On Second Order Rate Regions for the Static Scalar Gaussian Broadcast Channel
On Second Order Rate Regions for the Static Scalar Gaussian Broadcast Channel
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DOI：
10.1109/jsac.2023.3280991
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发表时间：
2022-09
影响因子：
16.4
通讯作者：
Daniela Tuninetti;P. Sheldon;B. Smida;N. Devroye
中科院分区：
文献类型：
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作者：
Daniela Tuninetti;P. Sheldon;B. Smida;N. Devroye
研究了有限块长条件下的单天线、静态、标量高斯广播信道。给出了二阶可达速率区和逆速率区。同时考虑了全局可靠性和每个用户的可靠性要求。对两用户情况进行了详细分析，并讨论了对$K$用户情况的推广。与不需要速率分割的(无限块长度，一阶)容量区域相反，这里给出的最大的二阶可实现区域在编码构造中需要叠加和速率分割两者。事实上，有限块长度惩罚单独导致叠加在该区域的某些部分中表现不佳于其他编码技术。此外，该方案使用联合同时译码，而不是连续干扰消除。有趣的是，在具有每用户可靠性要求的两用户情况下，实现叠加编码顺序(以接收信噪比最小的用户为云中心的码字)的容量不一定给出最大的二阶区域。相反，对于所提出的方案，应该在云中心对具有最小点对点二阶容量的用户的消息进行编码，以获得最大的二阶区域。
This paper considers the single antenna, static, scalar Gaussian broadcast channel in the finite blocklength regime. Second order achievable and converse rate regions are presented. Both a global reliability and per-user reliability requirements are considered. The two-user case is analyzed in detail, and generalizations to the $K$ -user case are also discussed. The largest second order achievable regions presented here require both superposition and rate splitting in the code construction, as opposed to the (infinite blocklength, first order) capacity region which does not require rate splitting. Indeed, the finite blocklength penalty causes superposition alone to under-perform other coding techniques in some parts of the region. In addition, the proposed scheme uses joint simultaneous decoding as opposed to successive interference cancellation. Interestingly, in the two-user case with per-user reliability requirements, the capacity achieving superposition encoding order (with the codeword intended for the user with the smallest received SNR as cloud center) does not necessarily give the largest second order region. Instead, the message of the user with the smallest point-to-point second order capacity should be encoded in the cloud center in order to obtain the largest second order region for the proposed scheme.