# tut3_sol - EE 4212 Information and Coding Solution to...

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1 EE 4212 Information and Coding Solution to Tutorial 3 1. Rate Distortion Theory (a) Case Probability Error / bit (i) the guess is correct 1/2 0 (ii) the guess is wrong 1/2 1 Information Rate symbol bits M M M R / 1 1 1 = = Distortion symbol bits M M D / 2 1 )] 1 ( 2 1 ) 0 ( 2 1 [ 1 = + = (b) From (a), M D 1 2 = symbol bits D D R / 2 1 ) ( = symbol bits R R D / 2 1 ) ( = (c) D = 0 R (0) = 1-2(0) = 1 bit / symbol symbol bit P P I P H ii i i i i / 1 2 log 2 1 2 log 2 1 1 log ) ( 2 2 1 0 1 0 = + = = = ∑∑ == X R (0)= H ( X ) For perfect reconstruction, we have to transmit all the bits. ( M -1) bits transmitted 1 bit not transmitted 0 1 1 0 0 0 1 . . . 1 1 0

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2 2 1 0 D 1 0 R D = 0 R (0) = H ( X ) = 1 bit / symbol (Perfect Reconstruction) 2 1 = D 0 ) 2 1 ( = R bit / symbol (No information need to be transmitted, all bits are guessed at the receiver.) R ( D ) R D R (0) = H ( X ) = 1 D=0.5 0
3 parity bits message bits 2. Parity Check Codes (a) (i) All single-bit, 3-bit and 5-bit error patterns can be detected. five single-bit error patterns: 00001, 00010, 00100, 01000, 10000 ten 3-bit error patterns: 00111, 01110, 11100, 11001, 10011 01011, 10110, 01101, 11010, 10101 one 5-bit error patterns: 11111
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tut3_sol - EE 4212 Information and Coding Solution to...

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