# Talk:Binary symmetric channel

WikiProject Telecommunications (Rated C-class, Mid-importance)
This article is within the scope of WikiProject Telecommunications, a collaborative effort to improve the coverage of Telecommunications on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
C  This article has been rated as C-Class on the project's quality scale.
Mid  This article has been rated as Mid-importance on the project's importance scale.

## Contents

${\displaystyle k}$ ${\displaystyle \leq }$ ${\displaystyle \lfloor }$ ${\displaystyle (1-H(p+\epsilon )n)}$ ${\displaystyle \rfloor }$

Is that last ')' misplaced? 68.239.116.212 (talk) 15:08, 2 January 2010 (UTC)

## 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.

the receiver will not be able to identify the correct codeword with vanishing probability -- I think there's a double negative here. 178.38.132.253 (talk) 14:43, 20 November 2014 (UTC)

## 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. 178.38.132.253 (talk) 14:40, 20 November 2014 (UTC)

Hello fellow Wikipedians,

I have just modified one external link on Binary symmetric channel. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:

When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.

You may set the |checked=, on this template, to true or failed to let other editors know you reviewed the change. If you find any errors, please use the tools below to fix them or call an editor by setting |needhelp= to your help request.

• If you have discovered URLs which were erroneously considered dead by the bot, you can report them with this tool.
• If you found an error with any archives or the URLs themselves, you can fix them with this tool.

If you are unable to use these tools, you may set |needhelp=<your help request> on this template to request help from an experienced user. Please include details about your problem, to help other editors.

Cheers.—InternetArchiveBot 15:44, 20 July 2017 (UTC)