci numbers. ...
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Comprehensive (d,k) sequences study is presented, complemented with the design of a new, efficient, Run-Length Limited (RLL) code. The new code belongs to group of constrained coding schemas with a coding rate of R = 2/5 and with the minimum run length between two successive transitions equal to 4. Presented RLL (4, ∞) code uses channel capacity highly efficiently, with 98.7% and consequently it achieves a high-density rate of DR = 2.0. It is implying that two bits can be recorded, or transmitted with one transition. Coding techniques based on the presented constraints and the selected coding rate have better efficiency than many other currently used codes for high density optical recording and transmission.
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A method and system for encoding a segment of user data words into a segment of code words so that both modulation constraints and a predetermined parity-check constraint are satisfied. Each segment of the user data is partitioned into several data words, and encoded separately by first and second types of component code, which are referred to as the normal constrained code and the parity-related constrained code, respectively. The parity-check constraint over the combined code word is achieved by concatenating the sequence of normal constrained code words with a specific parity-related constrained code word chosen from a candidate code word set. Both the component codes are finite-state constrained codes, which are designed to have rates close to the Shannon capacity. Furthermore, they are based on the same finite state machine (FSM), which enables them to be connected seamlessly, without violating the modulation constraints. Two preferred embodiments are provided to design a code in the non-return-to-zero inverted (NRZI) format and the non-return-to-zero (NRZ) format, respectively. Designing the codes in NRZ format may reduce the number of parity-check bits required for error detection and simplify error correction or post-processing. The parity-check constraint is defined by the parity-check polynomial or parity-check matrix of a systematic linear block code, which could detect any type of dominant error event as well as error event combinations of a given optical recording system. As a result, the information density of the system is improved.
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Bell System Technical Journal, also pp. 623-656 (October)
Chapter
Half-title pageSeries pageTitle pageCopyright pageDedicationPrefaceAcknowledgementsContentsList of figuresHalf-title pageIndex
Chapter
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An abstract is not available.
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A lower bound on the probability of decoding error of quantum communication channel is presented. The strong converse to the quantum channel coding theorem is shown immediately from the lower bound. It is the same as Arimoto's method except for the diculty due to noncommutativity. Keywords Quantum channel coding theorem, average error probability, strong converse, operator monotone 1 Introduction Recently, the quantum channel coding theorem was established by Holevo [9] and by Schumacher and Westmoreland [15], after the breakthrough of Hausladen et al. [7]. Furthermore, a upper bound on the probability of decoding error, in case rate below capacity, was derived by Burnashev and Holevo [2]. It is limited in pure signal state. They conjectured on a upper bound in general signal state, which corresponds to Gallager's bound [5] in classical information theory. We will show a lower bound on the probability of decoding error, in case rate above capacity, which corresponds to Arimoto's bou...
Codes for Mass Data Storage Systems The Netherlands: Shannon Foundation
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K. A. S. Immink, Codes for Mass Data Storage Systems. Den Haag, The Netherlands: Shannon Foundation, 1999.
3016 DK Rotterdam, The Nether-lands (e-mail: immink@iem.uni-due.de; kees@immink.nl)
  • Essen
  • Turing Germany
  • Inc
Essen, Germany, and Turing Machines Inc., 3016 DK Rotterdam, The Nether-lands (e-mail: immink@iem.uni-due.de; kees@immink.nl).
Theory and Applications 93-2218-E-194-012, NSC 94-2213-E-194-013, and NSC 94-2213-E-194-019. The author is with the Department of Communication Engineering
  • S Vajda
  • Lucas Numbers Fibonacci
  • Golden Section
S. Vajda, Fibonacci and Lucas Numbers, and the Golden Section: Theory and Applications. New York: Halsted, 1989. 93-2218-E-194-012, NSC 94-2213-E-194-013, and NSC 94-2213-E-194-019. The author is with the Department of Communication Engineering, National Chung-Cheng University, Min-Hsiung, Chia-Yi, 621 Taiwan, R.O.C.(e-mail: francis@ccu.edu.tw).
High-density recording systems using paritial response maximum likelihood with blue lader diode
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T. Iwanaga, S. Ogkubo, M. Nakano, M. Kubota, H. Honma, T. Ide., and R. Katayama, "High-density recording systems using paritial response maximum likelihood with blue lader diode," Japan J. Appl. Phys., vol. 42, no. 2B, pt. 1, pp. 1042-1043, Feb. 2003.
Codes for Mass Data Storage Systems. Den Haag, The Netherlands: Shannon Foundation
  • K A S Immink
K. A. S. Immink, Codes for Mass Data Storage Systems. Den Haag, The Netherlands: Shannon Foundation, 1999.
  • S Vajda
  • Lucas Numbers
  • The Golden
  • Section
S. Vajda, Fibonacci and Lucas Numbers, and the Golden Section: Theory and Applications. New York: Halsted, 1989.