If the input is 8 bits and the convolution code can be considered as a (24, 8) block code, then what is the generator matrix G?
If the input is 8 bits and the convolution code can be considered as a (24, 8) block code, then what is the generator matrix G?
Let G- be a generator matrix for a block code (not necessarily a "good" code) a) b) c) What is the n, k, the rate and the bandwidth expansion for this code? Find the parity check matrix H )Build the standard array for the code. Assume the coset leaders are vectors with one "l", starting from the left side of the vector, i.e., the first coset leader will be (1 0...), the second (01 0 ...) starting again from the...
1. Channel Coding We would like to add linear block code (3,6) using the generator matrix: 1 001 01 G-0 1 0 0 1 1 (a) (5 points) Determine the parity check matrix H (b) (20 points) What is the minimum distance of this code? How many error can this code correct? (c) (5 points) What is the code word for the data sequence 011000101111? (d) (20 points) If you receive the codeword 010001000010101010, what is the transmitted sequence?
Consider a generator matrix G for a nonsystematic (6, 3) code:Construct the code for this G, and show that dmin, the minimum distance between codewords is 3, Consequently, this code can correct at least one error.
(Applied Algebra
Construct a standard array for the (5, 3) code given by the generator matrix: G-0 1011 Hint: It should hove 4 rows and 8 columns
Construct a standard array for the (5, 3) code given by the generator matrix: G-0 1011 Hint: It should hove 4 rows and 8 columns
4. If the memory bus has 24 bits, and there are 8 words in a block in RAM, To design a 4 set-associative cache with 8K sets in cache, answer the following questions: (a). RAM size (b). How many blocks in RAM? (c). How many bits are w? (d). How many bits are d? (e). How many bits are s? (f). cache size in words? (g). How many lines in cache? (h). If we increase the cache size to 32K...
Consder the (7,4) cyclic code having the generator ploynomial G(x) = x3 +x2 + 1. a) What is the binary representation of G (x)? [15 Marks) b) Assume that the messgae is M(x) = (1 00 1). Determine the Block Check Code (BCC) mathemetically c) What is the transmitted codeword? d) Assume the received codeword is (1101110). Determine the corresponding syndrome. 11o NIO loooo1 bits There are e( r0s are deteted ron ceceeted Code we the e) Does the received...
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
The gray code is 8 code values for the three bits. A) Can the number of code values in a gray code by something other than the power of 2 of the number of bits? B) Can the number of code values in a gray code be odd?
Consider a (7, 4) code whose generator matrix isa) Find all the codewords of the code b) Find H, the parity check matrix of the code. c) Compute the syndrome for the received vector 1 101 1 0 1. Is this a valid code vector? d) What is the error-correcting capability of the code? e) What is the error-detecting capability of the code?
Two questions,please!
7. Assume C is a linear code. Prove that G is a generator matrix for C if and only if the columns of G form a basis of C 8. Let V. W U be vector spaces over F of finite dimension and φ: V → W, t : W → U linear maps. Prove that Im(φ)-ker( ) holds if and only if ψφ-0 and dimF1m(φ)-dimF kere).
7. Assume C is a linear code. Prove that G is...