ofdm_ldpc_sse2.lyx

软件无线电的平台

Figure 8: Using Packed addition in program.
\layout Standard

On the cnode side, 8 short integers are converted to 8 
\emph on 
floats
\emph default 
, 4 each in two xmm registers because there is no instruction for parallel
 divide of integers .
 lookup_tanh() of the messages is stored in the 3Dimensional array so that
 we don't need to call it again while calculating the message for vnode.
\layout Standard
\added_space_bottom bigskip 
vtomessage=lookup_atanh
\begin_inset Formula $(\frac{product}{lookup\_ tanh(cmessage)})$
\end_inset 


\layout Standard
\align center 

\begin_inset Graphics
	filename cnode.fig
	scale 60
	keepAspectRatio

\end_inset 


\layout Standard

Figure 9: Intermediate conversions between floats and integers for packed
 multiplication and division
\layout Standard

Now the division is also done parallely on each xmm register containing
 4 
\emph on 
floats
\emph default 
 each.
 Before sending the message to the vnodes the messages are converted back
 to short integers.
 We can see two chains of operations in Figure 9.
 We do the operations on the left and right chains in an interleaved manner
 i.e we do one operation on the left chain and then the same operation on
 the right chain.
 Like this, we can optimise a bit because the Pentium 4 processor can perform
 these operations parallelly as these operations are performed on different
 registers.
\layout Standard

We also used SSE instructions which worked on aligned memory because it
 was faster.
 For this we ensured that all the memory we used was 16 byte aligned.
 This final code was working in 24 ms.
\layout Subsection

Other Optimisations 
\layout Standard

We tried some other optimisations along the way.
 however these did not find a place in the final version of the program.
\layout Subsubsection

Lookup Tables for Log and Exp
\layout Standard

We had made a lookup table for the exp function and used the same table
 for looking up the log also by doing a search amongst the values of the
 lookup table.
\layout Standard

This was faster than the log/exp method and was fastest when we used only
 the lookup exp and the original log function because the lookup log was
 taking a lot of time, in fact sometimes more that the original math library
 log function.
\layout Standard

The time taken by the program for decoding a 0.25 rate code with lookup exp
 and math log was 167 ms.
\layout Standard

However it was difficult to convert this method to short integers and so
 we abandoned it.
\layout Subsubsection

Straight Line Approximation to tanh
\layout Standard

The tanh function can be approximated by a straight line of slope near 1
 and then it canbe made to saturate to 1 around 
\begin_inset Formula $\pm$
\end_inset 

0.9.
 This approximation however could not maintain the precision and so we couldn't
 use it in our final program.
\layout Subsubsection

The min Approximation
\layout Standard

At high SNR, the method involving the tanh and atanh can be approximated
 by taking the minimum of the absolute of all the incoming messages.
 In this method no multiplication or division of messages needs to be carried
 out.
 This yields low probability of error for positive SNR for the code rate
 0.25.
 We tried this but we couldn't get it to decode properly.
 This procedure may be considered for higher code rates which work at higher
 SNR range.
\layout Subsection

Usage of the Code Generator 
\layout Standard
\added_space_bottom medskip 
Because we were loading 8 short integers at a time in the xmm registers,
 we had to generate a new LDPC code in which the number of vnodes and cnodes
 of each degree are multiples of eight in order to avoid some check operations
 every time we loaded the xmm registers.
 We first made such a distribution by trying various permutations and in
 the process the number of vnodes dropped to 3992 from 4000 but the number
 of check nodes remained unchanged at 3000.
 So the rate of the code fell slightly from 0.25.
 The new degree distribution was as follows:
\layout Standard
\align center 

\begin_inset  Tabular
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<features>
<column alignment="center" valignment="top" leftline="true" width="0">
<column alignment="center" valignment="top" leftline="true" width="0">
<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
<row topline="true" bottomline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\layout Standard

vdegree
\end_inset 
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\layout Standard

no.
 of nodes
\end_inset 
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\layout Standard

percentage(%)
\end_inset 
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\layout Standard

2
\end_inset 
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\layout Standard

2368
\end_inset 
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\layout Standard

59.319
\end_inset 
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\layout Standard

3
\end_inset 
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\layout Standard

936
\end_inset 
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\layout Standard

23.447
\end_inset 
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\layout Standard

5
\end_inset 
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\layout Standard

248
\end_inset 
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\layout Standard

6.212
\end_inset 
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\layout Standard

6
\end_inset 
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\layout Standard

208
\end_inset 
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\layout Standard

5.210
\end_inset 
</cell>
</row>
<row topline="true" bottomline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\layout Standard

14
\end_inset 
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\layout Standard

236
\end_inset 
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\layout Standard

5.912
\end_inset 
</cell>
</row>
</lyxtabular>

\end_inset 


\layout Standard
\align center 

\begin_inset  Tabular
<lyxtabular version="3" rows="3" columns="3">
<features>
<column alignment="center" valignment="top" leftline="true" width="0">
<column alignment="center" valignment="top" leftline="true" width="0">
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<row topline="true" bottomline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\layout Standard

cdegree
\end_inset 
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\layout Standard

no.
 of nodes
\end_inset 
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\layout Standard

percentage(%)
\end_inset 
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\layout Standard

4
\end_inset 
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\layout Standard

1672
\end_inset 
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\layout Standard

55.733
\end_inset 
</cell>
</row>
<row topline="true" bottomline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\layout Standard

5
\end_inset 
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\layout Standard

1328
\end_inset 
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\layout Standard

44.267
\end_inset 
</cell>
</row>
</lyxtabular>

\end_inset 


\layout Standard
\added_space_top smallskip 
We took the code generator/simulator program from Abdelaziz Amraoui of the
 LTHC lab and put this new degree distribution in the 
\begin_inset Quotes eld
\end_inset 

param
\begin_inset Quotes erd
\end_inset 

 file.
 We also had to set a parameter to indicate that a new graph has to be generated
 and specified the file name into which the new graph would be written.
 We also tested the performance of this new code using the simulator for
 different SNR's and found that this was working well.
 In order to use this new code in our program, we had to convert it to a
 suitable format and for this we used the 
\begin_inset Quotes eld
\end_inset 

write
\begin_inset Quotes erd
\end_inset 

 program in the 
\begin_inset Quotes eld
\end_inset 

Main/Tools/LDPC
\begin_inset Quotes erd
\end_inset 

 directory to write this file into an array format in 
\begin_inset Quotes eld
\end_inset 

graphs.c
\begin_inset Quotes erd
\end_inset 

.
 We have plotted the performance of this new code along with the theoretically
 expected performance of a 0.25 code.
\layout Standard
\pagebreak_bottom \align left 

\begin_inset Graphics
	filename graphcomp.eps

\end_inset 


\newline 
Figure 10: Performance of new code with respect to theoretical performance.
\layout Section

Applications
\layout Subsection

FFT module
\layout Standard

The FFT module is being used for doing OFDM.
 It consists of an IFFT module in the sending chain to convert frequency
 domain samples to time domain samples, which are then sent on the channel
 after appropraite modulation.
 On the receiving side, FFT of the samples is taken.
 The output of the IFFT module gets scaled down by a factor which depends
 on the statistical nature of the input due to which the transmitter power
 falls.
 If the input is uniform and all samples are of amplitude A, then the IFFT
 output is an impulse of amplitude A.
 However when the input is random, the fall in amplitude is much more significan
t and one has to be careful because this can be a problem in the low SNR
 cases.
 So we have to put in appropriate amplification based on the input size
 in the IFFT module and deamplify the samples in the FFT module.
 The two graphs below show one slot of the OFDM-module in action.
 The data corresponds to transmission over air.
 The specifications of the system are:
\layout Standard

4-QAM
\layout Standard

256-FFT
\layout Standard

3 Mhz Bandwidth
\layout Standard

2.16 GHz Carrier
\layout Standard

9 FFT-blocks per slot
\layout Standard
\align center 

\begin_inset Graphics
	filename ofdm_complex.ps
	scale 65
	keepAspectRatio

\end_inset 


\layout Standard
\align center 
Figure 11: OFDM reciever showing QPSK modulated output
\layout Standard
\align center 

\begin_inset Graphics
	filename ofdm_abs.ps
	scale 70
	keepAspectRatio

\end_inset 


\layout Standard
\align center 
Figure 12: Magnitude of the OFDM receiver output.
\layout Standard

Figure 12 shows a periodic fluctuation of the signal which is due to the
 hardware.
 As can be clearly seen, there are 9 FFT-blocks in the slot (9 repetitions
 of the pattern).
\layout Subsection

LDPC module
\layout Standard
\added_space_bottom bigskip 
The LDPC module is being used to test the performance of various codes on
 the software radio platform.
 This helps in understanding the functionality of LDPC codes and their ability
 to attain channel capacity.
 
\layout Standard
\start_of_appendix 

\noun on 
Appendix
\noun default 
 :
\layout Standard

The final version of FFT is in /home/ysrini/Main.fft/Modules/Signal/FFT
\layout Standard

The final version of LDPC is in /home/ggupta/Main/Modules/Coding/LDPC.optimizeali
gned
\layout Standard

The additional files in LDPC which we have created are :
\layout Standard

1.
 lookup.h and lookup.c - These files contain the lookup tables for tanh and
 arctanh.
 These also contain the functions lookup_tanh() and lookup_atanh() which
 can be used to use these lookup tables.
\layout Standard

2.
 sse2mmx.h and sse2mmx.c - These files contain SSE2 code which basically consists
 of MMX instructions that have been adapted to work on 128 bit SSE2 registers.
 
\the_end