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I know that New Horizons uses turbo code with r=1/6 for space communication1, however I don’t know which is the encoding coefficient, because I din’t think it could be 6, it seems it high. Could you help me?

update: In response to comments, I'm referring to this answer to What is the modulation technique and what is the coding technique used to send information from the New Horizons spacecraft?:

Phil (Karn) has explained it nicely. Yes, it is BPSK with R=1/6 Turbo coding, that is used in New Horizons...

After encoding, a 6 times longer signal is sent, however it seems to me that an encoding coefficient of 6 is too high.

The data rate is

$$R \frac{\alpha_{\text{encoding}}}{\alpha_{\text{modulation}}}$$

so, 6 times the initial data rate. It seems strange to me. This is my doubt.

1from Wikipedia's Turbo code; Practical applications:

Recent NASA missions such as Mars Reconnaissance Orbiter use turbo codes as an alternative to Reed–Solomon error correction-Viterbi decoder codes.

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    $\begingroup$ do you have any basis for thinking 6 is too high? That rate is repeated in several answers and sources for those answers on this site, particularly CCSDS 101.0-B-4 (see Table 4-2), which spells out the same information and code lengths as the answer you linked to. What more do you want? $\endgroup$
    – Erin Anne
    May 13 at 17:45
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    $\begingroup$ It's not strange for an error-correcting code. The larger number of bits transmitted per bit of payload data allows detection and correction of a larger number of errors. Transmission errors are unavoidable, so when the data needs to be as perfectly transmitted as possible, you use as long a correction code as you can manage. There's no point in collecting twice as much data if it's twice as likely to be wrong, and you can't tell which part is wrong! Better to have a small amount of data that's less likely to lie to you, especially when you're trying to do new science. $\endgroup$
    – Ryan C
    May 13 at 20:05

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Reproducing CCSDS 101.0-B-4 Table 4-2:

Information block length k Codeblock length n for rate 1/2 for rate 1/3 for rate 1/4 for rate 1/6
1784 3576 5364 7152 10728
3568 7144 10714 14288 21432
7136 14280 24120 28560 42840
8920 17848 26772 35696 53544
16384 32776 49164 65552 98328

So no, to answer the question you posed in an answer you posted from a second account, 2000 bps of information being encoded to 12000 bps is not too high. That's the correct understanding of what a rate 1/6 encoding does (roughly--see further portions of the linked standard for more detail). If you're confused as to why six bits per data bit would be sent, this encoding is being used deliberately to minimize the energy spent per data bit or, equivalently, maximize the amount of data that can be sent given the spacecraft's power constraints. See other answers to that same question for further details on how low the New Horizons transmit power is.

So to reiterate: 1/6 is a valid turbo rate. 6 is not too high of an encoding coefficient.

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