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hw6_error_detection_correction

# hw6_error_detection_correction - MASSACHUSETTS INSTITUTE OF...

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6.02 Spring 2008 1 of 1 Homework #6 M ASSACHUSETTS I NSTITUTE OF T ECHNOLOGY D EPARTMENT OF E LECTRICAL E NGINEERING AND C OMPUTER S CIENCE 6.02 Introduction to EECS II Spring 2008 Homework #6: Channel Coding Issued: March 14, 2008 Due: March 21, 2008 Problem 1 . For each of the following codes indicate the code rate and describe the error detecting and correcting capability of the code: a. (15,11,3) code b. (10,1,10) code c. (154,132,7) code Problem 2 . Suppose management has decided to use 20-bit data blocks in the company’s new (n,20,3) error correcting code. What’s the minimum value of “n” that will permit the code to be used for single-bit error correction, i.e. that will achieve a minimum Hamming distance of 3 between codewords? Problem 3 . A set of five 4-bit data values has been encoded using the (8,4,3) code shown in lecture and then transmitted over a noisy channel. For each of the received codewords below make the appropriate corrections to remove any errors, or indicate that an uncorrectable error has been detected. a. 0 0 1 b. 1 0 1 c. 1 1 0 d. 0 0 1 e. 0 0 1 1 0 1 0 0 0 1 0 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 0 0 Problem 4 . Ben Bitdiddle woke up in the middle of the night with the following great idea: in order to implement double-bit error correction he would use the (8,4,3) code described in lecture – which can correct single-bit errors – to encode a message twice. In other words, after the message was encoded for the first time with the (8,4,3) code, the

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hw6_error_detection_correction - MASSACHUSETTS INSTITUTE OF...

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