29,050 research outputs found
Systematic redundant residue number system codes: analytical upper bound and iterative decoding performance over AWGN and Rayleigh channels
The novel family of redundant residue number system (RRNS) codes is studied. RRNS codes constitute maximumâminimum distance block codes, exhibiting identical distance properties to ReedâSolomon codes. Binary to RRNS symbol-mapping methods are proposed, in order to implement both systematic and nonsystematic RRNS codes. Furthermore, the upper-bound performance of systematic RRNS codes is investigated, when maximum-likelihood (ML) soft decoding is invoked. The classic Chase algorithm achieving near-ML soft decoding is introduced for the first time for RRNS codes, in order to decrease the complexity of the ML soft decoding. Furthermore, the modified Chase algorithm is employed to accept soft inputs, as well as to provide soft outputs, assisting in the turbo decoding of RRNS codes by using the soft-input/soft-output Chase algorithm. Index TermsâRedundant residue number system (RRNS), residue number system (RNS), turbo detection
Adaptive Integrand Decomposition in parallel and orthogonal space
We present the integrand decomposition of multiloop scattering amplitudes in
parallel and orthogonal space-time dimensions, , being
the dimension of the parallel space spanned by the legs of the
diagrams. When the number of external legs is , the corresponding
representation of the multiloop integrals exposes a subset of integration
variables which can be easily integrated away by means of Gegenbauer
polynomials orthogonality condition. By decomposing the integration momenta
along parallel and orthogonal directions, the polynomial division algorithm is
drastically simplified. Moreover, the orthogonality conditions of Gegenbauer
polynomials can be suitably applied to integrate the decomposed integrand,
yielding the systematic annihilation of spurious terms. Consequently, multiloop
amplitudes are expressed in terms of integrals corresponding to irreducible
scalar products of loop momenta and external momenta. We revisit the one-loop
decomposition, which turns out to be controlled by the maximum-cut theorem in
different dimensions, and we discuss the integrand reduction of two-loop planar
and non-planar integrals up to legs, for arbitrary external and internal
kinematics. The proposed algorithm extends to all orders in perturbation
theory.Comment: 64 pages, 4 figures, 8 table
Integrand Reduction for Two-Loop Scattering Amplitudes through Multivariate Polynomial Division
We describe the application of a novel approach for the reduction of
scattering amplitudes, based on multivariate polynomial division, which we have
recently presented. This technique yields the complete integrand decomposition
for arbitrary amplitudes, regardless of the number of loops. It allows for the
determination of the residue at any multiparticle cut, whose knowledge is a
mandatory prerequisite for applying the integrand-reduction procedure. By using
the division modulo Groebner basis, we can derive a simple integrand recurrence
relation that generates the multiparticle pole decomposition for integrands of
arbitrary multiloop amplitudes. We apply the new reduction algorithm to the
two-loop planar and nonplanar diagrams contributing to the five-point
scattering amplitudes in N=4 super Yang-Mills and N=8 supergravity in four
dimensions, whose numerator functions contain up to rank-two terms in the
integration momenta. We determine all polynomial residues parametrizing the
cuts of the corresponding topologies and subtopologies. We obtain the integral
basis for the decomposition of each diagram from the polynomial form of the
residues. Our approach is well suited for a seminumerical implementation, and
its general mathematical properties provide an effective algorithm for the
generalization of the integrand-reduction method to all orders in perturbation
theory.Comment: 32 pages, 4 figures. v2: published version, text improved, new
subsection 4.4 adde
Multi-leg One-loop Massive Amplitudes from Integrand Reduction via Laurent Expansion
We present the application of a novel reduction technique for one-loop
scattering amplitudes based on the combination of the integrand reduction and
Laurent expansion. We describe the general features of its implementation in
the computer code NINJA, and its interface to GoSam. We apply the new reduction
to a series of selected processes involving massive particles, from six to
eight legs.Comment: v3: 39 pages, minor typos and one benchmark point correcte
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