頁籤選單縮合
題名 | Group Codes: Toward Efficient Error-Control Coding= |
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作者 | Pan,Kuang-hung; |
期刊 | 中華民國資訊學會通訊 |
出版日期 | 20001200 |
卷期 | 3:4 2000.12[民89.12] |
頁次 | 頁37-60 |
分類號 | 312.9 |
語文 | eng |
關鍵詞 | Group codes; Error-control coding; |
英文摘要 | The purpose of this paper is to give a tutorial of group codes. Communication networks requireefficient error-control coding to provide better quality of services. Whether ARQ (automatic repeatrequest) or FEC (forward error control) is used for error control, efficient coding is required.Toward the development of wireless data networks, error-control coding plays an essential role. Group codes are not referred to as a specific coding scheme such as Hamming code. Rather, werefer to group codes as the study of error-control coding from the group-theoretic approach. Inalgebra, group is a structure more general than field and ring, and its applications in coding beganfrom the early days of error-control coding. The term "group codes" originated from Slepian's"group codes for the Gaussian channel". However, it is until recently, especially through the work byForney et al., that the group structure is fully utilized in characterizing the dynamics of codes. Codesover groups are investigated from Willem's view of systems and from symbolic dynamics. Thealgebraic system theory characterizes codes over groups by regarding a code as a system. Thesymbolic dynamics investigates the codes by a finite state labeled graph. The obtained results provideeffective methods to minimize the encoder complexity and to prevent the occurrence of acatastrophic encoder. Slepian's "group code" in fact refers to the group of transformations acting on the signal set. Itis also until recently that the symmetry groups of codes have become more meaningful, particularlythrough Forney's geometrically uniform codes, in which every code sequence has an equalprobability of error under additive white noise. With this property, the design and evaluation of trelliscodes can be done systematically. Homogeneity is a generalization of this notion. Group codes are proved useful in realizing rotational invariance. Rotational invariance is aneffective solution to the problem that the phase difference between the transmitter and the receiver isnot perfectly known. Rotationally invariant trellis codes can be successfully decoded regardless ofthe phase rotation. Rotational invariance has wide applications, especially in trellis coded modulation,which is power and bandwidth efficient by combing coding and modulation. There are many open problems remained for further study in this promising field, where theproblems can be approached from many ways such as coding theory, system theory, and symbolicdynamics. More applications of group codes are looked forward to. |
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