Erasure-proof coding with fusion frames
نویسندگان
چکیده
The main goal of this paper is the design of frames for transmitting vectors through a memoryless analog erasure channel. The channel transmits the frame coefficients perfectly or discards them, depending on the outcomes of Bernoulli trials with a failure probability q. For sufficiently small q, we construct frames which encode above a fixed non-zero rate and allow the receiver to recover part of the erased coefficients so that the remaining mean-square error vanishes as the frame size increases. We give examples for which the mean-square reconstruction error remaining after corrections are applied decays faster than any inverse power of the number of frame vectors.
منابع مشابه
FUSION FRAMES IN HILBERT SPACES
Fusion frames are an extension to frames that provide a framework for applications and providing efficient and robust information processing algorithms. In this article we study the erasure of subspaces of a fusion frame.
متن کاملDuality of $g$-Bessel sequences and some results about RIP $g$-frames
In this paper, first we develop the duality concept for $g$-Bessel sequences and Bessel fusion sequences in Hilbert spaces. We obtain some results about dual, pseudo-dual and approximate dual of frames and fusion frames. We also expand every $g$-Bessel sequence to a frame by summing some elements. We define the restricted isometry property for $g$-frames and generalize some resu...
متن کاملContinuous $k$-Fusion Frames in Hilbert Spaces
The study of the c$k$-fusions frames shows that the emphasis on the measure spaces introduces a new idea, although some similar properties with the discrete case are raised. Moreover, due to the nature of measure spaces, we have to use new techniques for new results. Especially, the topic of the dual of frames which is important for frame applications, have been specified completely for the c...
متن کاملCompare and contrast between duals of fusion and discrete frames
Fusion frames are valuable generalizations of discrete frames. Most concepts of fusion frames are shared by discrete frames. However, the dual setting is so complicated. In particular, unlike discrete frames, two fusion frames are not dual of each other in general. In this paper, we investigate the structure of the duals of fusion frames and discuss the relation between the duals of fusion fram...
متن کاملظرفیت شبکه های حذفی تحت کدینگ فضایی شبکه
We study the capacity of point-to-point erasure networks under a restricted form of network coding to which we refer as spatial network coding. In this form of coding, the nodes can not perform coding on successive packets which are received from one incoming link. The coding at a node is restricted to the packets received at the same time slot from different incoming links...
متن کامل