This work deals with communication over the AWGN channel with
additive discrete interference, where the sequence of interference
symbols is known causally at the transmitter. We use Shannon's
treatment for channels with side information at the transmitter as a
framework to derive ``optimal precoding" and ``channel code design
criterion" for the channel with known interference at the
transmitter.
Communication over Shannon's state-dependent discrete memoryless
channel where the state sequence is known causally at the
transmitter requires encoding over the so-called \emph{associated}
channel which has exponential input alphabet cardinality with
respect to the number of states. We show that by using at most
linearly many input symbols of the \emph{associated} channel, the
capacity is achievable.
In particular, we consider $M$-ary signal transmission over the AWGN
channel with additive $Q$-ary interference where the sequence of
i.i.d. interference symbols is known causally at the transmitter. We
investigate the problem of maximization of the transmission rate
under the uniformity constraint, where the channel input given any
current interference symbol is uniformly distributed over the
channel input alphabet. For this setting, we propose the general
structure of a communication system with optimal precoding. We also
investigate the extension of the proposed precoding scheme to
continuous channel input alphabet.
We also consider the problem of channel code design with causal side
information at the encoder. We derive the code design criterion at
high SNR by defining a new distance measure between the input
symbols of the Shannon's \emph{associated} channel. For the case of
the binary-input channel, i.e., $M=2$, we show that it is sufficient
to use only two (out of $2^Q$) input symbols of the
\emph{associated} channel in encoding as far as the distance
spectrum of code is concerned. This reduces the problem of channel
code design for the binary-input AWGN channel with known
interference at the encoder to design of binary codes for the binary
symmetric channel where the Hamming distance among codewords is the
major factor in the performance of the code.
| Identifer | oai:union.ndltd.org:WATERLOO/oai:uwspace.uwaterloo.ca:10012/3458 |
| Date | January 2007 |
| Creators | Farmanbar, Hamidreza |
| Source Sets | University of Waterloo Electronic Theses Repository |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
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