The Capacity of Linear Computation Broadcast

The two-user computation broadcast problem is introduced as the setting where user 1 wants message W
₁
and has side information W'
₁
, user 2 wants message W
₂
and has side information W
₂
', and (W
₁
, W'
₁
, W
₂
, W'
₂
) may have arbitrary dependencies. The goal is to minimize the entropy H(S) of the broadcast information S that simultaneously satisfies both users' demands. It is shown that H(S) > H(W
₁
|W'
₁
) + H(W
₂
|W'
₂
)-min (I(W
₁
; W
₂
, W'
₂
|W'
₁
), I (W
₂
; W
₁
, W'
₁
|W'
₂
)). Furthermore, for the linear computation broadcast problem, where W
₁
, W'
₁
, W
₂
, W'
₂
are comprised of arbitrary linear combinations of a basis set of independent symbols, the bound is shown to be tight.