Soft GRAND under Channel Switching and Drift
2026-08-24 • Information Theory
Information Theory
AI summaryⓘ
The authors study how errors occur when decoding messages over changing communication channels using a method called GRAND. They show that differences between expected and actual probabilities can increase decoding mistakes and provide mathematical bounds for these errors. They analyze specific cases where the channel switches or gradually changes, offering ways to keep errors low. Finally, they test their ideas using a specific signal type called BPSK under noise. Overall, the work helps understand and control decoding errors in varying channel conditions.
GRAND decodingposterior probabilitychannel switchingmemoryless channelscapacity-achieving inputlog-posterior mismatcherror boundsBPSKgeneralized Gaussian noisepilot refresh
Authors
Behrooz Razeghi
Abstract
Under channel switching or drift, the posterior used to order soft GRAND queries can differ from the matched correction posterior, which can increase rank and finite-budget decoding error. We bound log query rank by matched posterior self-information plus positive log-posterior mismatch; exact random-subset collision probabilities yield GRANDAB error bounds. For switching among memoryless channels with capacity-achieving uniform input, a state-path mixture yields vanishing error uniformly over admissible paths below the minimum constituent capacity when log path-class size is sublinear. For drift, pilot refresh bounds mismatch and yields the continuous minimizer of a tracking upper bound. Generalized-Gaussian BPSK experiments evaluate both.