← 研踪 PaperTrailarXiv:2611.16664 · v1
Information Spectrum Methods for MUltiple-Access Channels--Part III : The Strong Converse in the $K$-User Gaussian Case
首次提交 2026-11-12 19:40
版本更新 2026-11-12 19:40
雷达观测 2026-11-13 14:15
摘要
This paper, Part III of a series, treats -user multiple-access channels (MACs). Its starting point is a pair of fundamental lemmas, a random-coding lemma of Feinstein type and a converse lemma of Verdú--Han type, which are the -user extensions of the two lemmas underlying Han's information spectrum approach to the general two-user MAC. From them we derive the capacity region of the general -user MAC with cost constraint and show that it contains the polymatroid capacity region of the -user Gaussian MAC. We then prove, by an elementary information spectrum calculation that adapts a diffuse--exceptional subspace decomposition used in recent second-order converses for the Gaussian MAC, that for every subset $\cS$ of users and every independent input satisfying the power constraints, the conditional information spectral-sup rate of the -user Gaussian MAC does not exceed $\frac12\log(1+P_\cS/N)$, where $P_\cS$ is the total power of the users in $\cS$, with a probability bound that does not depend on the input. Consequently, the strong converse for the -user Gaussian MAC, in the sense that the error probability tends to one for every rate tuple outside the capacity region, follows directly from the converse lemma, without the wringing technique and without hypothesis-testing meta-converses. This strong converse was first established by Fong and Tan, whose per-blocklength bounds yield it, through wringing and quantization. It is the key ingredient in the converse parts of the coding theorems for mixed Gaussian MACs in Part I, where the -strong converse would not suffice.
作者备注：13 pages, 0 figures
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v1 · 2026-11-12 19:40 · 最新观测版本
Information Spectrum Methods for MUltiple-Access Channels--Part III : The Strong Converse in the $K$-User Gaussian Case
This paper, Part III of a series, treats -user multiple-access channels (MACs). Its starting point is a pair of fundamental lemmas, a random-coding lemma of Feinstein type and a converse lemma of Verdú--Han type, which are the -user extensions of the two lemmas underlying Han's information spectrum approach to the general two-user MAC. From them we derive the capacity region of the general -user MAC with cost constraint and show that it contains the polymatroid capacity region of the -user Gaussian MAC. We then prove, by an elementary information spectrum calculation that adapts a diffuse--exceptional subspace decomposition used in recent second-order converses for the Gaussian MAC, that for every subset $\cS$ of users and every independent input satisfying the power constraints, the conditional information spectral-sup rate of the -user Gaussian MAC does not exceed $\frac12\log(1+P_\cS/N)$, where $P_\cS$ is the total power of the users in $\cS$, with a probability bound that does not depend on the input. Consequently, the strong converse for the -user Gaussian MAC, in the sense that the error probability tends to one for every rate tuple outside the capacity region, follows directly from the converse lemma, without the wringing technique and without hypothesis-testing meta-converses. This strong converse was first established by Fong and Tan, whose per-blocklength bounds yield it, through wringing and quantization. It is the key ingredient in the converse parts of the coding theorems for mixed Gaussian MACs in Part I, where the -strong converse would not suffice.
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