mitted codeword using the methods - G matrix and check equations b) If an error occurs in bit 2 during transmission, determine the syndrome c) Show how the syndrome can b
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A: answer is
Information bits consisting of 1101 is to be transmitted using Hamming (7,4) code. a)
Determine the transmitted codeword using the methods - G matrix and check equations
b) If an error occurs in bit 2 during transmission, determine the syndrome
c) Show how the syndrome can be used to correct the error.
note: step by step process please, for easy understand. thanks.
Step by step
Solved in 2 steps
- A block of bits with n rows and k columns uses horizontal and vertical parity bits for error detection. Suppose that exactly 4 bits are inverted due to transmission errors. Drive a mathematical expression of n and k for the total number of different cases where these 4 error bits will be undetected. Show each important step of your derivation. (Hint: the error bits will be undetected if all the parity bits computed from the block remain unchanged.)Consider a convolutional code with k = 1, n = 3 and L = 3. The encoder generators aregiven by 91 = [110], 92 = [001] and 93 = [011].Assume the Viterbi algorithm is used for decoding at the receiver and considerthe received bit sequence at the input of the channel decoder being [10 0100110011].Answer the following questions.(a) What is the decoded information bit sequence? (b) What is the value of the cumulative metric (i.e., Hamming distance) of thefinal survivor path of the decoding process?(c) Draw the final survivor path of the trellis for the decoding process.Instruction for Part (c): An example of drawing a path in the trellis is shown below.Q) Consider the use of hamming codes to send 11-bit messages. Specifically, consider 10011011011. First, calculate the hamming code-word for this message. Second, invert one message bit in that Hamming code-word (to represent a 1-bit error) and show how the recipient can use the check bits to correct the inverted bit (that is, perform the error correction)
- Given the H matrix in a (n,k) block code ?=[0100110] 1001111 0011010 (a) Derive the G matrix, and find the codeword of the message m=(1100). (b) Find the detection and correction capabilities of the coding scheme.A cyclic redundancy check (CRC) is an error-detecting code commonly used in digital networks and storage devices to detect accidental changes to raw data. Propose your own Roll as data bits (e.g roll 1 to 100) and show how the sender adds the parity bits and write the final code word that will be sent. Value of Key is 1011 (derived from polynomial function). Also show in the receiver side that the correct data is received.a) Determine the 32-bit binary representation for floating point numbers in the form± I.F x be where I is the interger part,F is the fraction,b is the base, ande is the exponent.Using this format, represent the number -1.00011011101 x 225 as a 32 bit floating point number. b) During the process of digital sampling, data can be lost due to aliasing. Analyse this problem and provide at least two possible solutions. Also, determine the rate at which a signal should be sampled, if the highest frequency is 60MHz. c) In your own words, discuss the relationship between the hexadicimal number system and the binary number system. Use this relationship to convert the following hexadecimal values to binary.i) 5BC916 ii) 6EF816 iii) 8A4D16 iv) 9ED516
- A repetition code is an [n, 1] Code in which the n - 1 parity bits are repetitions of the information bit. Is this repetition code a linear code ? What is the minimum distance of the code ?please given step by step solution.For an 8 bit string 01011011, determine the Hamming bits required and show that if there is an error in the last bit it received, it can be corrected using Hamming codes.A bit stream 10011101 is transmitted using CRC method. The generator polynomial is x^3 + 1. Show the actual bit string transmitted. Suppose the third bit from the left is inverted during transmission. Show that this error is detected at the receivers end.
- 3).Let X=−123, n=8 (including 2 sign bit), then the complement of X is_______ .#45.! Consider the following bit stream-a. 00000000 b. 11111111 c. 01010101 d. 00110011 Draw the graph of the i. Manchester using each of the given data streams, assuming that the last signal level has been positive. From thegraphs, guess the bandwidth for this scheme using the average number of changes in the signal level... .Consider the 3rd ,6th , and7th digits of your student ID composed of seven digits. Convert it to binary format (each digit is represented by a maximum of 3 bits). For example, 1060385 is simplified to 685 and then converted to 0110 1000 0101. Assume now that we want to send your simplified student ID while being able to detect and correct single bit errors. 1.1) Using two-dimensional parity check show what will be transmitted using datawords of size 4 bits.