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EE4212~tut3 - (i What error pattern(s can the code...

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EE4212 Information and Coding Tutorial 3 1. Rate Distortion Theory Suppose that there is a binary memoryless source X with equiprobable output symbols 0 and 1. A sequence of M such symbols is generated and is to be transmitted through a perfect channel. In the transmission, only ( M -2) binary symbols are transmitted while the remaining two are guessed at the receiver based on tossing an unbiased coin. The distortion is measured by the Hamming distance between the original and the received message. (a) Express the information rate R and the distortion D in terms of M . (b) Find the expression of rate distortion function R ( D ) and distortion rate function D ( R ). (c) Show that the information rate should equal to the source entropy when perfect reconstruction is required. ( i.e., R (0) = H ( X ) ) 2. Parity Check Codes (a) Suppose that a (4,3) odd-parity code is used to encode a source of 3-bit messages.
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Unformatted text preview: (i) What error pattern(s) can the code detect? (ii) Calculate the redundancy and the code rate. (iii) Assume that all symbol errors are independent events and that the probability of a channel symbol error is p = 0.002. Calculate the probability of an undetected message error. (b) Suppose that the 3-bit messages are now grouped in two and encoded by a (12,6) rectangular code in order to improve the capability of error detection and correction. (i) Calculate the redundancy and the code rate. (ii) The advantage of using this encoding scheme instead of the single-parity code is that any single-bit error can be detected and corrected . However, any detected block error that is caused by two or more error bits still cannot be corrected. Find the block error probability that the decoded block is found to have an uncorrected error....
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