TY - GEN
T1 - Algorithmic Computability of the Capacity of Additive Colored Gaussian Noise Channels
AU - Boche, Holger
AU - Grigorescu, Andrea
AU - Schaefer, Rafael F.
AU - Poor, H. Vincent
N1 - Publisher Copyright:
© 2023 IEEE.
PY - 2023
Y1 - 2023
N2 - Designing capacity-achieving coding schemes for the band-limited additive colored Gaussian noise (ACGN) channel has been and is still a challenge. In this paper, the capacity of the band-limited ACGN channel is studied from a fundamental algorithmic point of view by addressing the question of whether or not the capacity can be algorithmically computed. For this purpose, the concept of Turing machines is used, which provides fundamental performance limits of digital computers. It is shown that there are band-limited ACGN channels having a computable continuous spectral density whose capacity is a non-computable number. Moreover, it is demonstrated that for these channels, it is impossible to find a computable sequence of asymptotically sharp upper bounds for their capacity.
AB - Designing capacity-achieving coding schemes for the band-limited additive colored Gaussian noise (ACGN) channel has been and is still a challenge. In this paper, the capacity of the band-limited ACGN channel is studied from a fundamental algorithmic point of view by addressing the question of whether or not the capacity can be algorithmically computed. For this purpose, the concept of Turing machines is used, which provides fundamental performance limits of digital computers. It is shown that there are band-limited ACGN channels having a computable continuous spectral density whose capacity is a non-computable number. Moreover, it is demonstrated that for these channels, it is impossible to find a computable sequence of asymptotically sharp upper bounds for their capacity.
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U2 - 10.1109/GLOBECOM54140.2023.10436918
DO - 10.1109/GLOBECOM54140.2023.10436918
M3 - Conference contribution
AN - SCOPUS:85187370969
T3 - Proceedings - IEEE Global Communications Conference, GLOBECOM
SP - 4375
EP - 4380
BT - GLOBECOM 2023 - 2023 IEEE Global Communications Conference
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2023 IEEE Global Communications Conference, GLOBECOM 2023
Y2 - 4 December 2023 through 8 December 2023
ER -