Linear system theory over finite fields has played a major role in unveiling the properties of linear error-correction codes, thus providing essential insights into key design parameters and features, such as minimal realizations, distance spectra, trapping sets, and efficient decoder structures, among others. A related thrust in error correction coding (linear or otherwise) is in secrecy systems, in the form of physical layer security that can complement and, in certain cases even replace, classical cryptography in some communication settings. This chapter reviews the basic principles of secrecy coding, focusing on the properties of linear codes that approach secrecy capacity, as a precursor to understanding design strategies that attain these properties. Applications beyond secure communications of these same coding techniques, notably in watermarking and steganography, are also outlined.

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Basics of Secrecy Coding

  • Phillip A. Regalia

摘要

Linear system theory over finite fields has played a major role in unveiling the properties of linear error-correction codes, thus providing essential insights into key design parameters and features, such as minimal realizations, distance spectra, trapping sets, and efficient decoder structures, among others. A related thrust in error correction coding (linear or otherwise) is in secrecy systems, in the form of physical layer security that can complement and, in certain cases even replace, classical cryptography in some communication settings. This chapter reviews the basic principles of secrecy coding, focusing on the properties of linear codes that approach secrecy capacity, as a precursor to understanding design strategies that attain these properties. Applications beyond secure communications of these same coding techniques, notably in watermarking and steganography, are also outlined.