GF (q) Precoding: Mutual information analysis in AWGN channels

In this paper, we propose a new precoding scheme that can introduce correlation between the original transmitted symbols. The precoding process is based on the operations in Galois Field with size q = 2^m (GF (q)). In the existing precoding schemes such as orthogonal space-time block code, the generated symbols carry the information of all coded symbols; this correlation can be utilized by the receiver to provide diversity in space and time domain. Similarly, the proposed precoding scheme that utilizes the operations defined in GF (q) can also introduce such correlation. We evaluate the mutual information of the system and conclude that mutual information is always no less than that in the system without the proposed precoding scheme regardless of the source distribution. In addition, when the source is uniformly distributed, the proposed GF (q) precoding scheme achieves the maximum mutual information of the channel, i.e. channel capacity. Hence, we can derive that the proposed precoding scheme in GF (q) can preserve source information during the transmission in the channel. Convinced by the potential benefit of the increased mutual information, the proposed GF (q) precoding scheme is promising in approaching channel capacity.