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**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

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**Free Space Optical Communication (FSO)**

Block Diagram; Features; Applications; Signal Propagation Impediments; Effect of Weather

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**Conventional FSO Block Diagram**

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**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.

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**Bit Error Rate (BER) Performance of FSO Link**

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**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

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**Terrestrial FSO Block Diagram**

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**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)

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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.

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

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**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.

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**Reed Solomon Code (RS Codes)**

Introduction; Results; Future Work

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**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

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**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

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**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.

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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.

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**Introduction; Decoding Algorithm; Implementation in Matlab; Results**

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

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**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

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**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

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**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)

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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:

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**Low-Density Parity-Check Code (LDPC Codes)**

Introduction; Sparse Matrix; Encoding; Decoding; Optimization; Results; Future Work

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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.

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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)

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**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

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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

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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.

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**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.

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**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.

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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:

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Comparative Study

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**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.

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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)”.

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