In this article there is a sentence like this

The groundbreaking fact about channel capacity, though, was not simply that it could be traded for or traded away

The whole circumstance is

Shannon’s paper was the first to define the idea of channel capacity, the number of bits per second that a channel can accurately handle. He proved a precise relationship between a channel’s capacity and two of its other qualities: bandwidth (or the range of frequencies it could accommodate) and its ratio of signal to noise. The groundbreaking fact about channel capacity, though, was not simply that it could be traded for or traded away. It was that there is a hard cap—a “speed limit” in bits per second—on accurate communication in any medium. Past this point, which was soon enough named the Shannon limit, our accuracy breaks down.

I don't really understand the meaning of that sentence. What does it mean by trade away and trade for in that sentence?

closed as off-topic by AmE speaker, JonMark Perry, MetaEd Jul 19 '18 at 17:47

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  • this really would be better somewhere else, this is technical language and not standard language. – WendyG Jul 16 '18 at 10:41
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    Implementing a communications channel is a trade-off between three interdependent attributes (capacity, bandwidth, S/N ratio), where optimising any one of those attribute values inevitably causes sub-optimal values in the other two. Per that linked definition, a trade-off is a balancing of factors all of which are not attainable at the same time, so if you trade for capacity you downgrade bandwidth and/or S/N ratio - but you could instead trade away capacity in return for improvements to those other attributes. – FumbleFingers Jul 16 '18 at 12:06
  • In that context there is no difference, as should easily be seen in the reconstruction, "traded away for…" – Robbie Goodwin Jul 19 '18 at 20:37

"Trade", "away" and "for" are used in the sense of the following definitions:

trade verb with object Exchange (something) for something else, typically as a commercial transaction. ‘they trade mud-shark livers for fish oil’ - ODO

away adverb 3 Into non-existence. ‘The train felt glum and groggy, as if the energy of Manhattan was draining away the further north we travelled.’ - ODO

for preposition In place of or in exchange for. ‘will you swap these two bottles for that one?’ - ODO

Trade away and trade for mean essentially the same thing: you have something (in this case, channel capacity), which you can exchange for something else. 'Trade away X' has the connotation that X is lost while 'trade for Y' has the connotation that 'Y' is gained. You can even say that you trade (away) X for Y.

In your case, the quote talks about either "trading (away)" channel capacity for something else (i.e. losing channel capacity), or trading something else "for" channel capacity (i.e. gaining channel capacity).

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    We're talking about comms channels having 3 attributes - capacity, bandwidth, and Signal-to-Noise ratio. And those attributes are interdependent, so changing the value of one affects the values of either or both the others. In the specific context here, I'd say trading for capacity implies increasing capacity by sacrificing bandwidth and/or Signal-to-Noise, whereas trading that capacity away implies accepting lower capacity in favour of improved bandwidth and/or Signal-to-Noise. Which appears to contradict (else) in your final sentence. – FumbleFingers Jul 16 '18 at 11:53
  • I don't fully understand the relationship between the three "attributes" (or whatever you'd call them) myself. It seems to me that "capacity" isn't an independent variable at all - it's just "bandwidth" (notional number of bits per second divided by "S/N ratio" (the proportion of those bits carrying accurate information). – FumbleFingers Jul 16 '18 at 12:10
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    @FumbleFingers I think the quote describes capacity as being defined in terms of bandwidth and SNR. You get to pick two and the third is determined. – Lawrence Jul 16 '18 at 12:23
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    Consider a possible "three-way trade-off" between health, wealth, and happiness. If I say I want to trade wealth for health that would probably imply sacrificing some of my wealth in favour of my health (by spending more on my healthcare). In which case I might say I'm glad my health can be traded for (i.e. - I'm glad I can buy more of it). But if I said I'm glad my wealth can be traded for that would imply I'm glad I can sacrifice some of my health or happiness in order to increase my wealth (which people do do, but it's not really something one would boast about). – FumbleFingers Jul 16 '18 at 12:33
  • @FumbleFingers Indeed. :) – Lawrence Jul 16 '18 at 12:35

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