Journal
IEEE TRANSACTIONS ON INFORMATION THEORY
Volume 63, Issue 7, Pages 4172-4182Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2017.2692214
Keywords
Additive white Gaussian noise channel; amplitude constraint; capacity
Funding
- German Federal Ministry of Education and Research
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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.
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