Modulation and Estimation with a Helper
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866912087017521152 |
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| author | Khina, Anatoly Merhav, Neri |
| author_facet | Khina, Anatoly Merhav, Neri |
| contents | The problem of transmitting a parameter value over an additive white Gaussian noise (AWGN) channel is considered, where, in addition to the transmitter and the receiver, there is a helper that observes the noise non-causally and provides a description of limited rate $R_h$ to the transmitter and/or the receiver. We derive upper and lower bounds on the optimal achievable $α$-th moment of the estimation error and show that they coincide for small values of $α$ and for high values of $R_h$. The upper bound relies on a recently proposed channel-coding scheme that effectively conveys $R_h$ bits essentially error-free and the rest of the rate - over the same AWGN channel without help, with the error-free bits being allocated to the most significant bits of the quantized parameter. We then concentrate on the setting with a total transmit energy constraint, for which we derive achievability results for both channel coding and parameter modulation for several scenarios: when the helper assists only the transmitter or only the receiver and knows the noise, and when the helper assists the transmitter and/or the receiver and knows both the noise and the message. In particular, for the message-informed helper that assists both the receiver and the transmitter, it is shown that the error probability in the channel-coding task decays doubly exponentially. Finally, we translate these results to those for continuous-time power-limited AWGN channels with unconstrained bandwidth. As a byproduct, we show that the capacity with a message-informed helper that is available only at the transmitter can exceed the sum of the capacity without help and the help rate $R_h$, when the helper knows only the noise but not the message. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_04277 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Modulation and Estimation with a Helper Khina, Anatoly Merhav, Neri Information Theory Signal Processing The problem of transmitting a parameter value over an additive white Gaussian noise (AWGN) channel is considered, where, in addition to the transmitter and the receiver, there is a helper that observes the noise non-causally and provides a description of limited rate $R_h$ to the transmitter and/or the receiver. We derive upper and lower bounds on the optimal achievable $α$-th moment of the estimation error and show that they coincide for small values of $α$ and for high values of $R_h$. The upper bound relies on a recently proposed channel-coding scheme that effectively conveys $R_h$ bits essentially error-free and the rest of the rate - over the same AWGN channel without help, with the error-free bits being allocated to the most significant bits of the quantized parameter. We then concentrate on the setting with a total transmit energy constraint, for which we derive achievability results for both channel coding and parameter modulation for several scenarios: when the helper assists only the transmitter or only the receiver and knows the noise, and when the helper assists the transmitter and/or the receiver and knows both the noise and the message. In particular, for the message-informed helper that assists both the receiver and the transmitter, it is shown that the error probability in the channel-coding task decays doubly exponentially. Finally, we translate these results to those for continuous-time power-limited AWGN channels with unconstrained bandwidth. As a byproduct, we show that the capacity with a message-informed helper that is available only at the transmitter can exceed the sum of the capacity without help and the help rate $R_h$, when the helper knows only the noise but not the message. |
| title | Modulation and Estimation with a Helper |
| topic | Information Theory Signal Processing |
| url | https://arxiv.org/abs/2309.04277 |