A class of geometrically structured quasi-cyclic low-density paritycheck codes with a cylinder structure graph and girth 12 is considered. The parity-check matrix of such a code consists of blocks of zeros and circulant permutation matrices. A class of convolutional codes is assigned to these codes. The convolutional form generator matrix of these codes is obtained by elementary row and column ...

We study pure exchange economies with symmetries on preferences up to taste intensity transformations. In a 2-person, 2-good endowment economy, we show that bilateral symmetry on each utility functional precludes a rectangle in the Edgeworth box as the location of Pareto optimal allocations. Under strictly quasi-concave preferences, a larger set can be ruled out. The inadmissible region is stil...

A graph is well-covered if all its maximal independent sets are of the same cardinality [25]. If G is a well-covered graph, has at least two vertices, and G − v is well-covered for every vertex v, then G is a 1-well-covered graph [26]. We call G a λ-quasi-regularizable graph if λ · |S| ≤ |N (S)| for every independent set S of G. The independence polynomial I(G;x) is the generating function of i...

We present an exact analytical solution of the fundamental systems of quasi-one-dimensional spin-1/2 fermions with infinite repulsion for an arbitrary confining potential. The eigenfunctions are constructed by the combination of Girardeau's hard-core contacting boundary condition and group theoretical method, which guarantees the obtained states to be simultaneously the eigenstates of S and S_{...

In this paper, we propose a construction method of nonbinary quasi-cyclic low-density parity-check (QC-LDPC) codes. The shift offset values of the circulant permutation submatrices are selected not only by maximising the girth but also by maximising the minimum distance upper bound. The proposed method provides a more rational optimisation way than only maximising the girth. Copyright © 2012 Jo...

A novel algebraic construction technique for LDPC convolutional codes (LDPCCCs) based on permutation polynomials over integer rings is presented. The underlying elements of this construction technique are graph automorphisms and quasi-cyclic (QC) codes. The algebraic structure of the obtained LDPCCCs, their encoding and decoding are discussed. These new codes have a special structure, which is ...

In these notes we solve a class of Riemann-Hilbert (inverse monodromy) problems with an arbitrary quasi-permutation monodromy group. The solution is given in terms of Szegö kernel on the underlying Riemann surface. In particular, our construction provides a new class of solutions of the Schlesinger system. We present some results on explicit calculation of the corresponding tau-function, and de...

In general, encoding for LDPC codes can be difficult to realize efficiently. This paper presents techniques and architectures for LDPC encoding that are efficient and practical for a particular class of codes. These codes are the irregular partitioned permutation LDPC codes recently introduced by the author at ICC’03, [4]. Since these codes are quasi-cyclic, it is known that a simpler encoding ...

We develop the technique of reduced word manipulation to give a range of results concerning reduced words and permutations more generally. We prove a broad connection between pattern containment and reduced words, which specializes to our previous work for vexillary permutations. We also analyze general tilings of Elnitsky’s polygon, and demonstrate that these are closely related to the pattern...