Constant Compositions in the Sphere Packing Bound for Classical-Quantum Channels
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Publication:4589396
DOI10.1109/TIT.2017.2726555zbMath1373.81162arXiv1401.6039MaRDI QIDQ4589396
Publication date: 10 November 2017
Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)
Abstract: The sphere packing bound, in the form given by Shannon, Gallager and Berlekamp, was recently extended to classical-quantum channels, and it was shown that this creates a natural setting for combining probabilistic approaches with some combinatorial ones such as the Lov'asz theta function. In this paper, we extend the study to the case of constant composition codes. We first extend the sphere packing bound for classical-quantum channels to this case, and we then show that the obtained result is related to a variation of the Lov'asz theta function studied by Marton. We then propose a further extension to the case of varying channels and codewords with a constant conditional composition given a particular sequence. This extension is then applied to auxiliary channels to deduce a bound which can be interpreted as an extension of the Elias bound.
Full work available at URL: https://arxiv.org/abs/1401.6039
Related Items (4)
The sphere packing bound for memoryless channels ⋮ Reliability function of quantum information decoupling via the sandwiched Rényi divergence ⋮ A simple derivation of the refined sphere packing bound under certain symmetry hypotheses ⋮ Properties of noncommutative Rényi and Augustin information
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