Writing on Dirty Paper with Feedback

摘要

加法的ガウスステートを有する加法的ガゥス雑音通信路の容量については,送信機においてステート情報が非因果的に入手できる場合,通信路容量はステートが存在しない場合の容量と一致することが知られている(M.Costa: Writing on dirty paper).本講演では,Costaの問題を受信機から無雑音フィードパックがある場合に拡張し,この場合の通信路容量が,ステートが存在しない場合のフィードバック付きガウス通信路の容量と一致することを示す.%Feedback plays an important role in interactive communication. One of the most interesting features is that feedback can increase the capacity of a channel with memory. In this paper we consider a feedback generalization of Costa's writing on dirty paper, more specifically, coding for additive Gaussian noise channels with additive Gaussian state available non-causally at the encoder using noiseless feedback, where the noise and state processes are not necessarily stationary or ergodic. We show that the feedback capacity of a Gaussian channel with Gaussian state available non-causally at the encoder is the same as the feedback capacity of the same Gaussian channel with no state, which is in general larger than the non-feedback capacity of the Gaussian channel with no state. It is known that feedback does not increase the capacity of a discrete memoryless channel with discrete memoryless state available non-causally at the encoder. Thus, our result makes a striking contrast to the discrete memoryless channel case and extends the writing-on-dirty-paper paradigm to feedback communication.