Capacity of the Generalized Pulse-Position Modulation Channel

We show the capacity of a generalized pulse-position modulation (PPM) channel, where the input vectors may be any set that allows a transitive group of coordinate permutations, is achieved by a uniform input distribution. We derive a simple expression in terms of the Kullback Leibler distance for the binary case, and the asymptote in the PPM order. We prove a sub-additivity result for the PPM channel and use it to show PPM capacity is monotonic in the order

The trumping relation and the structure of the bipartite entangled states

The majorization relation has been shown to be useful in classifying which transformations of jointly held quantum states are possible using local operations and classical communication. In some cases, a direct transformation between two states is not possible, but it becomes possible in the presence of another state (known as a catalyst); this situation is described mathematically by the trumping relation, an extension of majorization. The structure of the trumping relation is not nearly as well understood as that of majorization. We give an introduction to this subject and derive some new results. Most notably, we show that the dimension of the required catalyst is in general unbounded; there is no integer $k$ such that it suffices to consider catalysts of dimension $k$ or less in determining which states can be catalyzed into a given state. We also show that almost all bipartite entangled states are potentially useful as catalysts.Comment: 7 pages, RevTe

The CCSDS 123.0-B-2 Low-Complexity Lossless and Near-Lossless Multispectral and Hyperspectral Image Compression Standard: A comprehensive review

The Consultative Committee for Space Data Systems (CCSDS) published the CCSDS 123.0-B-2, “Low- Complexity Lossless and Near-Lossless Multispectral and Hyperspectral Image Compression” standard. This standard extends the previous issue, CCSDS 123.0-B-1, which supported only lossless compression, while maintaining backward compatibility. The main novelty of the new issue is support for near-lossless compression, i.e., lossy compression with user-defined absolute and/or relative error limits in the reconstructed images. This new feature is achieved via closed-loop quantization of prediction errors. Two further additions arise from the new near lossless support: first, the calculation of predicted sample values using sample representatives that may not be equal to the reconstructed sample values, and, second, a new hybrid entropy coder designed to provide enhanced compression performance for low-entropy data, prevalent when non lossless compression is used. These new features enable significantly smaller compressed data volumes than those achievable with CCSDS 123.0-B-1 while controlling the quality of the decompressed images. As a result, larger amounts of valuable information can be retrieved given a set of bandwidth and energy consumption constraints