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Consider linear block code with n=8 and k=4. The parity bits of Linear block code is obtained as c_1=m_2+m_3+m_4 c_2=m_1+m_2+m_3 c_3=m_1+m_2+m_4 c_4=m_1+m_3+m_4 where m_1,m_2,m_3 and m_4 are the message bits and c_1,c_2,c_3 and c_4 are the checkbits O
A 12-bit Hamming code word containing 8 bits of data and 4 parity bits is read from memory. What was the original 8-bit data word that was written into memory if the 12-bit word read out is as follows: 101110000110
Say you have an n block of bits message. You split it to 8 bits each (assume that 8 divides n). For each of the 8 bit we choose a permutation of the bits. How many different codes could come out of this? Explain or prove the correctness of your analysis.
o Problem 2. Consider an (n, k)-code. Randomly choose n bits, each of which assumes bit 0 with probability 1/2. Prove that the probability that the n-bits is a codeword is 2k-n
Consider the following code mapping for k = 2 bits of information with n = 5. How many errors at maximum can this code correct? What are the generator and parith check matrices of the code? (Enough to provide one valid parity check matrix). Information bits Codeword 00 00000 01 00111 10 11100 11 11011
5) (2 pt) A 12-bit Hamming code word containing 8 bits of data and 4 parity bits is read from memory. What was the original 8-bit data word that was written into memory if the 12-bit word read out is 010011111000? Show your work.
5) (2 pt) A 12-bit Hamming code word containing 8 bits of data and 4 parity bits is read from memory. What was the original 8-bit data word that was written into memory if the 12-bit...
Consider the LSFR (Linear Feedback Shift Register) with 4 register. Suppose the first 8 bits of the output stream are 0010 0011. What are the secret key(s)?
e) Consider a SEC (Single Error Correcting) code that protect 8 bit words with 4 parity bits. If we read the value 375H, is there an error? If so, correct the error. Problem
QUESTION 4 Consider the following block of Python code, where variables age_1, age_2 and age_3 each store integer values: if age_1 > age_2: if age_2 > age_3: print(age_3) else: print(age_2) elif age_1 > age_3: print(age_3) else: print(age_1) Which of the following options best describes the purpose of the above code? To print the largest of the values stored in age_1, age_2 and age_3 To print the largest of the values stored in age_1 and age_2 only To print the largest...
4. Consider the linear model Y = XB+e, where e MV N(0,021). (1) Derive the formula for , the least square estimate of B, using the matrix notation (2) Show that ß is an unbiased estimate for B. (3) Derive the formula for var(), using matrix notation.
4. Consider solving the linear system Ax = b, where A is an rn x n matrix with m < n (under- determined case), by minimizing lle subject to Ar-b. (a) Show that if A Rmxn is full (row) rank, where m n, then AA is invertible. Then show that r.-A7(AAT)-ibis a solution to Ax = b. (b) Along with part (a) and the solution aAT(AA)-b, show that l thus, z is the optimal solution to the minimization problem. and...