Fall03-quiz2 - University of California Berkeley College of...

Info icon This preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
1 University of California, Berkeley College of Engineering Computer Science Division EECS Spring 2003 John Kubiatowicz Midterm II December 1, 2003 CS252 Graduate Computer Architecture Your Name: SID Number: Problem Possible Score 1 25 2 25 3 20 4 30 Total 100
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
2 [ This page left for π ] 3.141592653589793238462643383279502884197169399375105820974944
Image of page 2
3 Problem #1: Checking the bits The error correction coding process can be viewed as a transformation from one space of bits (the unencoded data) to another (the coded data). 1a) For linear block codes, there are two matrices, the Generator ( G ) and Parity Check ( H ). What are they, how big are they (in terms parameters n and k ), and how are they used? 1b) Define the minimum Hamming distance, d min , of an error correction code (make sure that this definition makes sense for codes like Reed-Solomon of RAID-5 that have more than one bit per symbol): 1c) Name a constraint on the columns of the parity check matrix ( H ) which would indicate that a code had minimum distance d min . 1d) For a code with d min minimum distance, what is the formula for the maximum number of errors, E detect , that can be reliably detected? Why might you be able to detect more than the E detect errors?
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
4 1e) For a code with d min minimum distance, what is the formula for the maximum number of random errors, E correct , that can be corrected reliably? 1f) How does your answer to (1e) change if you have knowledge of which symbols are bad (i.e. which symbols have been erased ). How might erased symbols be detected? 1g) What is a systematic error-correction code? Why is this desirable? 1h) Suppose we start with a non-systematic, linear code described by generator G with distance d min . How can we produce a systematic code with generator G’ from G that still has distance d min ? ( hint: what happens if you subtract two code words from the original code? Now think of this operation on G ).
Image of page 4
5 1i) Suppose you are willing to use 5 parity bits. What is the maximum number of data bits ( k ) that you can protect with a Hamming code and still get a distance 4 code? What are the matrices G and H for this code? Prove that your code has distance 4. 1j) Explain the function that a circuit that detected and corrected errors in the above code would have to perform. You should tell how to (1) get an “Error detected” signal, E detect (2) get a double-error signal, E double , and (3) a bad bit identifier, E bad .
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern