DT-10

PERFORMANCE OFLOW DENSITY PARITY CHECK (LDPC) CODE? ON HIGH-DENSITY MAGNHI'IC TAPE RECORDING SIGNALS

Shilpi Sahu, Hongwei Song, and B.V.K. Vijaya Kumar Data Storage Systems Center

Camegie Mellon University, Pittsburgh, PA 15213

Introduction Low Density Parity Check (LDPC) codes introduced by Gallager [ I ] are error-comctiag codes. which ih iterative soft decoding sinlulations provide about 468 SNR gain over PRML channels making them iittriictive lor data sloragr applications. We have investigated the perfarmiince of LDPC codes with real high-density magnetic 1:lpe recording signals from metal particle (MP) media. It is believed that LDPC codes may be more appropriate for tape recording systems where the per-channel data rate requirement is significantly lower than that of hard dick drives.

Writing and Reading Blocks of hinwv dilta were encoded with a rate-819 LDPC code. The encoded blocks were write-equalized and were recorded many times on MP3 media at different recording densities, ranging from 250Khpi to 300Khpi. The data was read hack using a head from a commercial LTO tape drive. The analog readhack signal was then IOX oversampled and was fed offline to an equaliiation and timing recovery loop using VCO-haned Muller and Mueller timing e m r detection. The equalization target irrside the phase locked loop (PLL) was EPR4. Output of the PLL was then fed to the LDPC iterative soft decoder. No Run Length Limited code (RLL) was used for these experiments. Each encoded data block w a 4608 bits long and was preceded by a 4T preamble of length 200 bits.

~

Write and Read from tt:ir

Magnetic tape

User LDPC Encoded bits Encoding bits

Estimated ............................................................

............ f ......................................... ~ .... : ................. .Iterative soft decoding

Estimated user bits

Figure 1. Block Diagram of LDFC Code Evaluation with Real Magnetic Tape Recording Signals

Results The results presented here are for a palricular MP3 sample and with a commercia1 LTP tape drive head. This head/media combination was tested at various linear densities from 250 Kbpi to 300 Kbpi. Due to space liniilatioils. wc p i e ~ ~ t ~ t the results for a sample of 10 blocks at 300 Khpi.

Pigure2. ye pattern aner the EPR4 equalizer In the PLL

6

PLL bandwidth O.OOSX/r Estimdled SNR after- 13.3 dB

i 4 r 2

g o cuuilliziltion

-2

-4

-6 i 0 1000 2mO 3000 4000

Channel el'l'on are the e m i x after I Blo I Channel t LDPC Errors 3 thc chiinncl dccodcr in Fieurc I. Ncrt

Table 1. Results after decoding a sample of 10 blocks.

(iter 1-5)

n n n n n m o n o n o

cdunin represents crrors after each LDPC iteration.

In some blocks (e.g., block # 4). LDPC dccodcr can even correct 20 errors. Result.; were ohwrvcd for MI hlncks. ciich block 4608 hits long. Fivcn thc cntrccct timing iiifornutioti, after the channel decoder. -400 errors were ohserved. No errors were ohserved after LDPC decoding. Table I shows that eYen at 300Khpi. full potential of LDPC iterative decoding is yet to be exploited.

Conclusion Our results suggest that itcriltive LDPC decoding can play an importnnt rnle in increasing the linear recording density of magnetic tape vecording system.;. Howcvcr, ilt high rrcordirrg dcmsitics. iinotlm signific:int problcm is hccaiisc of timing rccovcry ilf low SNRc. M;my blocks suffer from Inss of lock due to paor timing rccnrery. So, along udh the implementation of LDPC codes, advmced signal processing and timing recovery schemes 121 need to he employed. We will present at the conference results at even higher densities. hut with more advanced timing recovery.

References [ I1 R.G. Gallager, Low Detisilj Porilj CRcd ro&s. Cambridge, MA, MIT Press, 1963. [2] I. Liu, H. Song, and B. V. K. Vijaye Kumiir, S p h o l 7inziqq Rernvo:\. for Lonm-SNR Parrial R C S ~ O I Z S C Rerorrliiig Cliomels, IEEE ClokCom 2002.

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