Mutual Information and Minimum Mean-square Error in Gaussian Channels
| dc.creator | Guo, Dongning | |
| dc.creator | Shamai, Shlomo | |
| dc.creator | Verdu, Sergio | |
| dc.date | 2004-12-23 | |
| dc.date.accessioned | 2026-07-07T08:15:17Z | |
| dc.date.available | 2026-07-07T08:15:17Z | |
| dc.description | This paper deals with arbitrarily distributed finite-power input signals observed through an additive Gaussian noise channel. It shows a new formula that connects the input-output mutual information and the minimum mean-square error (MMSE) achievable by optimal estimation of the input given the output. That is, the derivative of the mutual information (nats) with respect to the signal-to-noise ratio (SNR) is equal to half the MMSE, regardless of the input statistics. This relationship holds for both scalar and vector signals, as well as for discrete-time and continuous-time noncausal MMSE estimation. This fundamental information-theoretic result has an unexpected consequence in continuous-time nonlinear estimation: For any input signal with finite power, the causal filtering MMSE achieved at SNR is equal to the average value of the noncausal smoothing MMSE achieved with a channel whose signal-to-noise ratio is chosen uniformly distributed between 0 and SNR. | |
| dc.identifier | https://arxiv.org/abs/cs/0412108 | |
| dc.identifier | http://arxiv.org/abs/cs/0412108 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/133399 | |
| dc.subject | Information Theory | |
| dc.title | Mutual Information and Minimum Mean-square Error in Gaussian Channels | |
| dc.type | text |