1. PERFORMANCE ANALYSIS OF FREE SPACE OPTICAL (FSO) COMMUNICATION USING DIFFERENT CODING SCHEMES
Performed by :
Nidhi Gupta, 63/EC/07
Rupinder Singh, 83/EC/07
Siddi Jai Prakash, 101/EC/07
Electronics and Communication Division
Netaji Subhas Institute of Technology,
Delhi
Mentored by:
Prof. Subrat Kar
Dept. of Electrical Engineering
IIT Delhi
Dr. S.P. Singh
Electronics and Communication Division
Netaji Subhas Institute of Technology, Delhi

2. Free Space Optical Communication (FSO)
Block Diagram; Features; Applications; Signal Propagation Impediments; Effect of Weather

3. Conventional FSO Block Diagram

4. Free Space Optical Communication (FSO)
Features –
High Data Bandwidth of 2000 THz
Low BER, High SNR
Narrow Beam Size
Power Efficient and Data Security
Cheap
Quick to deploy and redeploy
In telecommunications, Free Space Optics (FSO) is an optical
communication technology that uses light propagating in free
space to transmit data between two points. The technology is useful
where the physical connections by the means of fiber optic cables are
impractical due to high costs or other considerations.

5. Bit Error Rate (BER) Performance of FSO Link

6. Areas of Application Last mile access Optical fibre back up link
Cellular Communication back haul
Disaster Recovery/ Temporary links
Multi Campus Communication network
Difficult terrains

7. Terrestrial FSO Block Diagram

8. Signal Propagation Impediments
Fog: Fog is vapour composed of water droplets, which are only a few hundred microns in diameter but can modify light characteristics or completely hinder the passage of light through a combination of absorption, scattering, and reflection.
Absorption: Absorption occurs when suspended water molecules in the terrestrial atmosphere extinguish photons.
Scattering: Scattering is caused when the wave collides with a scatterer. The physical size of the scatterer determines the type of scattering (Rayleigh, Mie, Geometric)

9. Physical obstructions: Flying birds, for instance, can temporarily block a single beam, but this tends to cause only short-term interruptions.
Building sway/seismic activity: The relative movement of buildings can upset receiver and transmitter alignment.
Safety: The technology uses lasers for transmission.

10. Effect of Weather
Figure showing different fog conditions. More the fog, greater the fading of the optical communication channel.

11. ERROR CORRECTING CODES
Error correcting codes are used to overcome the limitations of the FSO channel.
In computer science and telecommunication, error detection and correction or error control are techniques that enable reliable delivery of digital data over unreliable communication channels.
There are two types of error control codes namely block codes and convolution codes.
Here we use RS codes, Convolutional and Low Density Parity codes(LDPC) codes to determine the coding gain and hence the performance of the FSO communication channel.

12. Reed Solomon Code (RS Codes)
Introduction; Results; Future Work

13. They are non-binary cyclic codes.
Denoted by R-S (n,k) on m-bit symbols.
where, m is the no. of bit sequences in a symbol,
k is the number of data symbols being encoded, and
n is the total number of code symbols in encoded block.
The condition to be satisfied by variables is -
0 < k < n < 2m + 2
For the most conventional R-S (n, k) code,
(n, k) = (2m - 1, 2m t)
where, t is the error correcting capability of the code

14. For Reed- Solomon codes, the code minimum distance is given by
n - k = 2t is the number of parity symbols.
For Reed- Solomon codes, the code minimum distance is given by
dmin = n - k + 1
The code is capable of correcting any combination of t or fewer errors, where t can be expressed as

15. In the simulation, we have used
Figure A pictorial representation of the transmitted bits after Reed Solomon Encoding.
In the simulation, we have used
M = 5 is the no. of bit sequences in a symbol,
K = 10 is the number of data symbols being encoded, and
N = 3*K = 30 is the total number of code symbols in encoded block.

16. Results
Beneath 10^(-4), the bit error rate comes out to be 0. This is mainly because of using code rate = 1/3, which means that the ratio of the no. of the coded bits to the no. of message bits is 3:1. This implies that for every one message bit, three bits are transmitted. Hence, it can be said that though this coding technique gives good results but at the expense of increased Bandwidth requirement.
Figure BER vs SNR for RS codes in a lognormal channel having variance 0.3.

17. Introduction; Decoding Algorithm; Implementation in Matlab; Results
CONVOLUTIONAL CODES
Introduction; Decoding Algorithm; Implementation in Matlab; Results

18. Figure Convolutional Encoder
Convolutional codes are performed on bit to bit basis.
m-bit information symbol (each m-bit string) to be encoded is transformed into an n-bit symbol, where m/n is the code rate (n ≥ m)
transformation is a function of the last k information symbols, where k is the constraint length of the code, using the generator matrix.
Figure Convolutional Encoder

19. Figure: Trellis Diagram
Viterbi decoder allows optimal decoding.
It is a finite state machine.
The memory devices values are encoded to a codeword
using a generator matrix
Figure: Trellis Diagram

20. Implementation in MATLAB
Encoding using the function ‘convenc’ using a trellis structure ‘trellis’
[msg_enc_bi, stateEnc] = convenc(msg_orig, trellis, stateEnc)
Decoding using the function ‘vitdec’ and ‘hard’ decoding
[msg_dec, metric, stateDec, in] = vitdec(msg_demod_bi(:), trellis, tblen, 'cont', 'hard', metric, stateDec, in)

21. Result
We used a code rate of 3/4. As we increase Eb/N0, the bit error rate decreases from an initial value of 0.20 obtained at Eb/N0 = 0.1. For a 4-PPM modulation scheme through a lognormal channel with variance 0.01, the results were as follows:

22. Low-Density Parity-Check Code (LDPC Codes)
Introduction; Sparse Matrix; Encoding; Decoding; Optimization; Results; Future Work

23. Introduction
LDPC (Low Density Parity Check) codes are linear error-correcting codes characterized by sparse bipartite graphs.
In the adjacent figure, if G be a graph with n left nodes (message nodes) and k right nodes (check nodes), the graph gives rise to a linear code of block length n and dimension at least (n – k) in the following way: The codewords are those vectors (c1;......; cn) such that for all check nodes the sum of the neighbouring positions among the message nodes is zero.
n represents the total number of bits in a codeword.
k represents the number of information bits in a codeword.
(n-k) represents the number of parity bits in a codeword.

24. Sparse Matrix
Sparse Matrix is a matrix representation of the sparse bipartite graph.
It is an (n-k) x n matrix:
With binary values (0,1)
That has the value 1 at (i,j) if there exists an edge between ith check node and jth message node, and 0 at others
The last n-k columns in H must be an invertible matrix in GF(2)

25. Encoding in Principle Consider a sparse matrix H
2. The codewords can be obtained by putting the parity-check matrix H into the form [-PT | In-k] through basic row operations:
3. From this, the generator matrix G can be obtained as [Ik | P]
4. Finally, by multiplying all eight possible 3-bit strings by G, all eight valid codewords are obtained

26. Encoding in MATLAB
MATLAB has a fixed size of sparse matrix x 64800
Hence, we generate our own custom sparse matrix.
We then generate Parity Check bits using LU decomposition of sparse matrix
Finally, we solve for c in L(Uc) = B.s, where
H = [A|B], s = input vector

27. Decoding
The input to the LDPC decoder is the log-likelihood ratio (LLR), L(ci), which is defined by the following equation:
where ci is the ith bit of the transmitted codeword, c.

28. The Optimized Algorithm
Quoted in “Log Domain Decoding of LDPC code in GF (q)” by Henk W.,the algorithm, called simple Log Domain decoding, express log-likelihood calculations in the form of sums and products.
Advantage: Computationally less expensive.
Since we’re not calculating probability, simplified log-domain decoder does not need noise variance information.

29. The Optimized Algorithm
There are three key variables in the algorithm: L(rji), L(qij), and L(Qi). L(qij) is initialized as
L(qij) = L(ci). For each iteration, update L(rji), L(qij), and L(Qi) using the following equations:
At the end of each iteration, L(Qi) provides an updated estimate of the log-likelihood ratio for the transmitted bit ci.
The soft-decision output for ci is L(Qi). The hard-decision output for ci is 1 if L(Qi) < 0 , and 0 otherwise.

30. Result
We used a code rate of ½. As we increase Eb/N0, the bit error rate decreases from an initial value of 0.22 obtained at Eb/N0 = 0.1. For a 4-PPM modulation scheme through a lognormal channel with variance 0.001, the results were as follows:

31. Comparative Study

32. Future Work In the future we aim to investigate the effects of
Medium turbulence channels, namely gamma-gamma
High turbulence channels, namely exponential on the BER in the communication link.
Implement more coding techniques like Turbo coding and Trellis coded modulation (TCM).
Also investigate the effects of another modulation scheme - OOK.

33. References:
M. Karimi, M. Nesiri-Kenari, “BER Analysis of Cooperative Systems in Free-Space Optical Networks” J. of Lightwave Technology, vol. 27, no. 24, pp , Dec 15, 2009
E. W. B. R. Strickland, M. J. Lavan, V. Chan, “Effects of fog on the bit-error rate of a free space laser Communication system,” Appl.Opt., vol. 38, no. 3, pp. 424–431, 1999.
M. Uysal, J. Li, and M. Yu, “Error rate performance analysis of coded free-space optical links over gamma -gamma
atmospheric turbulence channels,” IEEE Trans . Wireless Communication, vol. 5, no. 6, pp.1229–1233,
L. Andrews, R. Phillips, C. Hopen, Laser Beam Scintillation With Applications. New York: SPIE Press, 2001.
Bernard Sklar, Reed – Solomon Codes.
Stephen B. Wicker, Vijay K. Bhargava, “An introduction to Reed Solomon Codes.
Ghassemlooy, Z. And Popoola, W.O Terrestrial Free Space optical Communication.
Gallager, Robert G., “Low-Density Parity-Check Codes”, Cambridge, MA, MIT Press, 1963.
Amin Shokrollahi, “LDPC Codes: An introduction”, Digital Fountain, Inc, April 2, 2003
Henk Wymeersch, Heidi Steendam and Marc Moeneclaey, DIGCOM research group, TELIN Dept., Ghent University, “Log-domain decoding of LDPC codes over GF(q)”.