Talk:Binary symmetric channel
|WikiProject Telecommunications||(Rated C-class, Mid-importance)|
Unclear proof in "Capacity of BSCp" section
Capacity of BSC
The capacity of the channel is 1 − H(p), where H(p) is the binary entropy function.
The converse can be shown by a sphere packing argument. Given a codeword, there are roughly 2n H(p) typical output sequences. There are 2n total possible outputs, and the input chooses from a codebook of size 2nR. Therefore, the receiver would choose to partition the space into "spheres" with 2n / 2nR = 2n(1 − R) potential outputs each. If R > 1 − H(p), then the spheres will be packed too tightly asymptotically and the receiver will not be able to identify the correct codeword with vanishing probability.
Converse -- What is intended here? A statement that two things are equal does not have a converse.
sphere packing argument -- It is not a sphere-packing argument, since the geometry of the pieces is not used.
Given a codeword, there are roughly 2n H(p) typical output sequences. -- What is a codeword in this context? A binary sequence of length n? What does a "typical output sequence" mean? A possible damaged version of the original sequence? Then why not 2^n?
There are 2n total possible outputs -- What is the difference between an "output" and an "output sequence"? I suppose they can't be the same since there's a factor of H(p).
the input chooses from a codebook of size 2nR -- What is the definition of the variable R? How do we deduce it has size 2nR, or is this a hypothesis? What is a codebook? A list of possible encodings of one desired message? That sounds like only one entry, a tiny fraction of the whole codebook.
Statement of Theorem 1 was incoherent
I've attempted to clarify the (previously incoherent) statement of this theorem to something plausible, but it still has the following defect: δ is not quantified. 184.108.40.206 (talk) 14:40, 20 November 2014 (UTC)
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