This paper presents the application of a new MAP algorithm to perpendicular recording in the presence of jitter noise

Ahmed, M.

Farhner, A.

Shah, P.

English

Middlesex University Research Repository

ASYMMETRIC MAP DECODING FOR PERPENDICULAR MAGNETICRECORDING WITH DATA DEPENDENT NOISEM.Z. Ahmed1, A. Fahrner2 and P. Shah11CRIST, University of Plymouth, PL4 8AA Devon, UK2TAIT, University of Ulm, D-89081 Ulm, GermanyIntroduction : This paper presents theapplication of a new MAP algorithm toperpendicular recording in the presence of jitternoise. Respecting the limit on references, thefollowing four references are provided as thefundamental basis for this work. For MaximumA Posteriori (MAP) decoding on trellis’s[1] andprevious work on jitter noise for longitudinalmagnetic recording[2]. For the perpendicularchannel model, we assume a hyperbolic tangentreadback signal from an isolated transition u(t),given byu(t) = tanh(ln(3)tD50)(1), where D50 is the normalised user density[3] andthe target Partial Response given in [4].We will present a modified trellis basedalgorithm that accounts for the differencesbetween electronics and jitter noise in the metriccomputations. The fact that the jitter noise isgreater in transitions compared to where there areno transitions can result in improved reliability ofthe metric computation. It has been found thatthis provides gains in performance over classicalMAP algorithms that assume the noise is not datadependent.Channel Model :Fig. 2bUser DataEncoderECCECCDecoderDibit Response0.5MAP/MLSDDecoder{−1,+1}{0,1}σΝ(0,  )PRh(t)Equalisationn(t)s(t)j(t)r(t)JitterGeneratorBERMeasurement PointBERMeasurement PointFig 2aFig. 1 : Simulation Block DiagramThe error correction code (ECC) is a (4096,3072)LDPC code. The received signal r(t) can bedescribed by the following equationr(t) = h(t) ∗ (s(t) + j(t) + n(t)) (2)where h(t) is the impulse response of the PRequaliser, s(t) is the channel readback waveform(with ISI), j(t) is the transition jitter noise andn(t) is AWGN, or the electronics noise and ∗denotes convolution. We use noise predictionwithin the decoder, resulting in the Log–MAPdecoded signal being described asr(t) = h(t) ∗ s(t) + j(t) + n(t) (3)Asymmetric Decoder (AD) : The ADincludes 1 addition and 1 mul per branchmetric computation in addition to the classicLog–MAP trellis decoder. Additionally, thedecoder uses the input branch labels to determineif a particular path would include transition noise,so two consecutive state needs to be consideredbefore the state metric is updated. Thisincreases the computational complexity will beexponential as more terms around the transitionare considered, and is seen as a limitation forhigher D50. The results compare fixed electronicsSNR, and varying the maximum transition jitterwithin a sector of 4096 bits are shown forGPR[0.74,0.83,0.33,0.08,0.01] at D50 = 1.0.1.0e-051.0e-041.0e-031.0e-021.0e-011.0e+000.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Bit Error RatePercentage Transitions in SectorBER with Fixed Electronics NoiseAD tmax/T = 0.0AD tmax/T = 0.5BCJR tmax/T = 0.0BCJR tmax/T = 0.51.0e-051.0e-041.0e-031.0e-021.0e-011.0e+000.0 0.1 0.2 0.3 0.4 0.5Bit Error RatePercentage Jitter tmax/TBER with Fixed Electronics NoiseADBCJRFig. 2 : (a) BER vs. percentage of transi-tions, measured before ECC, and (b)BER vs. maximum jitter, measured after ECC.The transition jitter is specified by tmax/T wheretmax represents the maximum deviation in a bitperiod T . The variance of n(t) for Fig 2a and Fig2b are different, and were chosen for convenience.Conclusion and Future Work : Results show aconsistent improvement over BCJR with the use ofECC, however improvements are also dependanton the percentage of transitions, and show amaximum at 60%. Of interest is the fact thatalthough the improvement in channel BER is notvery much, the gain in decoded BER (Fig 2b) is1 order of magnitude for large tmax/T . The jitternoise has been found not to be strictly Gaussian,due to the non–linear effect of ISI, and the futurework will investigate on the use of more accurateprobability density functions to decode it.REFERENCES : 1L. Bahl et al, IEEE TransInfo, 20, 284(1974). 2W. Zeng et al, IEEE TransMagn, 28(5), 2895(1992). 3Y. Okamoto et al, TechReport IEICE, MR2000–8, 1(2000). 4W. Tan etal, JMMM, 287(2005), 397–404.

Asymmetric MAP decoding for perpendicular magnetic recording

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Asymmetric MAP decoding for perpendicular magnetic recording

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