<p>I'm trying to calculate the probability that a random transmission error goes undetected.</p>

<p>The packet in question is being transmitted over a serial RS-232C interface using 8 data bits, even parity and 1 stop bit. The packet is transfered in ASCII and structured according to the following:</p>

<ul>
<li>Frame header (1 character - ASCII STX)</li>
<li>Telegram ID (3 characters, limited set of valid ID's)</li>
<li>Data (0 to 64 characters depending on the Telegram ID)</li>
<li>Checksum (4 characters, hex representation of CCITT CRC16 of Telegram ID + data)</li>
<li>End of frame (1 charcter - ASCII ETX)</li>
</ul>

<p>I've been trying to locate some papers etc, that describe the strength of the parity check as well as the CRC16 check but so far no luck.</p>

<p>In my own (pragmatic) mind, I've been thinking of something along the lines of:</p>

<p>P<sub>total</sub> = P<sub>parity</sub> * P<sub>crc</sub> * P<sub>content</sub></p>

<p>P<sub>parity</sub> is the probability that an error is undetected by the RS-232C parity check<br>
P<sub>crc</sub> is the probability the error is undetected by the CRC16 check<br>
P<sub>content</sub> is the probability that the error changes the content but is otherwise ok (syntax and semantics)</p>

<p>So what I'm asking for is help to calculate the P<sub>parity</sub> and P<sub>crc</sub>.</p>

<p>I'm not necessarily looking for the exacts mathmatical models, but some more "at least better than" models.</p>

<p>Any help, hints, indicators, etc. are greatly appreciated.</p>

CC BY-SA 2.5
2011-02-23T19:32:39.700Z
(1) You have not specified the error model.  (2) I am afraid that this is not a research-level question, but I may be wrong.
Tsuyoshi Ito
CC BY-SA 2.5
2011-02-24T04:54:10.583Z
it is not clear what is the question in your post. Are you looking for error models or do you have a specific error model and want help regarding the calculation of error in that model?
Kaveh
CC BY-SA 2.5
2011-02-24T07:54:47.940Z
What I'm asking for is help regarding calculation of the propability that a random transmission error will not be detected by the checksums. Pointers to whitepapers, publications, etc. will be fine.
Claus Broch
CC BY-SA 2.5
2011-02-24T23:28:47.857Z
You really need to specify what is the error model before you can do the math... That is, what do you mean by a "random transmission error"? What matters a lot is whether the errors are correlated (for example, if errors tend to occur in "bursts").
Jukka Suomela
<reference-request>
Probability of detecting a transmission error
Claus Broch
# Probability of detecting a transmission error

(Asked by: username_0 on 2011-02-23)

I'm trying to calculate the probability that a random transmission error goes undetected.

The packet in question is being transmitted over a serial RS-232C interface using 8 data bits, even parity and 1 stop bit. The packet is transfered in ASCII and structured according to the following:

* Frame header (1 character - ASCII STX)
* Telegram ID (3 characters, limited set of valid ID's)
* Data (0 to 64 characters depending on the Telegram ID)
* Checksum (4 characters, hex representation of CCITT CRC16 of Telegram ID + data)
* End of frame (1 charcter - ASCII ETX)

I've been trying to locate some papers etc, that describe the strength of the parity check as well as the CRC16 check but so far no luck.

In my own (pragmatic) mind, I've been thinking of something along the lines of:

Ptotal = Pparity \* Pcrc \* Pcontent

Pparity is the probability that an error is undetected by the RS-232C parity check  
Pcrc is the probability the error is undetected by the CRC16 check  
Pcontent is the probability that the error changes the content but is otherwise ok (syntax and semantics)

So what I'm asking for is help to calculate the Pparity and Pcrc.

I'm not necessarily looking for the exacts mathmatical models, but some more "at least better than" models.

Any help, hints, indicators, etc. are greatly appreciated.

**Tags:** reference-request
> **Comments:**
> **username_1**: (1) You have not specified the error model.  (2) I am afraid that this is not a research-level question, but I may be wrong.  
> **username_2**: it is not clear what is the question in your post. Are you looking for error models or do you have a specific error model and want help regarding the calculation of error in that model?  
> **username_0**: What I'm asking for is help regarding calculation of the propability that a random transmission error will not be detected by the checksums. Pointers to whitepapers, publications, etc. will be fine.  
> **username_3**: You really need to specify what is the error model before you can do the math... That is, what do you mean by a "random transmission error"? What matters a lot is whether the errors are correlated (for example, if errors tend to occur in "bursts").  

---

## 0 answers

