The alternating direction method of multipliers (ADMMs) decoding of low-density parity-check codes has received many attentions due to its excellent performance at the error floor region. In this letter, we develop a parameter-free decoder based on linear program decoding by replacing the binary constraint with the intersection of a box and an l(p) sphere. An efficient l(2)-box ADMM is designed to handle this model in a distributed fashion. Numerical experiments demonstrate that our decoder attains better adaptability to different signal-to-noise ratio and channels.
Zhu, Junlei; Bu, Yuehua; Pardalos, Miltiades P.; Du, Hongwei; Wang, Huijuan; Liu, Bin
The optimal channel assignment is an important optimization problem with applications in optical networks. This problem was formulated to the L(p,1)-labeling of graphs by Griggs and Yeh (SIAM J Discrete Math 5:586-595, 1992). A k-L(p,1)-labeling of a graph G is a function is the maximum vertex degree of G. Our proofs are constructive, which can be turned to a labeling (channel assignment) method to reach the upper bounds.
We define a p-adic character to be a continuous homomorphism from 1 + tF(q)[[t]] to Z(p) For p> 2, we use the ring of big Witt vectors over F-q to exhibit a bijection between p-adic characters and sequences (c(i))((i,p)=1) of elements in Z(q), indexed by natural numbers relatively prime to p, and for which lim(i ->infinity) c(i) =0. To such a p-adic character we associate an L-function, and we prove that this L-function is p-adic meromorphic if the corresponding sequence (c(i)) is overconvergent. If more generally the sequence is Clog-convergent, we show that the associated L-function is meromorphic in the open disk of radius q(C). Finally, we exhibit examples of Clog-convergent sequences with associated L-functions which are not meromorphic in the disk of radius q(C+is an element of) for any is an element of > 0.
For \(p\in [1,\infty )\) we study representations of a locally compact group \(G\) on \(L^p\)-spaces and \(\textit{QSL}^p\)-spaces. The universal completions \(F^p(G)\) and \(F^p_{\mathrm {QS}}(G)\) of \(L^1(G)\) with respect to these classes of representations (which were first considered by Phillips and Runde, respectively), can be regarded as analogs of the full group \(C^{*}\)-algebra of \(G\) (which is the case \(p=2\)). We study these completions of \(L^1(G)\) in relation to the algebra \(F^p_\lambda (G)\) of \(p\)-pseudofunctions. We prove a characterization of group amenability in terms of certain canonical maps between these universal Banach algebras. In particular, \(G\) is amenable if and only if \(F^p_{\mathrm {QS}}(G)=F^p(G)=F^p_\lambda (G)\). One of our main results is that for \(1\le p< q\le 2\), there is a canonical map \(\gamma _{p,q}:F^p(G)\rightarrow F^q(G)\) which is contractive and has dense range. When \(G\) is amenable, \(\gamma _{p,q}\) is injective, and it is never surjective unless \(G\) is finite. We use the maps \(\gamma _{p,q}\) to show that when \(G\) is discrete, all (or one) of the universal completions of \(L^1(G)\) are amenable as a Banach algebras if and only if \(G\) is amenable. Finally, we exhibit a family of examples showing that the characterizations of group amenability mentioned above cannot be extended to \(L^p\)-operator crossed products of topological spaces.
For p is an element of [1, infinity), we prove that simple, separable, monotracial UHF L-p-operator algebras are not classifiable up to (complete) isomorphism using countable structures, such as K-theoretic data, as invariants. The same assertion holds even if one only considers UHF L-p-operator algebras of tensor product type obtained from a diagonal system of similarities. For p =3D 2, it follows that separable nonselfadjoint UHF operator algebras are not classifiable by countable structures up to (complete) isomorphism. Our results, which answer a question of N. Christopher Phillips, rely on Borel complexity theory, and particularly Hjorth's theory of turbulence.
In this paper for p is an element of [1, +infinity) and a nonempty set I, we consider a natural preorder on l(p) (I), which is said to be "convex majorization". Then some interesting properties of all bounded linear operators T : l(P)(I) -> l(p) (I) preserving the convex majorization, are given. We also characterize these operators and assert one of the important properties of them, that is, the rows of matrix form of such an operator belongs to l(1) (I). (C) 2014 Elsevier Inc. All rights reserved.
For we study representations of a locally compact group on -spaces and -spaces. The universal completions and of with respect to these classes of representations (which were first considered by Phillips and Runde, respectively), can be regarded as analogs of the full group -algebra of (which is the case ). We study these completions of in relation to the algebra of -pseudofunctions. We prove a characterization of group amenability in terms of certain canonical maps between these universal Banach algebras. In particular, is amenable if and only if . One of our main results is that for , there is a canonical map which is contractive and has dense range. When is amenable, is injective, and it is never surjective unless is finite. We use the maps to show that when is discrete, all (or one) of the universal completions of are amenable as a Banach algebras if and only if is amenable. Finally, we exhibit a family of examples showing that the characterizations of group amenability mentioned above cannot be extended to -operator crossed products of topological spaces.
The problem of c-Approximate Nearest Neighbor (c-ANN) search in high-dimensional space is fundamentally important in many applications, such as image database and data mining. Locality-Sensitive Hashing (LSH) and its variants are the well-known indexing schemes to tackle the c-ANN search problem. Traditionally, LSH functions are constructed in a query-oblivious manner, in the sense that buckets are partitioned before any query arrives. However, objects closer to a query may be partitioned into different buckets, which is undesirable. Due to the use of query-oblivious bucket partition, the state-of-the-art LSH schemes for external memory, namely C2LSH and LSB-Forest, only work with approximation ratio of integer . In this paper, we introduce a novel concept of query-aware bucket partition which uses a given query as the "anchor" for bucket partition. Accordingly, a query-aware LSH function under a specific norm with is a random projection coupled with query-aware bucket partition, which removes random shift required by traditional query-oblivious LSH functions. The query-aware bucket partitioning strategy can be easily implemented so that query performance is guaranteed. For each norm , based on the corresponding p-stable distribution, we propose a novel LSH scheme named query-aware LSH (QALSH) for c-ANN search over external memory. Our theoretical studies show that QALSH enjoys a guarantee on query quality. The use of query-aware LSH function enables QALSH to work with any approximation ratio . In addition, we propose a heuristic variant named QALSH to improve the scalability of QALSH. Extensive experiments show that QALSH and QALSH outperform the state-of-the-art schemes, especially in high-dimensional space. Specifically, by using a ratio , QALSH can achieve much better query quality.
We deal with the relation between the Mittag-Leffler functions and the sum of the hypervolume of generalized l(p) n-balls. We derive from this result some simple properties of the Mittag-Leffler functions. We also define some new Abelian groups from the sum and the multiplication as well as the Pontryagin transform associated to them. We relate this approach to the calculus on measure chains.
We study finite subsets of l(p) and show that, up to a nowhere dense and Haar null complement, all of them embed isometrically into any Banach space that uniformly contains l(p)(n).