Talk:Channel capacity

message: The following information was deleted from this article (see  diff):
:Channel capacity, shown often as "C" in communication formulas, is the amount of discrete information bits that a defined area or segment in a communications medium can hold.  Thus, a telephone wire may be considered a channel in this sense.  Breaking up the frequency bandwidth into smaller sub-segments, and using each of them to carry communications results in a reduction in the number of bits of information that each segment can carry.  The total number of bits of information that the entire wire may carry is not expanded by breaking it into smaller sub-segments.
:In reality, this sub-segmentation reduces the total amount of information that the wire can carry due to the additional overhead of information that is required to distinguish the sub-segments from each other.
However, no reason for this deletion was given. Is this information faulty? Should it be rewritted?
WpZurp 16:46, 29 July 2005 (UTC)
replies: text: The above information is not very relevant to the article.  However, the article could definitely use some rewriting, as I have added some information to it in rather rough form. -- 130.94.162.61 02:34, 22 February 2006 (UTC)

text: This comment presumed that the framing information separating the sub-segments is
not part of the channel capacity, but it must be included in that, so commenting on
framing reducing channel capacity is incorrect/misleading.
For formatting -- the mention is that S/N is in power or volts(with exponent 2).  Unfortunately,
that exponent looks like a footnote reference, so it is misleading one to believe that the
ratio of voltages provides S/N (which it doesn't).  Perhaps someone can think of a better
way to format that so one doesn't go to reference #2 to see how the voltage ratio can
be the same as the power ratio.  —Preceding unsigned comment added by 76.14.50.174 (talk) 09:29, 31 December 2008 (UTC)
thread_title: deleted information -- worth rewriting?

message: The statement of the noisy-channel coding theorem does not agree well with the figure.  I will try to fix it. 130.94.162.64 19:10, 22 May 2006 (UTC)
thread_title: Figure-text agreement

message: The article currently reads "Let p(y | x) be the conditional probability distribution function of X given Y"
should this not be "Let p(y | x) be the conditional probability distribution function of Y given X"?
:Yes, you are right. Bob.v.R 14:24, 17 August 2006 (UTC)
thread_title: X given Y or Y given X

message: I'd like to make a few comments on the following wording. "Here X represents the space of messages transmitted, and Y the space of messages received during a unit time over our channel."
First, I wonder who "we" are, and whether that includes or excludes me.
It is evident from the illustration that the channel receives messages from the transmitter and transmits them to the receiver. One might suspect that "messages received...over our channel" are those which go around it somehow, or those that are received by it. The usual prepositions used with transmission and reception, namely "from," "to," "through," and "by" don't appear in the sentence. "Over" is certainly used in this way, but is less precise than "through." I find it troubling. Also, the concept of "space" enters the wording in a way which further complicates comprehension. Is it "the space of messages" which is transmitted?
I'm not familiar enough with the material to edit the sentence myself, but would like to suggest amending it to take advantage of the more universal prepositions and avoid ambiguity.
Perhaps one of the following, which avoid the hazards, may express the intended message.
"X represents the space of messages entering, and Y the space of messages leaving, the channel in one unit of time."
"X is the number of messages per unit time entering the channel from the transmitter, and Y, those it sends to the receiver."
"X is the flow of messages into, and Y out of, the channel."
D021317c 02:18, 24 March 2007 (UTC)
thread_title:  Prepositions 

message: There is a subsection of information theory that talks about the same. Should be merged.  —Preceding unsigned comment added by Besap (talk • contribs) 10:22, 7 November 2007 (UTC)
replies: text:  I don't think so, it's a part of Information Theory. Kavas (talk) 16:47, 22 August 2010 (UTC)
thread_title:  2 Channel capacity pages 

message: I added this link, which was then removed. That page is what originally brought me to this article. It seems like a particularly intuitive application of channel capacity that could make for some interesting examples. Particularly, the application of channel capacity to image quality seems like a good way to cut through shortcomings of other quality metrics such as megapixels, bit depth, sensor noise, and lens MTF. Can anyone comment on this application? —Ben FrantzDale (talk) 14:39, 9 January 2008 (UTC)
replies: text: That's one of many approximate hypothetical applications of the capacity concept, but otherwise doesn't contribute to understanding the concept or where it is known to really apply. Dicklyon (talk) 19:28, 9 January 2008 (UTC)
replies: text:  Fair enough. It's all interesting stuff. —Ben FrantzDale (talk) 16:24, 15 January 2008 (UTC)
thread_title:  Capacity of images 

message: There is a merge request concerning Information_theory#Capacity_of_particular_channel_models. Can someone look at this and address the issue here? Otr500 (talk) 13:49, 10 March 2011 (UTC)
thread_title:  Merge request 

message: I believe the bandwidth and power limited regions in the figure are swapped. An example with the regions correctly labeled can be found here. --Nerdenceman (talk) 20:15, 8 March 2012 (UTC)
replies: text:  You have overlooked the labeling of the x-axis of the figure, which is "Bandwidth W". This figure is obtained by fixing the SNR value and varying the bandwidth. The figure you linked is obtained the other way round. Anarkigr (talk) 21:12, 13 November 2012 (UTC)
thread_title:  Bandwidth/Power Limited Regions Mislabeled in Figure 

message: the formula for bandwidth-limited regime is incorrect. it should be: W*log2(1+EB/(No*W)).Ofir michael (talk) 13:03, 28 April 2012 (UTC)
replies: text:  It's an approximation. When \text{SNR}_\text{dB} \gg 0,~\log_2 (1+\text{SNR}) \approx \log_2(\text{SNR}), which gives the stated formula. However, your comment leads me to another thing. The usage of SNR is very inconsistent in this section. It is first defined as a ratio which is not in dB (lets call this the "linear" SNR). Then, when talking about "large" and "small" SNR, a dB value is used. The approximate formulas then use linear SNR again. I think that this can be confusing. In terms of linear SNR, "small" can be defined as \text{SNR} \approx 0 and "large" could remain unchanged. Anarkigr (talk) 21:09, 13 November 2012 (UTC)
thread_title:  bandwidth-limited regime 

message: Shannon capacity currently redirects here, but there is also the somewhat related Shannon capacity of a graph. What do you think about turning Shannon capacity into a disamb page? - Saibod (talk) 19:13, 3 October 2013 (UTC)
replies: text: A hatnote would be an alternative. See WP:2DABS. ~Kvng (talk) 14:52, 21 December 2018 (UTC)
thread_title:  Redirect from [[Shannon capacity]] 

message: The written article is too technical for a common person to understand.  — Preceding unsigned comment added by 202.12.103.120 (talk) 17:53, 11 January 2014 (UTC)
replies: text: This is certainly true, and worse -- even a professional mathematician person can't understand it, because the mathematics itself is handled in a spaghetti-like way. It is clearly written by an expert, but at a detail level, the flow of logic in the proofs is not presented crisply. I have done some inching improvements, but it is like slowly chewing granite: the result is good loam, but it takes a long time and there are some hard calculi to digest along the way. 178.38.152.228 (talk) 20:11, 20 November 2014 (UTC)
thread_title: Too technical for a general user to understand

message: The statement "channel capacity is the tight upper bound on the rate at which information can be reliably transmitted over a communications channel" seems to be using the word "reliably" inappropriately. It is, quite simply, a limit on the amount of information that can be transmitted, and it applies whether the information is reliable (certain) or not. I'll delete the word. —Quondum 00:04, 21 November 2014 (UTC)
replies: text: Would you like to clarify the definition of information you are working with when you made this revert?  The only rigorous and appropriate one in this context is that of Shannon, which can essentially be thought of as the reduction of entropy of the transmitter's state upon receiving the message.  Only noiseless real systems can transmit "information" reliably, if you by that you mean knowledge of some state at the transmitter is to be known with certainty.  In real systems, reliability (in the sense of certainty) is only approached on a channel with infinite total capacity (infinite time). IMO, adding the word only confuses things. Information is transmitted across finite noisy channels too. By including the word "reliably", you are confining the statement to highly reliable communication, which is unnecessary. —Quondum 05:44, 21 November 2014 (UTC)
replies: text: In Shannon's approach, reliably means that the error probability can be reduced below any finite bound, not with certainty.  Take a look into books to see what a common expression this is in this context, and for what it means.  Dicklyon (talk) 05:54, 21 November 2014 (UTC)
replies: text: How would you feel about "arbitrarily reliably"?  I guess from looking at the texts that the general focus is on the reliable limit (of an infinite total energy channel), though I intuitively feel that the theorem would cover (or at least generalize to) finite-energy channels, for example to answer the question: how much information can be transmitted via a AWGN channel of finite duration with finite energy? It should be clear that a bound on the quantity of information than can be transmitted (i.e. the mutual information) can be calculated, but that this will not be with arbitrary reliability. —Quondum 16:34, 21 November 2014 (UTC)
replies: text: I think it's not necessary to move away from the usual terminology used in this area.  Capacity arguments generally need to allow arbitrary large code sizes, so don't apply to channels with finite duration; it's more applicable to finite power but ongoing time, as bits per second.  Dicklyon (talk) 20:52, 21 November 2014 (UTC)
replies: text: I agree that this is the usual application. In this context (an encyclopaedia), it should be made clear that this is how a channel is being defined; this is currently left implicit. —Quondum 22:03, 28 November 2014 (UTC)
thread_title:  "reliably"? 

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thread_title:  External links modified