信道容量（香农极限）限制了什么？
What does channel capacity (Shannon limit) restrict?
它给出在给定噪声下可靠通信的最大速率（比特/秒），公式 C=B log₂(1+S/N)。超过它必出错；它是通信工程不可逾越的天花板。
It gives the maximum reliable communication rate under given noise: C=B log₂(1+S/N) bits per second. Exceeding it forces errors; it is the unbreakable ceiling of communications engineering.
难度 专业 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-10-04 · 2 条独立证据
来源 · Source
《信息论基础》Cover 与 Thomas
Elements of Information Theory by Cover and Thomas
独立核验依据 · Independent verification: 核验依据 1 ISBN 9780471241959 (2006) · 核验依据 2 ISBN 9780665590955 (2002)
#信息论 #信道
为什么‘密码’越长越难猜，和熵有关吗？
Why are longer passwords harder to guess, and does entropy relate?
密码的熵随可能字符数与长度指数增长：n 个字符、长度 L，则约 n^L 种组合。长度翻倍比加几种字符更能提升抗暴力破解能力。
A password's entropy grows exponentially with character set size and length: roughly n^L combinations. Doubling length beats adding a few character types for resisting brute force.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Graham, Knuth, Patashnik,《Concrete Mathematics》第2版,Addison-Wesley,1994
R. L. Graham et al., Concrete Mathematics, 2nd ed., Addison-Wesley, 1994
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL3951639W：Concrete mathematics（按标
#信息论 #密码
香农熵在衡量什么？
What does Shannon entropy measure?
它衡量一个随机来源的平均‘不确定性’或信息量，H=−Σ pᵢ log₂ pᵢ（比特）。越均匀的分布熵越大，越可预测的分布熵越小。
It measures the average 'uncertainty' or information content of a random source: H=−Σ pᵢ log₂ pᵢ (in bits). More uniform distributions have higher entropy; more predictable ones have lower.
难度 入门 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Graham, Knuth, Patashnik,《Concrete Mathematics》第2版,Addison-Wesley,1994
R. L. Graham et al., Concrete Mathematics, 2nd ed., Addison-Wesley, 1994
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL3951639W：Concrete mathematics（按标
#信息熵 #不确定性
为什么‘每个字符8比特’能表示256种东西？
Why can '8 bits per character' represent 256 things?
每个比特有0/1两种状态，8个比特的组合数是 2⁸=256。这就是二进制位数的指数表达力：n 位能区分 2ⁿ 种不同情况。
Each bit has two states 0/1, so 8 bits give 2⁸=256 combinations. That is the exponential power of binary: n bits distinguish 2ⁿ cases.
难度 入门 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Graham, Knuth, Patashnik,《Concrete Mathematics》第2版,Addison-Wesley,1994
R. L. Graham et al., Concrete Mathematics, 2nd ed., Addison-Wesley, 1994
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL3951639W：Concrete mathematics（按标
#信息论 #二进制