1,151 research outputs found
Density Evolution for Deterministic Generalized Product Codes with Higher-Order Modulation
Generalized product codes (GPCs) are extensions of product codes (PCs) where
coded bits are protected by two component codes but not necessarily arranged in
a rectangular array. It has recently been shown that there exists a large class
of deterministic GPCs (including, e.g., irregular PCs, half-product codes,
staircase codes, and certain braided codes) for which the asymptotic
performance under iterative bounded-distance decoding over the binary erasure
channel (BEC) can be rigorously characterized in terms of a density evolution
analysis. In this paper, the analysis is extended to the case where
transmission takes place over parallel BECs with different erasure
probabilities. We use this model to predict the code performance in a coded
modulation setup with higher-order signal constellations. We also discuss the
design of the bit mapper that determines the allocation of the coded bits to
the modulation bits of the signal constellation.Comment: invited and accepted paper for the special session "Recent Advances
in Coding for Higher Order Modulation" at the International Symposium on
Turbo Codes & Iterative Information Processing, Brest, France, 201
Approaching Capacity at High-Rates with Iterative Hard-Decision Decoding
A variety of low-density parity-check (LDPC) ensembles have now been observed
to approach capacity with message-passing decoding. However, all of them use
soft (i.e., non-binary) messages and a posteriori probability (APP) decoding of
their component codes. In this paper, we show that one can approach capacity at
high rates using iterative hard-decision decoding (HDD) of generalized product
codes. Specifically, a class of spatially-coupled GLDPC codes with BCH
component codes is considered, and it is observed that, in the high-rate
regime, they can approach capacity under the proposed iterative HDD. These
codes can be seen as generalized product codes and are closely related to
braided block codes. An iterative HDD algorithm is proposed that enables one to
analyze the performance of these codes via density evolution (DE).Comment: 22 pages, this version accepted to the IEEE Transactions on
Information Theor
Generalized product expansions for pair‐correlated wavefunctions
A correlated wavefunction in the form of a linear combination of generalized products is proposed for describing electron correlation in N‐electron systems. The generalized product configurations are group functional products describing the correlated behavior of a pair of electrons in an N‐2‐electron independent particle sea. The linear expansion includes terms for all possible pairs and thus includes correlation effects for every pair of electrons. The structure of the wavefunction is given, the matrix elements of the Hamiltonian are determined, and some of the variational equations determining the optimal total wavefunction are discussed. The relation between second‐order Nesbet‐Bethe‐Goldstone calculations and the pair at a time CI method of Sinanoğlu and the pair‐correlated wavefunction developed here is discussed, and a method is given for obtaining a complete generalized product wavefunction from these type independent pair approximations.<br/
Maps preserving peripheral spectrum of generalized products of operators
Let and be standard operator algebras on
complex Banach spaces and , respectively. For , let
be a sequence with terms chosen from , and
assume that at least one of the terms in appears exactly
once. Define the generalized product on elements in . Let
be a map with the range containing
all operators of rank at most two. We show that satisfies that
for all
, where stands for the peripheral spectrum of
, if and only if is an isomorphism or an anti-isomorphism multiplied
by an th root of unity, and the latter case occurs only if the generalized
product is quasi-semi Jordan. If and are complex Hilbert
spaces, we characterize also maps preserving the peripheral spectrum of the
skew generalized products, and prove that such maps are of the form or , where is a unitary
operator, .Comment: 17 page
Generalized product of fuzzy subgroups and t-level subgroups
Ray (Fuzzy Sets and Systems 105(1999)181-183) studied some results of the product of two fuzzy subsets and fuzzy subgroups. In this paper, Ray\u27s results will be generalized. Furthermore, we
define a t-level subset and t-level subgroups, and then we study some of their properties
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