Capacity Bounds for Discrete-Time, Amplitude-Constrained, Additive White Gaussian Noise Channels

The capacity-achieving input distribution of the discrete-time, additive white Gaussian noise (AWGN) channel with an amplitude constraint is discrete and seems difficult to characterize explicitly. A dual capacity expression is used to derive analytic capacity upper bounds for scalar and vector AWGN...

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Bibliographic Details
Published in:IEEE transactions on information theory 2017-07, Vol.63 (7), p.4172-4182
Main Authors: Thangaraj, Andrew, Kramer, Gerhard, Bocherer, Georg
Format: Article
Language:English
Subjects:
Additive white Gaussian noise channel
amplitude constraint
Amplitudes
AWGN channels
capacity
Channel capacity
Channels
Codes
Communication channels
Constellations
Electronic mail
Entropy
Lower bounds
Random noise
Random variables
Signal to noise ratio
Two dimensional analysis
Upper bound
Upper bounds
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Summary:The capacity-achieving input distribution of the discrete-time, additive white Gaussian noise (AWGN) channel with an amplitude constraint is discrete and seems difficult to characterize explicitly. A dual capacity expression is used to derive analytic capacity upper bounds for scalar and vector AWGN channels. The scalar bound improves on McKellips' bound and is within 0.1 bit of capacity for all signal-to-noise ratios (SNRs). The 2-D bound is within 0.15 bits of capacity provably up to 4.5 dB; numerical evidence suggests a similar gap for all SNRs. As the SNR tends to infinity, these bounds are accurate and match with a volume-based lower bound. For the 2-D complex case, an analytic lower bound is derived by using a concentric constellation and is shown to be within 1 bit of capacity.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2017.2692214