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Chebyshev centers and radii for sets induced by quadratic matrix inequalities. 二次矩阵不等式集合的切比雪夫中心和半径。
Mathematics of control, signals, and systems : MCSS Pub Date : 2025-01-01 Epub Date: 2025-10-23 DOI: 10.1007/s00498-025-00424-w
Amir Shakouri, Henk J van Waarde, M Kanat Camlibel
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引用次数: 0
Erasure decoding of convolutional codes using first-order representations. 使用一阶表示的卷积码的擦除解码。
Mathematics of control, signals, and systems : MCSS Pub Date : 2021-01-01 Epub Date: 2021-06-04 DOI: 10.1007/s00498-021-00289-9
Julia Lieb, Joachim Rosenthal
{"title":"Erasure decoding of convolutional codes using first-order representations.","authors":"Julia Lieb,&nbsp;Joachim Rosenthal","doi":"10.1007/s00498-021-00289-9","DOIUrl":"https://doi.org/10.1007/s00498-021-00289-9","url":null,"abstract":"<p><p>It is well known that there is a correspondence between convolutional codes and discrete-time linear systems over finite fields. In this paper, we employ the linear systems representation of a convolutional code to develop a decoding algorithm for convolutional codes over the erasure channel. In this kind of channel, which is important due to its use for data transmission over the Internet, the receiver knows if a received symbol is correct. We study the decoding problem using the state space description of a convolutional code, and this provides in a natural way additional information. With respect to previously known decoding algorithms, our new algorithm has the advantage that it is able to reduce the decoding delay as well as the computational effort in the erasure recovery process. We describe which properties a convolutional code should have in order to obtain a good decoding performance and illustrate it with an example.</p>","PeriodicalId":93472,"journal":{"name":"Mathematics of control, signals, and systems : MCSS","volume":"33 3","pages":"499-513"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00498-021-00289-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39642907","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
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