... )⎟⎟⎠⎞⎜⎜⎝⎛⎟⎠⎞⎜⎝⎛=⎟⎟⎠⎞⎜⎜⎝⎛⎟⎠⎞⎜⎝⎛≈MNREMQMMNEMQMpcbcππsinlog2log 2 sinlog2log 2 0 2 20 2 2cEbccERE =1001Lecture 9 20 Linear block codes – cont’dFor memory less channels, the probability that the decoder commits an erroneous decoding ... jnjntjMppjnP−+=−⎟⎟⎠⎞⎜⎜⎝⎛≤∑)1(1jnjntjBppjnjnP−+=−⎟⎟⎠⎞⎜⎜⎝⎛≈∑)1(11p Digital Communications I: Modulation and Coding CoursePeriod 3 - 20 07Catharina LogothetisLecture 9Lecture 9 22 Linear block codes –cont’dA matrix ... 23 Linear block codes – cont’dEncoding in (n,k) block codeThe rows of G, are linearly independent.mGU =knkknmmmuuummmuuuVVVVVV⋅++⋅+⋅=⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡⋅= 22 21 121 2 1 21 21),,,(),,,(),,,(KKMKKLecture...