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首页> 外文期刊>IEEE Transactions on Information Theory >Constant Compositions in the Sphere Packing Bound for Classical-Quantum Channels
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Constant Compositions in the Sphere Packing Bound for Classical-Quantum Channels

机译：古典量子通道的球填充边界中的常量成分

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摘要

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 Lovász 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 Lovász 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 finally applied to auxiliary channels to deduce a bound, which is useful in the low rate region and which can be interpreted as an extension of the Elias bound.
机译：以Shannon，Gallager和Berlekamp给出的形式的球体堆积边界最近扩展到了经典量子通道，这表明这为将概率方法与一些组合方法（如Lovásztheta函数）相结合创造了自然的环境。 。在本文中，我们将研究扩展到常数组成代码的情况。我们首先将经典量子通道的球面堆积边界扩展到这种情况，然后我们证明所获得的结果与Marton研究的Lovásztheta函数的变化有关。然后，我们建议对给定特定序列的，具有恒定条件组成的变化信道和码字的情况进行进一步扩展。最终将此扩展应用于辅助信道以得出边界，该边界在低速率区域中很有用，并且可以解释为Elias边界的扩展。

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