PERFORMANCE ANALYSIS OF FREE SPACE OPTICAL (FSO) COMMUNICATION USING DIFFERENT CODING SCHEMES

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 NetajiSubhas Institute of Technology, Delhi Mentored by: Prof. SubratKar Dept. of Electrical Engineering IIT Delhi Dr. S.P. Singh Electronics and Communication Division NetajiSubhas Institute of Technology, Delhi

2. Free Space Optical Communication (FSO)

3. Terrestrial FSO Block Diagram

4. 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.

5. CONVOLUTIONAL CODES

6. 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

7. 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

8. 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)

9. Low-Density Parity-Check Code(LDPC Codes)

10. 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 kright 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.

11. 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)

12. Encoding in MATLAB • MATLAB has a fixed size of sparse matrix 32400 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

13. 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. Quoted in “Log Domain Decoding of LDPC code in GF (q)” by HenkW.,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.

14. 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.

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

16. 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 - 1 - 2t) where, t is the error correcting capability of the code 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

17. 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.

18. Modulation Schemes • OOK • PPM

19. Communication Channels • Lognormal: • Gamma-Gamma:

20. 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.

21. 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. 5637-5649, 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, 2006. • 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. • AminShokrollahi, “LDPC Codes: An introduction”, Digital Fountain, Inc, April 2, 2003 • HenkWymeersch, Heidi Steendam and Marc Moeneclaey, DIGCOM research group, TELIN Dept., Ghent University, “Log-domain decoding of LDPC codes over GF(q)”.