problem6

# problem6 - UNIVERSITY OF CALIFORNIA SAN DIEGO Electrical...

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UNIVERSITY OF CALIFORNIA, SAN DIEGO ECE 259B - Winter Quarter 2011 Probabilistic Coding Problem Set #6 Due Thursday, March 3, 2011 1. Consider the Tanner graph of the (7,4) Hamming code deFned in class. (a) ±ind all stopping sets of weight 3 or less. (b) Augment the Tanner graph with one additional parity-check for the code such that the resulting graph has no weight-3 stopping sets other than the supports of weight-3 codewords. 2. (a) Describe a parity-check matrix for the rate- 1 5 repetition code that is low-density, in the sense that the number of 1s is less than half the number of entries in the matrix. What are the variable and check degree distributions from the node and edge perspectives? (b) Show that the corresponding Tanner graph has no cycles of length 4. (c) A systematic repeat-accumulate (RA) code is obtained by transmitting the input word along with the RA codeword. Consider a systematic RA encoder in which the input blocklength is 2, the repetition code is rate-

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problem6 - UNIVERSITY OF CALIFORNIA SAN DIEGO Electrical...

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