We model the secondary structure of an RNA molecule by means of a maximal non-crossing matching on a random word in a finite alphabet, where ties are only allowed between certain pairs of letters. We prove that the mean fraction of unmatched symbols does not vanish as the length of the word tends to infinity.
We propose a new ensemble of binary low-density parity-check codes with paritycheck matrices based on repetition codes and permutation matrices. The proposed class of codes is a subensemble of quasi-cyclic codes. For the constructed ensemble, we obtain minimum distance estimates. We present simulation results for the proposed code constructions under the (Sum-Product) iterative decoding algorithm for transmission over an additive white Gaussian noise channel using binary phase-shift keying.
We establish the strong Poisson hypothesis for symmetric closed networks. In particular, we prove asymptotic independence of nodes as the size of the system tends to infinity.