京都大学 情報学研究科 知能情報学専攻 2019年8月実施 専門科目 S-4
Author
Description
設問 以下の状態遷移図で示される単純マルコフ情報源から出力される系列

(1) 上記の通信路の通信路容量を求めよ。
(2) 受信した系列
(3) マルコフ情報源のエントロピーレート
(4)
(5)
Kai
(1)
The channel matrix is:
Note that when
Hence we have
(2)
Order of symbols
To find the order, we need the steady-state distribution of the states and the emission probabilities. The transition matrix
Solving for the stationary distribution
The probabilities of receiving
or we can simply calculate like this:
The order in decreasing order is
(3)
When
(4)
When
From the Markov matrix we know:
(5)
By the stationarity, we have
and
We calculate the conditional probabilities one by one.
similarly we have
and
Finally we have