In this paper we study the asymptotic behavior of the fraction of true formulas against all formulas over k propositional variables with equivalence as the only connective in the language. We consider two ways of measuring the asymptotic behavior. In the first case we investigate the size of the tautology fraction of length n against the number of all formulas of length n. The second case is ve...

Generalized low-density parity-check (GLDPC) codes are a class of LDPC in which the standard single parity check (SPC) constraints replaced by defined linear block code. These stronger typically result improved error floor performance, due to better minimum distance and trapping set properties, at cost some increased decoding complexity. In this paper, we study spatially coupled generalized (SC...

This paper studies turbo-like coded modulation in the block-fading channel. In particular we show that the performance of such coded modulation schemes is close to the information outage probability of the channel for any block length, as opposed to standard coded modulation schemes based on trellis-terminated convolutional codes. For large block length, asymptotic performance of the proposed s...

The MacLane’s class of analytic functions is the class of nonconstant analytic functions in the unit disk that have asymptotic values at a dense subset of the unit circle. In this paper, we define a subclass of consisting of those functions that have asymptotic values at a dense subset of the unit circle reached along rectifiable asymptotic paths. We also show that the class is a proper subclas...

In a communication network, asymptotic quality of service metrics specify the probability that the delay or buffer occupancy becomes large. An understanding of these metrics is essential for providing worst-case delay guarantees, provisioning buffer sizes in networks, and to estimate the frequency of packet-drops due to buffer overflow. Second, many network control tasks utilize queue length in...

Long binary sequences related to cyclic difference sets are investigated. Among all known constructions of cyclic difference sets we show that only sequences constructed from Hadamard difference sets can have an asymptotic nonzero merit factor. Maximal length shift register sequences, Legendre, and twin-prime sequences are all constructed from Hadamard difference sets. We prove that the asympto...

The ensemble of RNA secondary structures of uniform sequences is studied analytically. We calculate the partition function for very long sequences and discuss how the crossover length, beyond which asymptotic scaling laws apply, depends on thermodynamic parameters. For realistic choices of parameters this length can be much longer than natural RNA molecules. This has to be taken into account wh...