{"title":"关于 K-User 高斯干扰信道的叠加网格编码","authors":"María Constanza Estela, Claudio Valencia-Cordero","doi":"10.3390/e26070575","DOIUrl":null,"url":null,"abstract":"In this study, we work with lattice Gaussian coding for a K-user Gaussian interference channel. Following the procedure of Etkin et al., in which the capacity is found to be within 1 bit/s/Hz of the capacity of a two-user Gaussian interference channel for each type of interference using random codes, we work with lattices to take advantage of their structure and potential for interference alignment. We mimic random codes using a Gaussian distribution over the lattice. Imposing constraints on the flatness factor of the lattices, the common and private message powers, and the channel coefficients, we find the conditions to obtain the same constant gap to the optimal rate for the two-user weak Gaussian interference channel and the generalized degrees of freedom as those obtained with random codes, as found by Etkin et al. Finally, we show how it is possible to extend these results to a K-user weak Gaussian interference channel using lattice alignment.","PeriodicalId":11694,"journal":{"name":"Entropy","volume":null,"pages":null},"PeriodicalIF":2.1000,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Superposition Lattice Codes for the K-User Gaussian Interference Channel\",\"authors\":\"María Constanza Estela, Claudio Valencia-Cordero\",\"doi\":\"10.3390/e26070575\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this study, we work with lattice Gaussian coding for a K-user Gaussian interference channel. Following the procedure of Etkin et al., in which the capacity is found to be within 1 bit/s/Hz of the capacity of a two-user Gaussian interference channel for each type of interference using random codes, we work with lattices to take advantage of their structure and potential for interference alignment. We mimic random codes using a Gaussian distribution over the lattice. Imposing constraints on the flatness factor of the lattices, the common and private message powers, and the channel coefficients, we find the conditions to obtain the same constant gap to the optimal rate for the two-user weak Gaussian interference channel and the generalized degrees of freedom as those obtained with random codes, as found by Etkin et al. Finally, we show how it is possible to extend these results to a K-user weak Gaussian interference channel using lattice alignment.\",\"PeriodicalId\":11694,\"journal\":{\"name\":\"Entropy\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-07-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Entropy\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.3390/e26070575\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Entropy","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.3390/e26070575","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
摘要
在本研究中,我们对 K 用户高斯干扰信道进行格高斯编码。根据 Etkin 等人的研究方法,对于每种干扰类型,使用随机码的容量与双用户高斯干扰信道的容量相差在 1 比特/秒/赫兹以内。我们使用网格上的高斯分布来模拟随机码。通过对网格的平整度系数、公共和私人信息功率以及信道系数施加约束,我们找到了获得双用户弱高斯干扰信道最佳速率恒定差距的条件,以及与埃特金等人使用随机码获得的广义自由度相同的条件。
On Superposition Lattice Codes for the K-User Gaussian Interference Channel
In this study, we work with lattice Gaussian coding for a K-user Gaussian interference channel. Following the procedure of Etkin et al., in which the capacity is found to be within 1 bit/s/Hz of the capacity of a two-user Gaussian interference channel for each type of interference using random codes, we work with lattices to take advantage of their structure and potential for interference alignment. We mimic random codes using a Gaussian distribution over the lattice. Imposing constraints on the flatness factor of the lattices, the common and private message powers, and the channel coefficients, we find the conditions to obtain the same constant gap to the optimal rate for the two-user weak Gaussian interference channel and the generalized degrees of freedom as those obtained with random codes, as found by Etkin et al. Finally, we show how it is possible to extend these results to a K-user weak Gaussian interference channel using lattice alignment.
期刊介绍:
Entropy (ISSN 1099-4300), an international and interdisciplinary journal of entropy and information studies, publishes reviews, regular research papers and short notes. Our aim is to encourage scientists to publish as much as possible their theoretical and experimental details. There is no restriction on the length of the papers. If there are computation and the experiment, the details must be provided so that the results can be reproduced.