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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 paritycheck for the code such that
the resulting graph has no weight3 stopping sets other than the supports of weight3
codewords.
2.
(a) Describe a paritycheck matrix for the rate
1
5
repetition code that is lowdensity, 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 repeataccumulate (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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