147,899 research outputs found
Improved Successive Cancellation Decoding of Polar Codes
As improved versions of successive cancellation (SC) decoding algorithm,
successive cancellation list (SCL) decoding and successive cancellation stack
(SCS) decoding are used to improve the finite-length performance of polar
codes. Unified descriptions of SC, SCL and SCS decoding algorithms are given as
path searching procedures on the code tree of polar codes. Combining the ideas
of SCL and SCS, a new decoding algorithm named successive cancellation hybrid
(SCH) is proposed, which can achieve a better trade-off between computational
complexity and space complexity. Further, to reduce the complexity, a pruning
technique is proposed to avoid unnecessary path searching operations.
Performance and complexity analysis based on simulations show that, with proper
configurations, all the three improved successive cancellation (ISC) decoding
algorithms can have a performance very close to that of maximum-likelihood (ML)
decoding with acceptable complexity. Moreover, with the help of the proposed
pruning technique, the complexities of ISC decoders can be very close to that
of SC decoder in the moderate and high signal-to-noise ratio (SNR) regime.Comment: This paper is modified and submitted to IEEE Transactions on
Communication
An Extension of the Well-Posedness Concept for Fractional Differential Equations of Caputo's Type
It is well known that, under standard assumptions, initial value problems for
fractional ordinary differential equations involving Caputo-type derivatives
are well posed in the sense that a unique solution exists and that this
solution continuously depends on the given function, the initial value and the
order of the derivative. Here we extend this well-posedness concept to the
extent that we also allow the location of the starting point of the
differential operator to be changed, and we prove that the solution depends on
this parameter in a continuous way too if the usual assumptions are satisfied.
Similarly, the solution to the corresponding terminal value problems depends on
the location of the starting point and of the terminal point in a continuous
way too.Comment: 11 page
Maximal Area Triangles in a Convex Polygon
The widely known linear time algorithm for computing the maximum area
triangle in a convex polygon was found incorrect recently by Keikha et.
al.(arXiv:1705.11035). We present an alternative algorithm in this paper.
Comparing to the only previously known correct solution, ours is much simpler
and more efficient. More importantly, our new approach is powerful in solving
related problems
Stationary Solutions of Neutral Stochastic Partial Differential Equations with Delays in the Highest-Order Derivatives
In this work, we shall consider the existence and uniqueness of stationary
solutions to stochastic partial functional differential equations with additive
noise in which a neutral type of delay is explicitly presented. We are
especially concerned about those delays appearing in both spatial and temporal
derivative terms in which the coefficient operator under spatial variables may
take the same form as the infinitesimal generator of the equation. We establish
the stationary property of the neutral system under investigation by focusing
on distributed delays. In the end, an illustrative example is analysed to
explain the theory in this work
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