Integrated Systems Group | Prof. Vladimir Stojanovic
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TECHNIQUES FOR PERFORMANCE ESTIMATION OF CODED HIGH-SPEED LINKS

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MARCO Interconnect Focus Center

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Natasa Blitvic, Professor Lizhong Zheng, Professor Vladimir Stojanovic


Exact performance analysis of a coded communication system over a channel with long memory typically requires a combinatorial search, and is therefore impractical, if not prohibitive, due to the size of the resulting state-space. Many communication systems have little need for exhaustive simulations of this type, as they employ sophisticated equalization and/or modulation techniques with channel shortening to limit the number of channel states presented to the encoder/decoder blocks. These powerful methods bring the unwanted channel memory to a negligible level so that it can be treated as mean distortion and added to the noise term in the Gaussian
Signal-to-Interference-and-Noise (SINR) representation of the Bit-Error-Rate (BER). In some systems however, additional constraints on the system complexity (power, area) limit the extent to which the channel-memory can be controlled. This leaves a significant portion of unwanted channel memory as residual intersymbol-interference (ISI) and causes difficulty in accurate performance estimation, especially for systems operating with coded data. Monte Carlo-type simulators have the disadvantage of requiring a large number of samples for accurate performance estimation at low error rates. Sample-size reduction methods, such as importance sampling, exist, but long channel memory reduces their effectiveness of due to the dimensionality effect [1]. For channels with long memory, analytically computing the probability distributions associated with received signal is common practice [2]–[4] but all such simulators assume the transmitted symbols to be independent.

This work considers several techniques for rare-event simulation and performance estimation of channels with long memory. The resulting techniques are of particular use in performance estimation of high-speed links. Since the error rate of a pattern-eliminating code (PEC) is given by a closed-form expression [5], the work focuses instead on classical error control codes, with particular emphasis on systematic block codes.

Based on the characterization of the error mechanisms, introduced in [6], different simulation techniques are proposed in [7]. A useful technique for computing probability densities in a coded system, regardless of the underlying error mechanism, is introduced in [8]. The technique targets systematic linear block codes in particular and is based on a divide-and-conquer approach to computing probability densities. For a given code, the complexity of the method increases linearly with channel length. In contrast to the combinatorial approach, the complexity increases linearly with the number of information bits in a codeword. However, the complexity increases exponentially with the number of parity bits so the technique is of most use for high-rate codes. The accuracy of the method is controllable, so, given an adequate channel model, the results are valid at arbitrarily low error rates.

 

References

  1. P.J. Smith, M. Shafi, H. Gao ”Quick simulation: a review of importance
    sampling techniques in communications systems,” IEEE Journal on
    Selected Areas in Communications,vol. 15, no. 4, pp. 597-613, 1997.
  2. B.K. Casper, M. Haycock, R. Mooney ”An accurate and efficient analysis
    method for multi-Gb/s chip-to-chip signaling schemes,” IEEE Symposium
    on VLSI Circuits, pp. 54-57, June 2002.
  3. B. Ahmad, ”Performance Specification of Interconnects,” DesignCon
    2003.
  4. A. Sanders, M. Resso, J. D’Ambrosia ”Channel Compliance Testing
    Utilizing Novel Statistical Eye Methodology,” DesignCon 2004.
  5. N. Blitvic, L. Zheng, V. Stojanovic, "Low-complexity Pattern-eliminating Codes for ISI-limited Channels," to be presented at the IEEE International Conference on Communications, Beijing, China, 19-23 May, 2008.
  6. N. Blitvic, "Channel Coding for High-speed Links", S.M. thesis, MIT, 2007.
  7. N. Blitvic, V. Stojanovic, "Performance estimation of ISI-limited Coded Systems", journal publication in preparation.
  8. N. Blitvic, V. Stojanovic, "Statistical Simulator for Block Coded Channels with Long Residual Interference", presented at the IEEE International Conference on Communications, Glasgow, Scotland, 24-28 June, 2007. [paper] [talk]
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