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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.
Determine the generator polynomial and the rate of a triple-error-correcting Reed-Solomon code with block length.
What is the weight distribution function of the Reed-Solomon code designed in Problem.
Prove that in the product code shown in Figure the (n1 - k1) × (n2 - k2) bits in the lower right corner.
Find the transfer function and the free distance of this code. Verify whether or not this code is catastrophic.
Using the Viterbi algorithm, find the transmitted sequence, assuming that the convolutional code is terminated at the zero state.
Find the transfer function and the free distance of this code.
Assume that a message has been encoded by this code and transmitted over a binary symmetric channel with an error probability of p = 10-5.
Two students, A and B, make the following arguments on error detection capability of this code.
Two elements belonging to two distinct cosets of a standard array have distinct syndromes.