4 Schemes to Reduce Computational Complexity of 2D-MAP
5.3 Other Implementation Issues
The architecture of 2D-MAP detector is an array of the aforementioned basic processing elements. As the feasible page size grows with improvement of material technology, it may become impractical for the detector array to cover the entire page, so that a block-wise operation needs to be devised. The determination of the coverage range depends on a trade-off between the hardware cost and throughput rate. For example, assume a basic processing element consisting of 50 adders and 1 multiplier operates at a basic clock cycle of 400 MHz. Then it takes around 10 basic clock cycles to complete one iteration. That is, the iteration clock is around 40 MHz. In the scheme of iteration reduction, we know the detection usually converges within around 10
iterations, so the complete detection for one pixel takes roughly 0.25 μsec. If the coverage range contains N pixels, the throughput rate would be N bit/0.25 μsec = 4N Mbit/sec. As is seen, higher throughput rate is acquired at the cost of more basic processing elements. To satisfy a data transfer rate of 160 Mbit/sec, as is specified for
tapestry
TM300r, a latest product from InPhase TechnologiesInc. [3], we will then need 40 basic processing elements.A quite rough idea of trade-off in hardware implementation is provided above.
However, more details in the hardware design are remained to be considered. Some examples are suggested below. First, the resource sharing between basic processing elements: although these processing elements are designed to work in parallel, some hardware resource can still be shared among them, such as the multipliers which are only active before every round of iteration starts. A balance has to be found between parallelism and independence. Second, the scheduling of tasks in one basic processing element needs to be considered too, so as to efficiently utilize the hardware resources.
Third, the coverage range of detector array must overlap in some extent with each other so as to take care of boundaries in the coverage. This is a factor we omit for simplicity in previous implementation example. The presence of redundancy could lead to a decrease in final throughput rate. Additional design work must also be done in the future before a final implementation strategy can be established.
Chapter 6
Conclusion and Outlook
In this thesis, the channel characteristics are first described for holographic data storage systems by introducing two channel models: the complete channel model, which most accurately depicts the realistic channel condition, and the incoherent intensity channel model, which is a simplified and linearized version of the former one.
The first model helps us derive more general conclusions from simulations, while the second one, though not appropriate for all kinds of channel settings, facilitates simpler detector design.
To combat IPI, which severely deteriorates signal fidelity, two iterative detection schemes have been presented: the hard detection scheme, PDFE, and the soft detection scheme, 2D-MAP detection. They are intended to approximate the optimal MLPD by iteratively updating the hard decision or LLR on each pixel through combining information from corresponding neighborhood and the pixel itself. The simulations turn out that 2D-MAP detection greatly outperforms PDFE.
Then, to reduce the computational complexity of 2D-MAP detection, a suite of schemes have been proposed and effectively reduced the number of iterations, the
number of candidates, and the number of arithmetic operations associated with each candidate. With the complete channel model, the total number of additions and multiplications are reduced to 13.9% and 19.5% respectively. And with the incoherent intensity channel model, the total number of additions and multiplications can be further reduced to 7.4% and 0.27% owing to an extra scheme of multiplication reduction. The amount of arithmetic operations has been significantly decreased, while the performance degradation is verified to be negligible.
In addition to improving the algorithm, the hardware implementation is also considered. We have proposed the design for basic processing element of this fully-parallel detection scheme, and then some other implementation issues are discussed, suggesting a few possible research directions in the future.
In summary, to mitigate the undesirable IPI effect, this thesis follows an approach from the view of digital signal processing, and eventually suggests a powerful detecting strategy with reduced computational complexity for the next-generation optical storage system.
Bibliography
[1] Wikipedia, http://en.wikipedia.org/wiki/, entries “History of Optical Storage Media”, “Blu-ray Disc”, “Holographic Versatile Disc”.
[2] Optware Corp., official website, http://www.optware.co.jp.
[3] InPhase Technologies Inc., official website, http://www.inphase-technologies.com [4] “Holographic data storage”, Psaltis D.(California Institute of Technology), Burr
G.W.(IBM Almaden Research Canter), COMPUTER Magazine, Vol. 31, Issue 2, Feb. 1998, Page: 52-60.
[5] V. Vadde and B. Kumar, "Channel modeling and estimation for intrapage
equalization in pixel-matched volume holographic data storage," Applied Optics, vol. 38, pp. 4374-4386, Jul 1999.
[6] M. Keskinoz and B. Kumar, "Discrete magnitude-squared channel modeling, equalization, and detection for volume holographic storage channels," Applied
Optics, vol. 43, pp. 1368-1378, Feb 2004.
[7] Chi-Yun Chen and Tzi-Dar Chiueh, “A Low-Complexity High-Performance Modulation Code for Holographic Data Storage,” unpublished.
[8] G. W. Burr, J. Ashley, H. Coufal, R. K. Grygier, J. A. Hoffnagle, C. M. Jefferson, and B. Marcus, “Modulation coding for pixel-matched holographic data storage,”
Opt. Lett. 22, 639–641 (1997).
[9] M. M. Wang, S. C. Esener, F. B. McCormick, I. C okgr, A. S. Dvornikov, and P.
M. Rentzepis, "Experimental characterization of a two-photon memory," Opt. Lett.
22, 558-560 (1997).
[10] B. H. Olson, R. Paturi, and S. C. Esener, "Biorthogonally accessed
three-dimensional two-photon memory for relational database operations,"
Applied Optics, vol. 36, pp. 3877-3888, Jun 1997.
[11] J. F. Heanue, K. Gurkan, and L. Hesselink, "Signal detection for page-access optical memories with intersymbol interference," Applied Optics, vol. 35, pp.
2431-2438, May 1996.
[12] M. Mark A. Neifeld, IEEE, K. M. Chugg, and B. M. King, "Parallel data
detection in page-oriented optical memory," Optics Letters, vol. 21, p. 3, Mar. 27 1996.
[13] Xiapeng Chen, Keith M. Chugg, and M. A. Neifeld, "Near-Optimal Parallel Distributed Data Detection for Page-Oriented Optical Memories," IEEE Journal of Selected Topics in Quantum Electronics, vol. 4, p. 14, September 1998.
[14] W. C. Chou and M. A. Neifeld, "Soft-decision array decoding for volume holographic memory systems," Journal of the Optical Society of America a-Optics Image Science and Vision, vol. 18, pp. 185-194, Jan 2001.
[15] M. A. Neifeld and Y. Wu, "Parallel image restoration with a two-dimensional likelihood-based algorithm," Applied Optics, vol. 41, pp. 4812-4824, Aug 2002.
[16] P. M. Shankar and M. A. Neifeld, "Multiframe superresolution of binary images,"
Applied Optics, vol. 46, pp. 1211-1222, Mar 2007.
[17] J. Hagenauer, E. Offer, and L. Papke, “Iterative decoding of binary block and convolutional codes,” IEEE Trans. Inf. Theory 42, 409–445 (1996).
[18] R. Y. Shao, S. Lin, and M. P. C. Fossorier, "Two simple stopping criteria for turbo decoding," IEEE Transactions on Communications, vol. 47, pp. 1117-1120, Aug 1999.
[19] J. Heo, K. Chung, and K. M. Chugg, "Simple stopping criterion for min-sum iterative decoding algorithm," Electronics Letters, vol. 37, pp. 1530-1531, Dec 2001.