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A voice-band telephone channel passes the frequencies in the band from 300 to 3300 Hz. It is desired to design a modem that transmits at a symbol rate of 2400.
Determine the value of Ps if it is desired to expand the bandwidth of the system to 10 kHz, while maintaining the same SNR at the detector.
Determine G(D) for the RSCC equivalent to this code, and sketch a block diagram of it.
If the code is used on a channel with hard decision Viterbi decoding, assuming the crossover probability of the channel is p = 10-6.
Determine the transfer function T (Y, Z, J ), and from this, specify the minimum free distance.
A k = 1, K = 3, and n = 2 convolutional code is characterized by g1 = [001] and g2 = [101].
Assuming that this code is used for binary data transmission over a binary symmetric channel with crossover probability of 10-3.
Determine the transfer function T (Y, Z) for this code, and find its free distance.
Determine the encoded sequence for the input sequence u = (1001111001) using G(D) found in part 1.
If the code is used on an AWGN channel using BPSK with hard decision Viterbi decoding, assuming Eb/N0 = 12.6 dB, find an upper bound on the average bit error.
Show the output sequence and the distance of the output sequence from the all-zero sequence.
Suppose that the code is used on a binary symmetric channel and the received sequence for the first eight branches is 0001100000001001.
Soft-decision decoding Compare the performance by plotting the results of the computation on the same graph.
Draw the state diagram for the convolutional code generated by the encoder shown in Figure , and thus determine whether the code is catastrophic.
By how much is the distance between adjacent signal points increased as a result of partitioning?
A recursive systematic convolutional code is characterized by G(D) = [1 1/D+1].
This code is used with antipodal signaling with ec = ±1 over an additive white Gaussian noise channel with noise power spectral density of N0/2 = 2 W/Hz.
Show that this polynomial can generate a cyclic code for any choice of n. Find the corresponding k.
Design a (6, 2) cyclic code by choosing the shortest possible generator polynomial.
Is Cmax a cyclic code? Why? If yes, what is its generator polynomial and its minimum distance?
If this code is employed for transmission over a channel which uses binary antipodal signaling with hard decision decoding and the SNR per bit of the channel.
What are the possible rates for cyclic codes with block length 23?
The minimum weight of a cyclic code is equal to the number of nonzero coefficients of its generator polynomial.
Let s(X) denote the syndrome corresponding to error sequence e(X) in an (n, k) cyclic code with generator polynomial g(X).
Determine the generator polynomial and the rate of a double-error-correcting BCH code with block length n = 31.