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

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.

Terrestrial FSO Block Diagram

ERROR CORRECTING CODES Error correcting codes are used to overcome the limitations of the FSO channel. Error detection and correction enable reliable delivery of digital data over unreliable communication channels. Two types of error control codes: Block codes and Convolution codes. We consider RS, Convolutional and Low Density Parity Check codes(LDPC) codes to determine the coding gain and hence the performance of the FSO communication channel.

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. CONVOLUTIONAL CODES

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

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)

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.

Sparse Matrix Sparse Matrix is a matrix representation of the sparse bipartite graph. It is an (n-k) x n matrix: 1. With binary values (0,1) 2. That has the value 1 at (i,j) if there exists an edge between i th check node and j th message node, and zero at others 3. The last n-k columns in H must be an invertible matrix in GF(2)

Encoding in MATLAB MATLAB has a fixed size of sparse matrix x 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

Decoding Input to the LDPC decoder is the log-likelihood ratio (LLR), L(c i ):, where c i is the ith bit of the t transmitted codeword, c. Quoted in Reference [11] by Henk W, the algorithm, called simple Log Domain decoding, expresses LLR calculations in sums and products. Advantage: Computationally less expensive. Since we’re not calculating probability, simplified log-domain decoder does not need noise variance information.

There are three key variables in the algorithm: L(r ji ), L(q ij ), and L(Q i ). L(q ij ) is initialized as L(q ij ) = L(c i ). For each iteration, update L(r ji ), L(q ij ), and L(Q i ) using the following equations: At the end of each iteration, L(Q i ) provides an updated estimate of the log-likelihood ratio for the transmitted bit c i. The soft-decision output for c i is L(Q i ). The hard-decision output for c i is 1 if L(Q i ) < 0, and 0 otherwise.

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 < 2 m + 2 For the most conventional R-S (n, k) code, (n, k) = (2 m - 1, 2 m t) where, t is the error correcting capability of the code n - k = 2t is the number of parity symbols. Reed Solomon Code (RS Codes)

Figure A pictorial representation of the transmitted bits after Reed Solomon Encoding. 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 In the simulation, we have used M = 5 is the no. of bit sequences in a symbol, K = 127 is the number of data symbols being encoded, and N = 255 is the total number of code symbols in encoded block. Therefore, Code Rate = 127/255 ~ 0.5

Modulation Schemes Adaptive OOK PPM

Communication Channels Lognormal: Gamma-Gamma:

RESULTS 4-PPM under Lognormal (var=0.1)

4-PPM under Lognormal (var=0.01)

4-PPM under Lognormal (var=0.001)

OOK under Lognormal (var=0.1)

OOK under Lognormal (var=0.01)

OOK under Lognormal (var=0.001)

4-PPM under Gamma-Gamma (var=0.1)

4-PPM under Gamma-Gamma (var=0.01)

4-PPM under Gamma-Gamma (var=0.001)

OOK under Gamma-Gamma (var=0.1)

OOK under Gamma-Gamma (var=0.01)

OOK under Gamma-Gamma (var=0.001)

Effect of PPM index on curve (LDPC)

Effect of Coding Rate on Coding Gain

Recommendations for Future Work One can investigate the effects of Medium turbulence channels, namely gamma-gamma using Accept Reject Method. High turbulence channels, namely exponential on the BER in the communication link. Implement more coding techniques like Turbo coding and Trellis coded modulation (TCM).

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