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Unformatted text preview: UNIVERSITY OF CALIFORNIA, SAN DIEGO Electrical & Computer Engineering Department ECE 259B - Winter Quarter 2011 Probabilistic Coding Problem Set #5 Problems 1, 2 and 3 due Thursday, February 24. Problem 4 is due Thursday, March 10. 1. Consider an encoder for an ( n, k ) linear block code C (codeword length n and dimension k ). Let A C w,h , w = 0 , . . . , k ; h = 0 , . . . , n denote the Input Output Weight Enumerator (IOWE) corresponding to the encoder, i.e., the coeﬃcients in the Input Output Weight Enumerator Function (IOWEF) A C ( W, Z ) = X w,h A C w,h W w Z h . (a) Suppose the encoder for C is obtained by a parallel concatenation through uniform interleavers of p encoders for constituent codes C i , i = 1 , . . . , p , where each C i is an ( n i , k ) linear block code with corresponding IOWE A ( i ) w,h , w = 0 , . . . , k ; h = 0 , . . . , n i . Express the IOWE A C w,h for the code C in terms of the IOWEs of the constituent codes. (b) Now, suppose the encoder for C is obtained by a serial concatenation through uniform interleavers of p codes C i , i = 1 , . . . , p , where each C i is an ( n i , k i ) linear block code with corresponding IOWE A ( i ) w,h , w = 0 , . . . , k i...
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- Spring '11
- Trigraph, Coding theory, Error detection and correction, Linear code, Convolutional code