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Conference on Optical Transmission Systems and Equipment for Networking V

作者： Djordjevic, Ivan B. Vasic, Bane Univ Arizona Dept Elect & Comp Engn Tucson AZ 85721 USA

ISBN: (纸本)0819464864

High-speed optical transmission systems operating at 40 Gb/s or higher are severely limited by intrachannel nonlinearities such as intrachannel four-wave mixing (IFWM) and intrachannel cross-phase modulation (IXPM). Approaches to deal with intrachannel nonlinearities may be classified into three broad categories: modulation formats, constrained (or line) coding, and equalization techniques. The IFWM is a phase-sensitive effect, and the aim of the first approach is to remove the phase short-term coherence of the pulses emitted in a given neighborhood. The role of constrained coding is to avoid those waveforms in the transmitted signal that are most likely to be received incorrectly. In this paper we describe two alternative techniques for suppression of intrachannel nolinearities: (i) constrained coding techniques, and (ii) combined nonlinear ISI cancellation and error control. Three different constrained coding techniques will be presented: (a) the use of constrained encoding itself, (b) combined constrained and error control coding and (c) deliberate error insertion. The nonlinear ISI cancellation scheme employs the maximum a posteriori probability (MAP) symbol decoding based on Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm, while the forward error correction is based on low-density parity-check (LDPC) codes. The nonlinear ISI channel is modeled by a finite state machine (FSM) whose transition and output functions describe the dependency of the channel statistics and the ISI on transmitted patterns. The BCJR algorithm operates on a trellis of the corresponding FSM, and creates the soft information (detected bit likelihoods) used in the iterative decoder. To improve the BER performance of nonlinear BCJR equalizer further, a noise-predictive BCJR equalizer is introduced. The main feature of these schemes is that they can operate in the regime of very strong intrachannel nonlinearities where FEC schemes such as turbo or LDPC codes are not designed to operate.

关键词： Kerr nonlinearities fiber-optics communications constrained coding forward error correction maximum a posteriori probability (MAP) detection low-density parity-check (LDPC) codes noise-predictive filter

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An efficient modulation technique for suppressing intrachannel FWM in 40Gb/s optical transmission systems

An efficient modulation technique for suppressing intrachann...

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Conference on Optical Transmission Systems and Equipment for Networking V

作者： Batshon, Hussam G. Djordjevic, Ivan B. Vasic, Bane Univ Arizona Dept Elect & Comp Engn Tucson AZ 85721 USA

ISBN: (纸本)0819464864

In high bit-rate return-to-zero (RZ) on-off keying (OOK) systems operating at 40Gb/s and beyond ghost pulses induced by intrachannel four-wave mixing (IFWM), and intrachannel cross-phase modulation (IXPM) are dominant factors affecting the performance of a high-speed optical transmission system. As the creation of ghost pulses is a phase sensitive effect, the common approach to deal with IFWM is to remove short-term phase coherence by employing a proper modulation format. Another approach, known as constrained or line coding, is to identify the most troublesome sequences and to forbid them during encoding process. This paper presents an efficient method for testing the efficiency of a modulation techniques for countering the effects of IFWM by calculating the sum of all the contributors at a given resonance position. For a modulation technique to counter these effects the initial pulses phases must be chosen properly so that different contributors to the ghost pulse creation cancel each other in bit being in "resonance". In addition to this method, we are proposing a modulation technique that shows a significant Q-factor improvement of up to 7.5dB (depending on the number of spans and the phase sequence implemented) over the uncoded RZ-OOK as will be demonstrated. Finally, implementation of this phase modulation technique is very efficient in extending the non-linearity tolerance and enhancing the performance of a high-speed optical transmission system.

关键词： intrachannel four-wave mixing intrachannel cross-phase modulation constrained coding low-density parity-check (LDPC) codes optical communications

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AN APPLICATION OF RAMSEY THEORY TO coding FOR THE OPTICAL CHANNEL

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SIAM JOURNAL ON DISCRETE MATHEMATICS 2005年第4期19卷 921-937页

作者： Kashyap, Navin Siegel, Paul H. Vardy, Alexander Queens Univ Dept Math & Stat Kingston ON K7L 3N6 Canada Univ Calif San Diego Dept Elect & Comp Engn La Jolla CA 92093 USA

In this paper, we analyze bi-infinite sequences over the alphabet {0, 1,..., q - 1}, for an arbitrary q >= 2, that satisfy the q-ary ghost pulse (qGP) constraint. A sequence x = (x(k))(k is an element of Z) is an element of {0, 1, ... , q - 1}(Z) satisfies the qGP constraint if for all k, l, m is an element of Z such that x(k), x(l) and x(m) are nonzero and equal, x(k+l-m) is also nonzero. This constraint arises in the context of coding for communication over a fiber optic medium. We show, using techniques from Ramsey theory, that if x satisfies the qGP constraint, then the set supp(x) = {l is an element of Z : x(l) not equal 0} is the disjoint union of cosets of some subgroup, kZ, of Z, and a set of zero density. We provide much sharper results in the special cases of q = 2 and q = 3. In the former case, we show that the corresponding binary ghost pulse constraint has zero capacity, and based on our results for the latter case, we conjecture that the capacity of the ternary ghost pulse constraint is also zero.

关键词： optical communication constrained coding ghost pulse constraints Ramsey theory

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constrained coding for the deep-space optical channel

Constrained coding for the deep-space optical channel

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Conference on Free-Space Laser Communication Technologies XIV

作者： Moision, B Hamkins, J CALTECH Jet Prop Lab Pasadena CA 91109 USA

ISBN: (纸本)0819443743

We investigate methods of coding for a channel subject to a large dead-time constraint, i.e., a constraint on the minimum spacing between transmitted pulses, with the deep-space optical channel as the motivating example. Several constrained codes designed to satisfy the dead-time constraint are considered and compared on the basis of throughput, complexity, and decoded error-rate. The performance of an iteratively decoded serial concatenation of a modulation code with an outer code is evaluated and shown to provide significant gains over Reed-Solomon concatenated with Pulse Position Modulation.

关键词： constrained coding error-correcting codes convolutional codes Reed-Solomon codes concatenated codes pulse position modulation deep-space communications optical communications

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Soft-output decoding of LDPC-MTR codes concatenation over two-track two-head E²PR4 channel

Soft-output decoding of LDPC-MTR codes concatenation over tw...

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7th International Conference on Telecommunications in Modern Satellite, Cable and Broadcasting Services

作者： Duric, N Fac Engn Novi Sad 21000 Serbia Monteneg

ISBN: (纸本)0780391640

Log-likelihood ratio (LLR) algebra implementation in Boolean logic mappings for maximum transition run (MTR) codes is presented. Consequently, soft-output decoding of low-density parity-check (LDPC) and MTR codes concatenation has been investigated in magnetic recording system. Two-track two-head E(2)PR4 partial response model with symmetrical intertrack interference (ITI) was assumed. Effortless hardware implementation of the soft-output MTR decoder and the overall decoding complexity reduction is offered by proposed simulation scheme, while benefits have been confirmed with the computer simulation results.

关键词： soft-output coding/decoding constrained coding multiple-track multiple-head channel magnetic recording

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Soft-output decoding approach of maximum transition run codes

Soft-output decoding approach of maximum transition run code...

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International Conference on Computer as a Tool (EUROCON 2005)

作者： Duric, N Despotovic, M Fac Engn Novi Sad 21000 Serbia Monteneg

ISBN: (纸本)142440049X

In this paper propagation of soft-output information through the Boolean logic circuits is considered. As the result, an implementation of log-likelihood ratio (LLR) algebra in Boolean logic mappings is presented. The consequence of this approach to the soft-output decoding of maximum transition run (MTR) codes and their utilization in iterative decoding has been simulated and evaluated over E(2)PR4 magnetic recording channel.

关键词： soft-output coding/decoding constrained coding partial response channel magnetic recording

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Links between complexity theory and constrained block coding

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IEEE TRANSACTIONS ON INFORMATION THEORY 2002年第1期48卷 59-88页

作者： Stockmeyer, L Modha, DS IBM Corp Almaden Res Ctr Div Res San Jose CA 95120 USA

The goal of this paper is to establish links between computational complexity theory and the theory and practice of constrained block coding. In particular, the complexities of several fundamental problems in constrained block coding are precisely classified in terms of the existing complexity-theoretic structure. One type of problem studied is that of designing encoder and decoder circuits using minimum or approximately minimum hardware;for our purposes, an "input" to this problem is i) a deterministic, irreducible finite-state transition diagram (abbreviated DIF) defining a set of constrained binary sequences, and ii) a desired rate p : q. Several of these minimum-encoder and minimum-decoder problems are shown to be NP-hard, and more interestingly some are shown to be complete in the second and third levels of the polynomial hierarchy. Another fundamental problem is that of computing the maximum rate of a block code;that is, given a DIF and a codeword length q, find the maximum p such that a rate p : q block code exists for the constraint defined by the DIE This problem is shown to be NP#P-complete. Although it is not known whether NP#P contains problems of super-polynomial complexity, it lies "higher" in the complexity-class structure than N-P in the sense that it is possible, given current knowledge, that NP#P contains problems of super-polynomial complexity even if P = NP. Another question studied is whether maximum rate block codes can always be implemented by encoders and decoders of polynomial size. The answer to this question is shown to be closely related to whether the class #P lies "lower" in the complexity-class structure than currently believed-a proof of either answer would have major implications in complexity theory.

关键词： block code circuit size complexity constrained coding decoder encoder #P polynomial-time hierarchy rate

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Links between complexity theory and constrained block coding

Links between complexity theory and constrained block coding

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IEEE International Symposium on Information Theory

作者： Stockmeyer, L Modha, DS IBM Corp Almaden Res Ctr Div Res San Jose CA 95120 USA

关键词： block code circuit size complexity constrained coding decoder encoder #P polynomial-time hierarchy rate

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Exploiting faster-than-Nyquist signaling

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IEEE TRANSACTIONS ON COMMUNICATIONS 2003年第9期51卷 1502-1511页

作者： Liveris, AD Georghiades, CN Texas A&M Univ Dept Elect Engn College Stn TX 77843 USA

Faster-than-Nyquist signaling introduces inter-symbol interference, but increases the bit rate while preserving the signaling bandwidth. For sinc pulses, it has been established that with a small increase in the signaling rate beyond the Nyquist rate, there is no reduction in the minimum Euclidean distance for binary signaling. In this paper, we generalize these observations to the family of raised-cosine pulses. The structure of the error events that reduce the minimum distance is examined, and constrained coding ideas are suggested that theoretically allow even faster signaling. Then we propose ways of practically achieving these gains by designing appropriate constrained codes and through equalization and iterative joint equalization and decoding (turbo equalization).

关键词： bandwidth-efficient signaling constrained coding long intersymbol interference (ISI) Nyquist rate soft intersymbol interference (ISI) cancellation

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constrained coding for binary channels with high intersymbol interference

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IEEE TRANSACTIONS ON INFORMATION THEORY 1999年第6期45卷 1777-1797页

作者： Karabed, R Siegel, PH Soljanin, E Siemens Microelect Scotts Valley CA 95066 USA Univ Calif San Diego La Jolla CA 92093 USA AT&T Bell Labs Math Sci Res Ctr Murray Hill NJ 07974 USA

Partial-response (PR) signaling 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 higher order partial-response channels, such as the "extended" class-4 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 partial-response channels are the best models of real channels. In this paper, we consider partial-response channels for which ISI is so severe that the channels fail to achieve the matched-filter bound (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 high-rate constrained codes for E(2)PR4 and E(3)PR4 channels and evaluate their performance by simulation.

关键词： constrained coding magnetic recording partial response

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