Celebratio Mathematica — Berlekamp

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E. R. Berlekamp, R. J. Currie, R. J. McEliece, C. K. Rushforth, and P. Tong: “An error-control code with an imbalance of ones and zeros to provide a residual carrier component,” pp. 31.1.1–31.1.4 in Communications-computers: Teamed for the ’90’s (Monterey, CA, 5–9 October 1986), vol. 2. IEEE (Piscataway, NJ), 1986. incollection

We consider in this paper a direct sequence spread-spectrum communication system employing an error-control code having an imbalance of ones and zeroes. The primary motivation for using such a code is to provide a carrier component for synchronization as an alternative to the transmisson of a separate pilot tone. We evaluate the performance of this system when a concatenated code whose inner code is a constant-weight subcode of the \( (24,12) \) extended Golay code and whose outer code is a Reed–Solomon code. We consider the effects of both white Gaussian noise and burst jamming, and we evaluate several decoding algorithms with different complexities and different coding gains. Near-maximum-likelihood decoding can be realized at the lowest data rates of interest, while successively less complicated algorithms achieving corresponding smaller coding gains must be used as the data rate increases. The performance of this system compares favorably with that of a more conventional pilot-tone system.

Craig K. Rushforth	Related
Robert J. McEliece	Related
R. J. Currie	Related
Po Tong	Related

E. Berlekamp, G. Seroussi, and P. Tong: “A hypersystolic Reed–Solomon decoder,” pp. 205–241 in Reed–Solomon codes and their applications. Edited by S. B. Wicker and V. K. Bhargava. IEEE Press (Piscataway, NJ), 1994. Zbl 1126.94356 incollection

Vijay K. Bhargava	Related
Gadiel Seroussi	Related
Po Tong	Related
Stephen B. Wicker	Related