Polar coding to achieve the Holevo capacity of a pure-loss optical channel
Polar coding to achieve the Holevo capacity of a pure-loss optical channel
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极化编码实现纯损耗光通道的 Holevo 容量
DOI：
10.1109/isit.2012.6284250
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
M. Wilde
中科院分区：
文献类型：
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作者：
S. Guha;M. Wilde
在经典光通信的低能量高能效机制中（与深空光通道相关），通过传统光接收器可实现的可靠通信速率与最终（Holevo）容量之间存在很大差距。实现 Holevo 容量不仅需要最优代码，还需要对长（调制）码字波形进行集体测量的接收器，并且不可能通过逐个符号检测以及经典后处理来实现这些集体测量 [1]、[2]。在这里，我们将经典量子极性码 [3]（第一个近显式、线性、对称 Holevo 速率实现代码）的最新结果应用于有损光通道，并且我们表明它几乎缩小了低光子数状态下与 Holevo 容量的整个差距。相比之下，Arikan 的原始极化码应用于由与任何可想象的结构化光接收器（包括光零差、外差或直接检测）配对的物理光通道引起的 DMC，未能实现通道容量的最终 Holevo 限制。然而，我们的Polar码构造（使用量子保真度作为通道参数而不是经典的Bhattacharyya量来选择Polar码构造中的“好通道”）与量子连续消除接收器配对（涉及对接收到的码字波形的联合量子态进行一系列集体非破坏性二进制投影测量）可以达到Holevo极限，因此原则上可以实现比Arikan的Polar码和直接应用于光通道的解码器更高的速率。然而，即使是构建量子连续抵消接收器的光学实现的理论配方仍然是一个悬而未决的问题。
In the low-energy high-energy-efficiency regime of classical optical communications - relevant to deep-space optical channels - there is a big gap between reliable communication rates achievable via conventional optical receivers and the ultimate (Holevo) capacity. Achieving the Holevo capacity requires not only optimal codes but also receivers that make collective measurements on long (modulated) codeword waveforms, and it is impossible to implement these collective measurements via symbol-by-symbol detection along with classical postprocessing [1], [2]. Here, we apply our recent results on the classical-quantum polar code [3] - the first near-explicit, linear, symmetric-Holevo-rate achieving code - to the lossy optical channel, and we show that it almost closes the entire gap to the Holevo capacity in the low photon number regime. In contrast, Arikan's original polar codes, applied to the DMC induced by the physical optical channel paired with any conceivable structured optical receiver (including optical homodyne, heterodyne, or direct-detection) fails to achieve the ultimate Holevo limit to channel capacity. However, our polar code construction (which uses the quantum fidelity as a channel parameter rather than the classical Bhattacharyya quantity to choose the “good channels” in the polar-code construction), paired with a quantum successive-cancellation receiver - which involves a sequence of collective non-destructive binary projective measurements on the joint quantum state of the received codeword waveform - can attain the Holevo limit, and can hence in principle achieve higher rates than Arikan's polar code and decoder directly applied to the optical channel. However, even a theoretical recipe for construction of an optical realization of the quantum successive-cancellation receiver remains an open question.