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Error Control Systems for Digital Communication and Storage
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TLDR
This work has shown that polynomials over Galois Fields, particularly the Hadamard, Quadratic Residue, and Golay Codes, are good candidates for Error Control Coding for Digital Communication Systems.Abstract:
1. Error Control Coding for Digital Communication Systems. 2. Galois Fields. 3. Polynomials over Galois Fields. 4. Linear Block Codes. 5. Cyclic Codes. 6. Hadamard, Quadratic Residue, and Golay Codes. 7. Reed-Muller Codes 8. BCH and Reed-Solomon Codes. 9. Decoding BCH and Reed-Solomon Codes. 10. The Analysis of the Performance of Block Codes. 11. Convolutional Codes. 12. The Viterbi Decoding Algorithm. 13. The Sequential Decoding Algorithms. 14. Trellis Coded Modulation. 15. Error Control for Channels with Feedback. 16. Applications. Appendices: A. Binary Primitive Polynomials. B. Add-on Tables and Vector Space Representations for GF(8) Through GF(1024). C. Cyclotronic Cosets Modulo 2m-1. D. Minimal Polynomials for Elements in GF (2m). E. Generator Polynomials of Binary BCH Codes of Lengths Through 511. Bibliography.read more
Citations
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On the union bound applied to convolutional codes
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