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High-Rate Self-Synchronizing Codes

Fujiwara, Yuichiro and Tonchev, Vladimir D. (2013) High-Rate Self-Synchronizing Codes. IEEE Transactions on Information Theory, 59 (4). pp. 2328-2335. ISSN 0018-9448. doi:10.1109/TIT.2012.2234501.

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Self-synchronization under the presence of additive noise can be achieved by allocating a certain number of bits of each codeword as markers for synchronization. Difference systems of sets are combinatorial designs which specify the positions of synchronization markers in codewords in such a way that the resulting error-tolerant self-synchronizing codes may be realized as cosets of linear codes. Ideally, difference systems of sets should sacrifice as few bits as possible for a given code length, alphabet size, and error-tolerance capability. However, it seems difficult to attain optimality with respect to known bounds when the noise level is relatively low. In fact, the majority of known optimal difference systems of sets are for exceptionally noisy channels, requiring a substantial amount of bits for synchronization. To address this problem, we present constructions for difference systems of sets that allow for higher information rates while sacrificing optimality to only a small extent. Our constructions utilize optimal difference systems of sets as ingredients and, when applied carefully, generate asymptotically optimal ones with higher information rates. We also give direct constructions for optimal difference systems of sets with high information rates and error tolerance that generate binary and ternary self-synchronizing codes.

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Additional Information:© 2012 IEEE. Manuscript received August 25, 2012; revised November 28, 2012; accepted December 11, 2012. Date of publication December 20, 2012; date of current version March 13, 2013. Y. Fujiwara was supported by JSPS Postdoctoral Fellowships for Research Abroad. V. Tonchev was supported by an NSA Grant. This paper was presented in part at the International Symposium on Information Theory and its Applications, Honolulu, HI, October 2012. The authors thank Yukiyasu Mutoh for sharing his unpublished manuscript [34], and are grateful to the anonymous referees and Associate Editor Kyeongcheol Yang for careful reading and valuable comments. This research was conducted while the first author was visiting the Department of Mathematical Sciences, Michigan Technological University. He thanks the department for the hospitality.
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Japan Society for the Promotion of Science (JSPS)UNSPECIFIED
National Security Agency (NSA)UNSPECIFIED
Subject Keywords:Comma-free code, cyclotomy, difference system of sets (DSS), redundancy, self-synchronizing code, synchronization.
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INSPEC Accession Number13371609
Issue or Number:4
Record Number:CaltechAUTHORS:20130501-081551103
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Official Citation:Fujiwara, Y.; Tonchev, V.D., "High-Rate Self-Synchronizing Codes," Information Theory, IEEE Transactions on , vol.59, no.4, pp.2328,2335, April 2013 doi: 10.1109/TIT.2012.2234501
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38194
Deposited By: Ruth Sustaita
Deposited On:01 May 2013 15:29
Last Modified:09 Nov 2021 23:35

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