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<H1><FONT color=#9400d3><FONT size=+4>Turbo Code
Demo</FONT></FONT></H1></CENTER>
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<H2><IMG src="Turbo Code Demo.files/new.gif"><FONT color=#ff1493>MATLAB code for
experiment on turbo codes (updated June 07, 1999).</FONT></H2>The following
MATLAB funtions will allow you to simulate the classical Turbo Coding system,
which is also known as parallel concantenated convolutional codes. They are
written to be shared with fellow researchers working on Turbo Codes. Please
download all the .m files and run <B>turbo_sys_demo.m</B> file in MATLAB
environment.
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</CENTER>This <B>NEW</B> version includes both the Log-MAP [1] and SOVA [2]
algorithms for decoding. The information bits are randomly generated which
assume a uniform distribution. For each frame of bits, a random interleaver is
generated for it. Thus the code performance stands for the average performance
among all interleavers. You can set the following parameters yourself:
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<TD><IMG src="Turbo Code Demo.files/redball.gif">decoding algorithm (
Log-MAP / SOVA )</TD></TR>
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<TD><IMG src="Turbo Code Demo.files/redball.gif">frame size</TD>
<TD><IMG src="Turbo Code Demo.files/redball.gif">code generator</TD>
<TD><IMG src="Turbo Code Demo.files/redball.gif">puncture /
unpuncture</TD></TR>
<TR>
<TD><IMG src="Turbo Code Demo.files/redball.gif">maximum number of
iterations</TD>
<TD><IMG src="Turbo Code Demo.files/redball.gif">number of frame errors to
terminate</TD>
<TD><IMG src="Turbo Code Demo.files/redball.gif">signal to noise ratio (
Eb / No )</TD></TR></TBODY></TABLE></CENTER>
<UL>
<LI><A href="http://www.ee.vt.edu/~yufei/turbo/bin_state.m">bin_state.m </A>,
utility to convert an integer to a vector of binary bits.
<LI><A
href="http://www.ee.vt.edu/~yufei/turbo/demultiplex.m">demultiplex.m</A>,
serial to parallel demultiplex at the receiver.
<LI><A href="http://www.ee.vt.edu/~yufei/turbo/encode_bit.m">encode_bit.m
</A>, two RSC (Recursive Systematic Convolutional) encoder to encode frames of
information bits. a single bit.
<LI><A href="http://www.ee.vt.edu/~yufei/turbo/encoderm.m">encoderm.m </A>,
turbo encoding process.
<LI><A href="http://www.ee.vt.edu/~yufei/turbo/int_state.m">int_state.m </A>,
utility to convert from vector of bits to integer.
<LI><A href="http://www.ee.vt.edu/~yufei/turbo/logmapo.m">logmapo.m </A>,
Log-MAP component decoder.
<LI><A href="http://www.ee.vt.edu/~yufei/turbo/rsc_encode.m">rsc_encode.m
</A>, encodes a block of data using a RSC encoder.
<LI><A href="http://www.ee.vt.edu/~yufei/turbo/sova0.m">sova0.m </A>, SOVA
(Soft Output Viterbi Algorithm) component decoder.
<LI><A href="http://www.ee.vt.edu/~yufei/turbo/trellis.m">trellis.m</A>, set
up the trellis for a given code generator.
<LI><A
href="http://www.ee.vt.edu/~yufei/turbo/turbo_sys_demo.m">turbo_sys_demo.m
</A>, turbo encoding and turbo decoding system simulation. Topmost function.
<B><FONT color=#ff00ff>Start Here!</FONT><I><FONT color=#004000>(An error
corrected for SOVA application!)</FONT></I></B> </LI></UL>
<P><BR><FONT face=Arial,Helvetica>[1] <I>Patrick Robertson, Peter Hoeher,
</I></FONT><I><FONT face="Arial Black">Optimal and sub-optimal maximum a
posteriori algorithms suitable for turbo decoding</FONT><FONT
face=Arial,Helvetica>, European Trans. on Telecommun.,Vol. 8, No. 2, March-April
1997, p. 119-125.</FONT></I><FONT face=Arial,Helvetica></FONT>
<P>[2] <I><FONT face=Arial,Helvetica>Joachim Hagenauer, Elke Offer, and Lutz
Papke, </FONT><FONT face="Arial Black">Iterative decoding of binary block and
convolutional codes</FONT><FONT face=Arial,Helvetica>, IEEE Trans. Inform.
Theory, Vol. 42, No. 2, March 1996, p. 429-445.</FONT></I>
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<H2><FONT color=#ff1493>Some simulation results</FONT></H2><I><U><FONT
color=#000099><FONT size=+1>1. Small frame size:</FONT></FONT></FONT></U></I>
<H3><I><FONT size=+0>Setting:</FONT></I></H3>
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<TD><IMG src="Turbo Code Demo.files/blueball.gif">frame size = 1024</TD>
<TD><IMG src="Turbo Code Demo.files/blueball.gif">code generator = [07;
05] (default)</TD>
<TD><IMG src="Turbo Code Demo.files/blueball.gif">punctured (default) into
rate 1/2</TD></TR>
<TR>
<TD><IMG src="Turbo Code Demo.files/blueball.gif">maximum number of
iterations = 8</TD>
<TD><IMG src="Turbo Code Demo.files/blueball.gif">terminate with frame
errors 30</TD></TR></TBODY></TABLE></CENTER>
<H3><I><FONT size=+0>Plots:</FONT></I></H3>
<UL><IMG src="Turbo Code Demo.files/redball.gif"><A
href="http://www.ee.vt.edu/~yufei/turbo/demolber.jpg">Bit Error Rate with
Log-MAP, Eb/N0 = [1.0:0.5:2.5]</A>
<P></P><IMG src="Turbo Code Demo.files/redball.gif"><A
href="http://www.ee.vt.edu/~yufei/turbo/demolfer.jpg">Frame Error Rate with
Log-MAP, Eb/N0 = [1.0:0.5:2.5]</A>
<P></P><IMG src="Turbo Code Demo.files/redball.gif"><A
href="http://www.ee.vt.edu/~yufei/turbo/demosber.jpg">Bit Error Rate with
SOVA, Eb/N0 = [1.5:0.5:3.0]</A>
<P></P><IMG src="Turbo Code Demo.files/redball.gif"><A
href="http://www.ee.vt.edu/~yufei/turbo/demosfer.jpg">Bit Error Rate with
SOVA, Eb/N0 = [1.5:0.5:3.0]</A>
<P></P></UL><I><U><FONT color=#000099><FONT size=+1>2. Large frame size
</FONT></FONT></U></I>(original setting in Berrou's paper with Log-MAP):
<H3><I><FONT size=+0>Setting:</FONT></I></H3>
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<TD><IMG src="Turbo Code Demo.files/blueball.gif">frame size = 65536</TD>
<TD><IMG src="Turbo Code Demo.files/blueball.gif">code generator = [037;
021]</TD>
<TD><IMG src="Turbo Code Demo.files/blueball.gif">punctured into rate
1/2</TD></TR>
<TR>
<TD><IMG src="Turbo Code Demo.files/blueball.gif">maximum number of
iterations = 18</TD>
<TD><IMG src="Turbo Code Demo.files/blueball.gif">terminate with frame
errors 35</TD>
<TD><IMG src="Turbo Code Demo.files/blueball.gif">Eb/N0 = 0.2 - 2
db</TD></TR></TBODY></TABLE></CENTER>
<H3><I><FONT size=+0>Plots:</FONT></I></H3>
<UL><IMG src="Turbo Code Demo.files/redball.gif"><A
href="http://www.ee.vt.edu/~yufei/turbo/berrouber.jpg">Bit Error Rate</A> is
lower than 1e-5 at 0.7 db, which is 0.5 db from the Shannon limit. Notice the
error floor after it.
<P></P><IMG src="Turbo Code Demo.files/redball.gif"><A
href="http://www.ee.vt.edu/~yufei/turbo/berroufer.jpg">Frame Error Rate</A>
doesn't drop as much.
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<H3><IMG src="Turbo Code Demo.files/mailbutt.gif">Please send your precious
comment to:</H3>
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<ADDRESS><A href="mailto:yufei@vt.edu">yufei@vt.edu</A></ADDRESS></CENTER>
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Back to <A href="http://www.ee.vt.edu/valenti/turbo.html">Turbo Codes
</A>homepage
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