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A LINEAR ALGEBRA APPROACH TO MINIMAL CONVOLUTIONAL ENCODERS
JOHANNESSON, R; WAN, ZX
1993-07-01
Source PublicationIEEE TRANSACTIONS ON INFORMATION THEORY
ISSN0018-9448
Volume39Issue:4Pages:1219-1233
AbstractThis semitutorial paper starts with a review of some of Forney's contributions on the algebraic structure of convolutional encoders on which some new results on minimal convolutional encoders rest. An example is given of a basic convolutional encoding matrix whose number of abstract states is minimal over all equivalent encoding matrices. However, this encoding matrix can be realized with a minimal number of memory elements neither in controller canonical form nor in observer canonical form. Thus, this encoding matrix is not minimal according to Forney's definition of a minimal encoder. To resolve this difficulty, the following three minimality criteria are introduced: minimal-basic encoding matrix (minimal overall constraint length over equivalent basic encoding matrices), minimal encoding matrix (minimal number of abstract states over equivalent encoding matrices), and minimal encoder (realization of a minimal encoding matrix with a minimal number of memory elements over all realizations). Among other results, it is shown that all minimal-basic encoding matrices are minimal, but that there exist (basic) minimal encoding matrices that are not minimal-basic! Several equivalent conditions are given for an encoding matrix to be minimal. It is also proven that the constraint lengths of two equivalent minimal-basic encoding matrices are equal one by one up to a rearrangement. All results are proven using only elementary linear algebra. Most important among the new results are a simple minimality test, the surprising fact that there exist basic encoding matrices that are minimal but not minimal-basic, the existence of basic encoding matrices that are nonminimal, and a recent result, due to Forney, that states exactly when a basic encoding matrix is minimal.
KeywordCONVOLUTIONAL CODE BASIC ENCODING MATRIX MINIMAL-BASIC ENCODING MATRIX MINIMAL ENCODING MATRIX MINIMAL ENCODER
Language英语
WOS Research AreaComputer Science ; Engineering
WOS SubjectComputer Science, Information Systems ; Engineering, Electrical & Electronic
WOS IDWOS:A1993MG07500010
PublisherIEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/27569
Collection中国科学院数学与系统科学研究院
Corresponding AuthorJOHANNESSON, R
AffiliationCHINESE ACAD SCI,INST SYST SCI,BEIJING 100080,PEOPLES R CHINA
Recommended Citation
GB/T 7714
JOHANNESSON, R,WAN, ZX. A LINEAR ALGEBRA APPROACH TO MINIMAL CONVOLUTIONAL ENCODERS[J]. IEEE TRANSACTIONS ON INFORMATION THEORY,1993,39(4):1219-1233.
APA JOHANNESSON, R,&WAN, ZX.(1993).A LINEAR ALGEBRA APPROACH TO MINIMAL CONVOLUTIONAL ENCODERS.IEEE TRANSACTIONS ON INFORMATION THEORY,39(4),1219-1233.
MLA JOHANNESSON, R,et al."A LINEAR ALGEBRA APPROACH TO MINIMAL CONVOLUTIONAL ENCODERS".IEEE TRANSACTIONS ON INFORMATION THEORY 39.4(1993):1219-1233.
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