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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.
How many code words are in this code? What is the dmin for this code?
What is the rate of this code? What is the minimum distance of this code? What is the minimum weight for this code?
Construct the standard array and determine the correctable error patterns and their corresponding syndromes.
If the received sequence (using hard decision decoding) is y = 100000, what is the transmitted sequence using a maximum-likelihood decoder?
What rate, minimum distance, and the coding gain can C provide in soft decision decoding when BPSK is used over an AWGN channel?
Determine a generator matrix G for this code in systematic form.
For the (7, 4) cyclic Hamming code with generator polynomial g(X) = X3 + X2 + 1, construct an (8, 4) extended Hamming code .
An (8, 4) linear block code is constructed by shortening a (15, 11) Hamming code generated by the generator polynomial g(X) = X4 + X + 1.
How many random errors per codeword can be corrected? How many errors can be detected by this code?