مرکز منطقه ای اطلاع رساني علوم و فناوري - On the Schalkwijk-Kailath coding scheme with a peak energy constraint

Abstract :

In a recent series of papers, [2]-[4] Schalkwijk and Kailath have proposed a block coding scheme for transmission over the additive white Gaussian noise channel with one-sided spectral density $N_{0}$ using a noiseless delayless feedback link. The signals have bandwidth $W (W \\leq \\infty )$ and average power $\\bar{P}$ . They show how to communicate at rates $R < C = W \\log (1 + \\bar{P}/N_{0}W)$ , the channel capacity, with error probability $P_{e} = \\exp {-e^{2(C-R)T+o(T)}}$ (where $T$ is the coding delay), a "double exponential" decay. In their scheme the signal energy (in a $T$ -second transmission) is a random variable with only its expectation constrained to be $\\bar{P}T$ . In this paper we consider the effect of imposing a peak energy constraint on the transmitter such that whenever the Schalkwijk-Kailath scheme requires energy exceeding a $\\bar{P}T$ (where $a > 1$ is a fixed parameter) transmission stops and an error is declared. We show that the error probability is degraded to a "single exponential" form $P_{e} = e^{-E(a)T+o(T)}$ and find the exponent $E(a)$ . In the case $W = \\infty , E(a) = (a - 1)^{2}/4a C$ . For finite $W, E(a)$ is given by a more complicated expression.