[论文解读] New inner and outer bounds for the discrete memoryless cognitive interference channel and some capacity results

Stefano Rini, Daniela Tuninetti+1 more|arXiv (Cornell University)|Mar 23, 2010

Wireless Communication Security Techniques参考文献 31被引用 38

一句话总结

本论文为离散无记忆认知干扰广播信道提出了新的可计算外 bounds，并扩展了可实现速率区域，引入了一种不依赖辅助随机变量的新外 bounds。它在“更好认知解码”体制下建立了容量，并通过 Gelf'and-Pinsker 分组编码与联合码书设计，完全表征了半确定性认知干扰广播信道（其中认知接收机的输出是输入的确定性函数）的容量。

ABSTRACT

The cognitive interference channel is an interference channel in which one transmitter is non-causally provided with the message of the other transmitter. This channel model has been extensively studied in the past years and capacity results for certain classes of channels have been proved. In this paper we present new inner and outer bounds for the capacity region of the cognitive interference channel as well as new capacity results. Previously proposed outer bounds are expressed in terms of auxiliary random variables for which no cardinality constraint is known. Consequently it is not possible to evaluate such outer bounds explicitly for a given channel model. The outer bound we derive is based on an idea originally devised by Sato for the broadcast channel and does not contain auxiliary random variables, allowing it to be more easily evaluated. The inner bound we derive is the largest known to date and is explicitly shown to include all previously proposed achievable rate regions. This comparison highlights which features of the transmission scheme - which includes rate-splitting, superposition coding, a broadcast channel-like binning scheme, and Gel'fand Pinsker coding - are most effective in approaching capacity. We next present new capacity results for a class of discrete memoryless channels that we term the "better cognitive decoding regime" which includes all previously known regimes in which capacity results have been derived as special cases. Finally, we determine the capacity region of the semi-deterministic cognitive interference channel, in which the signal at the cognitive receiver is a deterministic function of the channel inputs.

研究动机与目标

• 为解决由于辅助随机变量的基数约束未知，导致认知干扰广播信道缺乏显式、可计算外 bounds 的问题。
• 构建一个更大、统一的内 bounds，涵盖所有先前提出的可实现速率区域。
• 识别并表征新的容量达到体制，包括“更好认知解码体制”与半确定性认知干扰广播信道。
• 证明 Gelf'and-Pinsker 分组编码可用于确定性信道的容量达到方案。

提出的方法

• 利用广播信道中 Sato 的思想，推导出一种新外 bounds，通过消除辅助随机变量以实现直接可计算性。
• 构建一种新内 bounds，通过整合速率分割、叠加编码、分组编码与 Gelf'and-Pinsker 编码，推广先前方案。
• 提出一种传输策略：认知发射机利用对主消息的了解，设计码字以同时在两个接收机处消除干扰。
• 采用确定性信道模型，实现显式码书设计并达到外 bounds，从而证明容量。
• 在认知编码器处应用 Gelf'and-Pinsker 分组编码，以管理主接收机处的干扰。
• 通过有限字母表的显式示例验证可实现性，表明可通过直接观测输出实现解码。

实验结果

研究问题

• RQ1 能否在不使用辅助随机变量的情况下，为认知干扰广播信道导出可计算的外 bounds？
• RQ2 是否存在一个最大的已知可实现速率区域，能统一涵盖所有先前方案？
• RQ3 在何种条件下，认知发射机对主消息的了解可实现容量达到的传输？
• RQ4 对于认知接收机输出为输入的确定性函数的半确定性认知干扰广播信道，其容量区域是否已知？
• RQ5 Gelf'and-Pinsker 分组编码能否用于确定性认知干扰广播信道的容量达到方案？

主要发现

• 所提出的外 bounds 是可计算的，且不依赖辅助随机变量，可对任意信道模型进行显式评估。
• 新内 bounds 是目前已知最大的，且包含所有先前提出的可实现速率区域作为特例。
• 在一种新体制“更好认知解码体制”下建立了容量，该体制统一了“非常弱”与“非常强”干扰情形。
• 对于半确定性认知干扰广播信道（认知接收机输出为输入的确定性函数），其容量区域已完全表征。
• 通过在认知编码器处使用 Gelf'and-Pinsker 分组编码，演示了一种容量达到方案，可在两个接收机处同时实现干扰消除。
• 通过一个有限字母表的显式示例达到了外 bounds，证实该外 bounds 在某些确定性信道下是紧的。