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MARCO Interconnect Focus Center
People
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
- 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.
- 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.
- B. Ahmad, ”Performance Specification of Interconnects,”
DesignCon
2003.
- A. Sanders, M. Resso, J. D’Ambrosia ”Channel Compliance
Testing
Utilizing Novel Statistical Eye Methodology,” DesignCon
2004.
- 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.
- N. Blitvic, "Channel Coding for High-speed
Links", S.M. thesis, MIT, 2007.
- N. Blitvic, V. Stojanovic, "Performance
estimation of ISI-limited Coded Systems", journal publication
in preparation.
-
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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