\documentclass[10pt,a4paper]{article}
\usepackage{amsmath, mathrsfs}
\usepackage{amssymb, graphicx, epsfig, subfigure}

\title{\textbf{Channel coding}}
\author{Jinkyu Kang}
\date{2008.01.20}

\begin{document}
\maketitle


\section{Simulation result}
Figure 5, 6 show coded error performance with convolutional code.
Figure 5 include Soft and Hard decision for QPSK and 16QAM in
AWGN, figure 6 include Soft and Hard decision for QPSK and 16QAM
in Rayleigh. This figures denote the coded versus uncoded error
performance. As you can see, coded and uncoded error performance
graphs intersect at one point. Coded error performance is worse
than uncoded error performance at low value of $E_{b}/N_{0}$ which
based on intersecting point and is better than uncoded error
performance at high value of $E_{b}/N_{0}$ which based on
intersecting point. Because, if there are more errors within a
block than the code is capable of correcting, the system will
perform poorly. When that intersecting point is crossed, we can
interpret the degraded performance as being caused by the
redundant bits consuming energy but giving back nothing beneficial
in return. As you can see, soft decision is better than hard
decision all the range. For a Gaussian channel, eight-level soft
decision decoding can provide the same probability of bit error as
that of hard-decision decoding, but requires 2dB less
$E_{b}/N_{0}$ for the same performance. However, when figure 5 and
figure 6 compare, improvement of performance by soft decision
decoding in Rayleigh isn't bigger than improvement of performance
by soft decision decoding in AWGN.

\begin{figure}[h]
\centering%
\includegraphics[width=8cm,height=5cm]{BERwithConvolutioncodinginAWGN}\\
\caption{BER Graph with convolution coding in AWGN}\label{fig5}
\end{figure}
\begin{figure}[h]
\centering%
\includegraphics[width=8cm,height=5cm]{BERwithConvolutioncodinginRayleigh}\\
\caption{BER Graph with convolution coding in
Rayleigh}\label{fig6}
\end{figure}

\section{Conclusion}


\end{document}