東京大学 情報理工学系研究科 電子情報学専攻 2026年1月実施 専門 第5問

标签：

• Tokyo-University
• Source-Extension
• Entropy
• Huffman-Coding
• Markov-Information-Source
• Channel-Capacity
• Cyclic-Redundancy-Check

Author

瑞穂

Description

(1) Calculate entropy of a system $S$ with $p(0)=0.9$ and $p(1)=0.1$, and its second-level entropy $H(S^2)$. Also give a Huffman coding for this system, and calculate the average code length.

(2) Given system transation diagram, calculate stable probability.

(3) Calculate the capacity of channel, where $(a)$ not stable $S$, and $(b)$ stable $S$.

(4) Give the transation matrix of $S$ with error probability $p$ and error code average length $l$.

(5) What is CRC code, and give the capacity of CRC with $G(x)=x^{16}+x^{12}+x^{5}+1$.