Gaussian arbitrarily varying channels

• Published in: IEEE transactions on information theory Vol. 33; no. 2; pp. 267 - 284
• Main Authors: Hughes, B., Narayan, P.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.03.1987; Institute of Electrical and Electronics Engineers
• Subjects: Applied sciences; Block codes; Codes; Electrical engineering; Encoding; Error probability; Exact sciences and technology; Ions; Jamming; Random variables; Receivers; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments); Transmitters; Transmission channel; Time variable channel; Gaussian channel
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.1987.1057288

The {\em arbitrarily varying channel} (AVC) can be interpreted as a model of a channel jammed by an intelligent and unpredictable adversary. We investigate the asymptotic reliability of optimal random block codes on Gaussian arbitrarily varying channels (GAVC's). A GAVC is a discrete-time memoryless Gaussian channel with input power constraint P_{T} and noise power N_{e} , which is further corrupted by an additive "jamming signal." The statistics of this signal are unknown and may be arbitrary, except that they are subject to a power constraint P_{J} . We distinguish between two types of power constraints: {\em peak} and {\em average.} For peak constraints on the input power and the jamming power we show that the GAVC has a random coding capacity. For the remaining cases in which either the transmitter or the jammer or both are subject to average power constraints, no capacities exist and only \lambda -capacities are found. The asymptotic error probability suffered by optimal random codes in these cases is determined. Our results suggest that if the jammer is subject only to an average power constraint, reliable communication is impossible at any positive code rate.