Polynomial theory of error correcting codes. ([2014])

• Record Type: Book
• Further Information: Note: Giovanni Cancellieri.
• Authors: Cancellieri, Giovanni
• Contents: Preface; Contents; Acronyms; Part I Generator Matrix; 1 Generator Matrix Approach to Linear Block Codes; 1.1 Additive n x n Linear Transformation of a Binary Sequence; 1.2 Generator Matrix G of a Linear Block Code; 1.3 Polynomial Description of the Generator Matrix in a Linear Block Code; 1.4 Properties of a Linear Block Code Derived from the Structural Characteristics of g(x); 1.5 Systematic Encoder Circuit; 1.6 Code Concatenation: Effects on G Matrix; 1.7 Code Puncturation: Effects on G Matrix; 1.8 Cyclic Block Codes; 1.9 Enumeration of all the Possible Cyclic Codes of Length N. 1.10 Shortened Cyclic (SC) Codes1.11 Lengthened Cyclic (LC) Codes; 1.12 Subcode of an s.s. Time-Invariant Polynomial Code; 1.13 Modified Lengthened Cyclic (MLC) Codes; 1.14 State Diagrams; 1.15 Direct Product Codes; 1.16 Generator Matrix of a Direct Product Code; 1.17 Direct Product Codes as MLC Codes; 1.18 Interpretation of Particular Direct Product Codes by Means of GPC Codes; 1.19 Cyclic and Pseudo-Cyclic Codes in a Non-binary Alphabet; 1.20 Q-ary State Diagrams; 1.21 Main Families of Non-binary Block Codes; 1.22 Reed-Solomon Codes and Other MDS Non-binary Codes. 1.23 Trellis for an s.s. Time-Invariant Block Code Obtained from Its Generator MatrixReferences; 2 Wide-Sense Time-Invariant Block Codes in Their Generator Matrix; 2.1 Periodically Time-Varying Generator Matrix; 2.2 Quasi-Cyclic Codes (QC) as a Widening in the Concept of Cyclic Codes; 2.3 Quasi-Cyclic Codes with Distributed Control Symbols Described with Their G Matrix; 2.4 Representation of Known Block Codes as QC Codes with Distributed Control Symbols; 2.5 Relation Between Some Binary QC-Codes and Cyclic or Pseudo-Cyclic Codes in a Q-Ary Alphabet. 2.6 Encoder Circuits Based on the G Matrix for a QC Code2.7 Shortened Quasi-Cyclic (SQC) Codes; 2.8 Lengthened Quasi-Cyclic (LQC) Codes; 2.9 Subcode of a w.s. Time-Invariant Polynomial Code; 2.10 Modified Lengthened Quasi-Cyclic (MLQC) Codes; 2.11 Trellis for a w.s. Time-Invariant Block Code Obtained from Its Generator Matrix; References; 3 Generator Matrix Approach to s.s. Time-Invariant Convolutional Codes; 3.1 Traditional View of Non-systematic s.s. Time-Invariant Convolutional Codes; 3.2 State Diagram and Minimum Distance; 3.3 Systematic Convolutional Codes. 3.4 Low-Rate Convolutional Codes3.5 High-Rate Punctured Convolutional Codes; 3.6 Recursive Systematic Convolutional (RSC) Codes; 3.7 Equivalence Between MLC Codes and s.s. Time-Invariant Convolutional Codes; 3.8 Strict-Sense Time-Invariant High-Rate Convolutional (MLC) Codes; 3.9 A First Bridge Between Cyclic Block Codes and s.s. Time-Invariant Convolutional Codes; 3.10 Tail-Biting s.s. Time-Invariant Convolutional Codes; 3.11 Trellis of an s.s. Time-Invariant Convolutional Code Obtained from Its Generator Matrix; References.
• Publisher Details: Cham : Springer
• Publication Date: 2014
• Copyright Date: 2015
• Extent: 1 online resource (xviii, 732 pages), illustrations
• Subjects: 005.7/17; Engineering; Error-correcting codes (Information theory); Polynomials; COMPUTERS -- Data Processing; Error-correcting codes (Information theory); Polynomials; Engineering & Applied Sciences; Electrical & Computer Engineering; Electrical Engineering; Applied Physics; Telecommunications; Mathematics -- Algebra -- Abstract; Computers -- Logic Design; Algebra; Algorithms & data structures; Field theory (Physics); Computer science; Technology & Engineering -- Electronics -- General; Imaging systems & technology; Electronic books
• Languages: English
• ISBNs: 9783319017273; 3319017276
• Related ISBNs: 9783319017266; 3319017268
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (SpringerLink, viewed December 17, 2014).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.