Outage Behavior of Discrete Memoryless Channels (DMCs) Under Channel Estimation Errors

Communication systems are usually designed by assuming perfect channel state information (CSI). However, in many practical scenarios, only a noisy estimate of the channel is available, which may strongly differ from the true channel. This imperfect CSI scenario is addressed by introducing the notion of estimation-induced outage (EIO) capacity. We derive a single-letter characterization of the maximal EIO rate and prove an associated coding theorem and its strong converse for discrete memoryless channels (DMCs). The transmitter and the receiver rely on the channel estimate and the statistics of the estimate to construct codes that guarantee reliable communication with a certain outage probability. This ensures that in the non-outage case the transmission meets the target rate with small error probability, irrespective of the quality of the channel estimate. Applications of the EIO capacity to a single-antenna (non-ergodic) Ricean fading channel are considered. The EIO capacity for this case is compared to the EIO rates of a communication system in which the receiver decodes by using a mismatched ML decoder. The effects of rate-limited feedback to provide the transmitter with quantized CSI are also investigated.

💡 Research Summary

The paper tackles a fundamental gap between information‑theoretic channel design and practical wireless systems: the assumption of perfect channel state information (CSI) at both transmitter and receiver. In real deployments, only a noisy estimate of the channel is available, and this estimate may deviate significantly from the true channel transition probabilities. To address this, the authors introduce the notion of estimation‑induced outage (EIO) capacity.

EIO capacity is defined with respect to a prescribed outage probability ε. Given a channel estimate (\hat{W}) and the statistical relationship (P_{\hat{W}|W}) between the estimate and the true channel (W), the set of admissible true channels that are compatible with the estimate is denoted (\mathcal{W}(\hat{W},\epsilon)). An outage occurs when the actual channel falls outside this set; otherwise communication must succeed with a small error probability δ. The maximal achievable rate under these constraints is expressed in a single‑letter form:

\