TY - JOUR
T1 - Asymptotic behavior of error exponents in the wideband regime
AU - Wu, Xinzhou
AU - Srikant, R.
N1 - Funding Information:
Manuscript received January 6, 2004; revised July 3, 2006. This work was supported by DARPA under Grant F30602-00-2-0542, AFOSR URI under Grant F49620-01-1-0365, and the National Science Foundation under ITR Grant 00-85929.The material in this paper was presented in paart at the IEEE International Symposium on Information Theory, Chicago, IL, Jun./Jul. 2004. X. Wu is with QUALCOMM Flarion Technologies, Bedminster, NJ 07921 USA (e-mail: [email protected]). R. Srikant is with the Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801 USA (e-mail: [email protected]). Communicated by A. Lapidoth, Associate Editor for Shannon Theory. Digital Object Identifier 10.1109/TIT.2007.892786
PY - 2007/4
Y1 - 2007/4
N2 - In this paper, we investigate the fundamental tradeoff between rate and bandwidth when a constraint is imposed on the error exponent. Specifically, we consider both additive white Gaussian noise (AWGN) and Rayleigh-fading channels where the input symbols are assumed to have a peak constraint. For the AWGN channel model, the optimal values of Rz(0) and Rz(0) are calculated, where Rz (1/B) is the maximum rate at which information can be transmitted over a channel with bandwidth B when the error-exponent is constrained to be greater than or equal to z. The computation of Rz(0) follows Gallager's infinite-bandwidth reliability function computation, while the computation of Rz(0) is new and parallels Verdu's second-order calculation for channel capacity. Based on these calculations, we say that a sequence of input distributions is near optimal if both Rz(0) and Rz(0) are achieved. We show that quaternary phase-shift keying (QPSK), a widely used signaling scheme, is near optimal within a large class of input distributions for the AWGN channel. Similar results are also established for a fading channel where full channel side information (CSI) is available at the receiver.
AB - In this paper, we investigate the fundamental tradeoff between rate and bandwidth when a constraint is imposed on the error exponent. Specifically, we consider both additive white Gaussian noise (AWGN) and Rayleigh-fading channels where the input symbols are assumed to have a peak constraint. For the AWGN channel model, the optimal values of Rz(0) and Rz(0) are calculated, where Rz (1/B) is the maximum rate at which information can be transmitted over a channel with bandwidth B when the error-exponent is constrained to be greater than or equal to z. The computation of Rz(0) follows Gallager's infinite-bandwidth reliability function computation, while the computation of Rz(0) is new and parallels Verdu's second-order calculation for channel capacity. Based on these calculations, we say that a sequence of input distributions is near optimal if both Rz(0) and Rz(0) are achieved. We show that quaternary phase-shift keying (QPSK), a widely used signaling scheme, is near optimal within a large class of input distributions for the AWGN channel. Similar results are also established for a fading channel where full channel side information (CSI) is available at the receiver.
KW - Error exponent
KW - Low signal-to-noise ratio (SNR)
KW - Near-optimality signaling
KW - Wideband
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U2 - 10.1109/TIT.2007.892786
DO - 10.1109/TIT.2007.892786
M3 - Article
AN - SCOPUS:34147120592
SN - 0018-9448
VL - 53
SP - 1310
EP - 1325
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 4
ER -