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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?
Find the lowest-rate cyclic code with generator polynomial g(X). What is the rate of this code?
Prove that the Hamming distance between two sequences of length n, denoted by dH (x, y).
Determine the parity check matrix H for the code. Construct the table of syndromes for the code.
Find the generator and the parity check matrices of a second-order (r = 2) Reed-Muller code with block length n = 16.
Determine the bandwidth expansion factor for the M orthogonal waveforms, and compare this with the bandwidth requirements of orthogonal FSK detected coherently.
Show that the signaling waveforms generated from a maximum-length shift register code by mapping each bit in a codeword into a binary PSK signal .
From this conclude that if p < ½, P( y|x) is a decreasing function of d and hence ML decoding is equivalent to minimum-Hamming-distance decoding.
Using a symbolic computation program (e.g., Mathematica or Maple), find the weight enumeration polynomial for a (15, 11) Hamming code
Find the capacity of the cascade connection of n binary symmetric channels with the same crossover probability e.
Let C denote the capacity of the third channel and C1 and C2 represent the capacities of the first and second channels.
Let C denote the capacity of a discrete memoryless channel with input alphabet X = {x1, x2,..., xN}.
Find the input probability distribution that achieves capacity.
Find theFind the capacity of an additive white Gaussian noise channel with a bandwidth 1 MHz, power 10 W.
For each source output one use of channel is possible. The fidelity measure is squared-error distortion, i.e., d(x,xˆ ) = (x -xˆ )2.
Assume that this channel is used with optimal hard decision decoding at the output. What is the crossover probability of the resulting BSC channel?
Consider the two channels with the transition probabilities as shown in Figure.