This thesis focuses on designing Low-Density Parity-Check (LDPC)
codes for forward-error-correction. The target application is
real-time multimedia communications over packet networks. We
investigate two code design issues, which are important in the
target application scenarios, designing LDPC codes with low
decoding latency, and constructing capacity-approaching LDPC codes
with very low error probabilities.
On designing LDPC codes with low decoding latency, we present a
framework for optimizing the code parameters so that the decoding
can be fulfilled after only a small number of iterative decoding
iterations. The brute force approach for such optimization is
numerical intractable, because it involves a difficult discrete
optimization programming. In this thesis, we show an asymptotic
approximation to the number of decoding iterations. Based on this
asymptotic approximation, we propose an approximate optimization
framework for finding near-optimal code parameters, so that the
number of decoding iterations is minimized. The approximate
optimization approach is numerically tractable. Numerical results
confirm that the proposed optimization approach has excellent
numerical properties, and codes with excellent performance in terms
of number of decoding iterations can be obtained. Our results show
that the numbers of decoding iterations of the codes by the proposed
design approach can be as small as one-fifth of the numbers of
decoding iterations of some previously well-known codes. The
numerical results also show that the proposed asymptotic
approximation is generally tight for even non-extremely limiting
cases.
On constructing capacity-approaching LDPC codes with very low error
probabilities, we propose a new LDPC code construction scheme based
on $2$-lifts. Based on stopping set distribution analysis, we
propose design criteria for the resulting codes to have very low
error floors. High error floors are the main problems of previously
constructed capacity-approaching codes, which prevent them from
achieving very low error probabilities. Numerical results confirm
that codes with very low error floors can be obtained by the
proposed code construction scheme and the design criteria. Compared
with the codes by the previous standard construction schemes, which
have error floors at the levels of $10^{-3}$ to $10^{-4}$, the codes
by the proposed approach do not have observable error floors at the
levels higher than $10^{-7}$. The error floors of the codes by the
proposed approach are also significantly lower compared with the
codes by the previous approaches to constructing codes with low
error floors.
| Identifer | oai:union.ndltd.org:WATERLOO/oai:uwspace.uwaterloo.ca:10012/3440 |
| Date | January 2007 |
| Creators | Ma, Xudong |
| Source Sets | University of Waterloo Electronic Theses Repository |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
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