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project6

# project6 - CSE4214 DIGITAL COMMUNICATIONS PROJECT 3...

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CSE4214: DIGITAL COMMUNICATIONS PROJECT 3: CONVOLUTIONAL CODES Instructor: Dr. Amir Asif Department of Computer Science and Engineering York University, Toronto, ON M3J 1P3 The students will complete the following project in Matlab and submit their solutions along with a soft copy of the code in the form of a report. Introduction: In this project, we will run a Monte-Carlo simulation to characterize the performance of a binary communication system that uses convolutional encoding with pulse shift keying (PSK) modulation. Figure 1 illustrates the block diagram of such a digital communication system where the input message is denoted by the Information Source a45 Convolutional Encoder a45 Modulator s i ( t ) a63 AWGN Channel a27 Demodulator hatwide s i ( t ) a27 Convolutional Decoder a27 Information Sink Input Sequence m = m 1 , m 2 , . . . , m i , . . . Codeword Sequence U = G ( m ) = U 1 , U 2 , . . . , U i , . . . with U i = u 1 i , u 2 i , . . . , u ji , . . . , u ni Demodulated Codeword Sequence Z = Z 1 , Z 2 , . . . , Z i , . . . with Z i = z 1 i , z 2 i , . . . , z ji , . . . , z ni Detected Sequence hatwide m = hatwide m 1 , hatwide m 2 , . . . , hatwide m i , . . . Figure 1: A digital communication system emphasizing channel encoding and modulation. sequence m with each m i representing a binary digit (bit). The index i in m i is the time index, thus m 1 is transmitted before m 2 and so on with the remaining bits. The channel encoder encodes the input message m U = G ( m ) (1) producing the codeword U that is transmitted through an AWGN channel with power spectral density of N o . In this project, a ( n, 1 , K ) binary convolutional encoder is used as the channel encoder. Therefore, a codeword of length n is produced for each input bit. More on convolutional encoder later where we illustrate its operation through an example. The modulation and demodulation scheme used in the digital communication system modeled in figure 1, is the M-ary PSK. Recall that the general representation for the PSK waveforms is s i ( t ) = radicalbigg 2 E T cos bracketleftbig ω o t - 2 πi M bracketrightbig , i = 1 , . . . , M, 0 t T (2)

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where ω o is the carrier frequency in radians/s and is assumed an integer multiple of 2 π/T . The transmitted signal s i ( t ) has a constant envelope with a duration of T and energy E . In project 2, we implemented the PSK modulator and demodulator using Matlab. These functions are made available to you for this project. In the following section, we focus on the binary convolutional encoder and decoder. Convolutional Encoder: A binary convolutional code is generated by passing the information sequence to be transmitted through a linear finite-state shift register. For a ( n, 1 , K ) convolution code, the shift register consists of K stages and n linear modulo-2 function generators. The input data is shifted into and along the shift register a single bit at a time producing a n -tuplet output for each shift. Consequently, the code rate for a ( n, 1 , K ) convolutional encoder is 1 /n . To illustrate the working of a convolutional encoder, consider the (3,1,3) convolutional
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project6 - CSE4214 DIGITAL COMMUNICATIONS PROJECT 3...

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