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Tagged with gray-codes hamming-distance
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Why standardized LDPC codes, such 5G NR, have 4 cycles in its parity check matrix?
We all know that short cycles in Tanner Graph are detrimental in error performance. So, Why standardized 5G NR LDPC codes have 4-cycles? 3rd generation Partnership Project (3GPP) had announced Base ...
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Multiset of Hamming distances for a tour of all subsets
Consider a list of all the subsets of $\{1,\ldots,n\}$, in any order. Using binary notation, one such list for $n=3$ is
$$ 010, 100, 110, 011, 000, 111, 001, 101. $$
Now consider the Hamming distance ...