Basic Concepts in Information Theory and Coding pp 131-205 | Cite as

# Synchronizable Codes

## Abstract

Agent 00111 continued to muse over his success as a secret agent. His compatriots, adversaries, and contacts had all declared him to be without parallel in the history of espionage, and who was he to disagree? However, he knew full well that their praise was to some degree self-serving. After all, it was better to be outwitted by someone brilliant than to confess to one’s own stupid mistakes. Obviously, it was not in his interest to dispute his own high standing, but, in truth, he had ran into some very stupid people in the course of his career. Sinking back into his overstuffed chair in front of the glowing fireplace, sipping a large brandy, he started to reminisce. He could not help but chuckle as his thoughts ran to a particularly strange sequence of events.

## Keywords

Word Length Code Word Cyclic Shift Word Sequence Dictionary Size## Preview

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## References

- E. R. Berlekamp. 1968.
*Algebraic Coding Theory*. McGraw-Hill, New York: p. 28.zbMATHGoogle Scholar - G. D. Birkhoff and H. S. Vandiver. 1904. “On the Integral Divisors ofa n— bn .”
*Ann. Math*. 5: 173–80.MathSciNetCrossRefGoogle Scholar - J. Brillhart, D. Lehmer, J. Selfridge, B. Tuckerman, and S. Wagstaff Jr. 1983.
*Factorizations of bn ± 1*. Vol. 22 in Contemporary Mathematics Series Providence, RI: American Math. Society.Google Scholar - L. J. Cummings. 1976. “Comma-Free Codes and Incidence Algebras.” In
*Combinatorial Mathematics IV*. Lecture Notes in Math. 560. Berlin: Springer-Verlag.Google Scholar - L. J. Cummings. 1985. “Synchronizable Codes in the de Bruin Graph.”
*Ars Comb*. 19: 73–90.MathSciNetzbMATHGoogle Scholar - L. J. Cummings. 1987. “Aspects of Synchronizable Coding.”
*Journal of Combinatorial Mathematics and Combinational Computing*1: 17–84.MathSciNetGoogle Scholar - J. S. Devitt and D. M. Jackson. 1981. “Comma-Free Codes: An Extension of Certain Enumerative Techniques to Recursively Defined Sequences.”
*J. Comb. Theory (A)*30: 1–18.MathSciNetzbMATHCrossRefGoogle Scholar - J. S. Devitt. 1983. “An Enumerative Interpretation of the Scholtz Construction for Comma-Free Codes.” In
*Combinatorics on Words, Progress and Perspectives*, edited by L. J. Cummings. Academic Press.Google Scholar - W. L. Eastman. 1965. “On the Construction of Comma-Free Codes. ”
*IEEE Trans. Inform. Theory*. IT-11: 263–66.MathSciNetzbMATHCrossRefGoogle Scholar - W. L. Eastman and S. Even. 1964. “On Synchronizable and PSK Synchronizable Block Codes.”
*IEEE Trans. Inform. Theory*IT-10: 351–56.zbMATHCrossRefGoogle Scholar - F. M. Gardner and W. C. Lindsey, eds. 1980. Special issue on Synchronization.
*IEEE Trans. Commun*. COM-28.Google Scholar - E. N. Gilbert. 1960. “Synchronization of Binary Messages.”
*IRE Trans. Inform. Theory*IT-6: 470–77.CrossRefGoogle Scholar - S. W. Golomb and B. Gordon. 1965. “Codes with Bounded Synchronization Delay.”
*Inform. Control*8: 355–76.MathSciNetzbMATHCrossRefGoogle Scholar - S. W. Golomb, B. Gordon, and L. R. Welch. 1958. “Comma-Free Codes.”
*Canad. J. of Math*. 10: 202–9.MathSciNetzbMATHCrossRefGoogle Scholar - S. W. Golomb, L. R. Welch, and M. Delbrück. 1958. “Construction and Properties of CommaFree Codes.”
*Biol. Medd. K. Dan. Vidensk. Selsk*. 23: 1–34.Google Scholar - S. W. Golomb et al. 1963. “Synchronization.”
*IEEE Trans. Commun*. 11: 481–91.CrossRefGoogle Scholar - B. H. Jiggs. 1963. “Recent Results in Comma-Free Codes.”
*Canad. J. of Math*. 15: 178–87.MathSciNetzbMATHCrossRefGoogle Scholar - W. B. Kendall and I. S. Reed. 1962. “Path-Invariant Comma-Free Codes.”
*IRE Trans. Inform. Theory*IT-8: 350–55.MathSciNetzbMATHCrossRefGoogle Scholar - V. I. Levenshtein. 1961. “Certain Properties of Code Systems.”
*Dokl. Akad. Nauk. SSSR*140: 1274–277.Google Scholar - W. C. Lindsey, F. Ghazvinian, W. C. Hagmann, and K. Dessouky. 1985. “Network Synchronization.”
*Proc. IEEE*73, pp. 1445–1467.CrossRefGoogle Scholar - J. H. van Lint. 1985. “{ 0, 1, *} Distance Problems in Combinatorics.” In
*Surveys in Combinatorics 1985*. Invited papers for the Tenth British Combinatorial Conference, London Mathematical Society Lecture Note Series 103. Cambridge: Cambridge University Press. Pp. 113–35.Google Scholar - Y. Niho. 1973. “On Maximal Comma-Free Codes,”
*IEEE Trans. Inform. Theory*IT-19: 580–81.zbMATHCrossRefGoogle Scholar - H. Reisel. 1968.
*En Bok Om Primtal*. Odense, Denmark: Studentlitteratur.Google Scholar - R. A. Scholtz. 1966. “Codes with Synchronization Capability.”
*IEEE Trans. Inform. Theory*IT12: 135–42.MathSciNetCrossRefGoogle Scholar - 1969. “Maximal- and Variable-Word-Length Comma-Free Codes.”
*IEEE Trans. Inform. Theory*IT-15: 300–6.CrossRefGoogle Scholar - R. A. Scholtz and R. M. Storwick. 1970. “Block Codes for Statistical Synchronization.”
*IEEE Trans. Inform. Theory*IT-16, pp. 432–438.MathSciNetzbMATHCrossRefGoogle Scholar - R. A. Scholtz and L. R. Welch. 1970. “Mechanization of Codes with Bounded Synchronization Delays.”
*IEEE Trans. Inform. Theory*IT-16: 438–46.MathSciNetzbMATHCrossRefGoogle Scholar - J. J. Stiffler. 1971.
*Theory of Synchronous Communications*. Prentice-Hall, New York.Google Scholar - B. Tang, S. W. Golomb, and R. L. Graham. 1987. “A New Result on Comma-Free Codes of Even Wordlength.”
*Canad. J. of Math*. 39: 513–26.MathSciNetzbMATHCrossRefGoogle Scholar - V. K. W. Wei and R. A. Scholtz. 1980. “On the Characterization of Statistically Synchronizable
*Codes.” IEEE Trans. Inform. Theory*IT-26, pp. 733–735.MathSciNetCrossRefGoogle Scholar