“…Since we have defined the covariance messages that are consistent to the state evolution recursions in the large system limit, we have V A→B,τ,τ a.s. → V A→B,τ,τ and V B→A,τ,τ a.s. → V B→A,τ,τ . Thus, (50) and ( 52) reduce to (54) and (58), respectively. This justifies the replacement of v suf B→A,t,t in W t with vsuf B→A,t,t .…”