{"title":"沿厄米特多项式编码高斯噪声信道","authors":"E. Abbe, Lizhong Zheng","doi":"10.1109/ISIT.2009.5205789","DOIUrl":null,"url":null,"abstract":"This paper shows that the capacity achieving input distribution for a fading Gaussian broadcast channel is not Gaussian in general. The construction of non-Gaussian distributions that strictly outperform Gaussian ones, for certain characterized fading distributions, is provided. The ability of analyzing non-Gaussian input distributions with closed form expressions is made possible in a local setting. It is shown that there exists a specific coordinate system, based on Hermite polynomials, which parametrizes Gaussian neighborhoods and which is particularly suitable to study the entropic operators encountered with Gaussian noise.","PeriodicalId":412925,"journal":{"name":"2009 IEEE International Symposium on Information Theory","volume":"85 9 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2009-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"14","resultStr":"{\"title\":\"Coding along Hermite polynomials for Gaussian noise channels\",\"authors\":\"E. Abbe, Lizhong Zheng\",\"doi\":\"10.1109/ISIT.2009.5205789\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper shows that the capacity achieving input distribution for a fading Gaussian broadcast channel is not Gaussian in general. The construction of non-Gaussian distributions that strictly outperform Gaussian ones, for certain characterized fading distributions, is provided. The ability of analyzing non-Gaussian input distributions with closed form expressions is made possible in a local setting. It is shown that there exists a specific coordinate system, based on Hermite polynomials, which parametrizes Gaussian neighborhoods and which is particularly suitable to study the entropic operators encountered with Gaussian noise.\",\"PeriodicalId\":412925,\"journal\":{\"name\":\"2009 IEEE International Symposium on Information Theory\",\"volume\":\"85 9 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2009-06-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"14\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2009 IEEE International Symposium on Information Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISIT.2009.5205789\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2009 IEEE International Symposium on Information Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISIT.2009.5205789","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Coding along Hermite polynomials for Gaussian noise channels
This paper shows that the capacity achieving input distribution for a fading Gaussian broadcast channel is not Gaussian in general. The construction of non-Gaussian distributions that strictly outperform Gaussian ones, for certain characterized fading distributions, is provided. The ability of analyzing non-Gaussian input distributions with closed form expressions is made possible in a local setting. It is shown that there exists a specific coordinate system, based on Hermite polynomials, which parametrizes Gaussian neighborhoods and which is particularly suitable to study the entropic operators encountered with Gaussian noise.