Capacity and Coding for Symmetric Channels with Side Information at the Transmitter

The capacity of a discrete memoryless channel (DMC) P S (yjx), with (random) state information S 2 S available at the transmitter, is given by the capacity of an equivalent DMC with an extended input space X jSj commonly interpreted as a space of strategies. This well known solution, due to Shannon, is in general hard to compute and apply. We consider the special case of a symmetric (modulo-additive noise) channel Y = X + Z S , where the transmitter (but not the receiver) has access to the state S that governs the distribution of the noise Z S. For this channel we nd a concise symmetric form for the equivalent DMC: Y = e X + t(S) + Z S , where t : S ! X is a function to be optimized. Consequently, the capacity is given by C = log jXj ? min t:S!X H(t(S) + Z S), and the optimal transmitter has a simple modular structure, consisting of a conventional (i.e., state independent) encoder at rate C followed by a memoryless \shifting" device t (S). We further generalize our result to channels whose state sequence has memory. 1 B A p(y|x,s) w x Encoder Channel Decoder State Generator w y s s n n ^ Figure 1: Channel connguration