Causal state quantization with or without cribbing for the MAC with a state-cognizant receiver

A two-to-one memoryless state-dependent multiple-access channel is studied in a setting where helpers that observe the state sequence causally provide rate-limited (lossy) causal descriptions of it to the encoders. It is shown that, when the receiver is cognizant of the channel state, the optimal causal descriptions take the form of scalar symbol-by-symbol quantizers whose descriptions of the current state do not depend on the past states. This holds irrespective of whether the description is provided to both encoders (the "common description" architecture), to one of the encoders (the "one-sided description" architecture), or whether different descriptions are provided to the different encoders (the "general" architecture). In fact, in the common description architecture, it also holds when the encoders can crib. Thus, the prevalent assumption that the receiver is cognizant of the channel state greatly simplifies the design of the state quantizer.