Channel Coding - Probability of Error - Page 1
Forum section: electronics / testgear

author: tec5c
author_rank: Frequent Contributor
timestamp: October 25, 2015, 06:24:18 am
content: I know this is the wrong thread for this topic, though I have received no responses for it in other threads so I thought I'd try one that had more activity. My apologies for any inconveniences this may cause.I'm a little confused in calculating the probability of error when using error correction coding.I am fine with finding the probability of error when there is no error correction code involved though I don't quite understand the difference between the probability of error between the demodulator output and the pr. of error at the decoder output.Anyone have experience in this field that could offer me some insight?

author: tec5c
author_rank: Frequent Contributor
timestamp: October 25, 2015, 10:30:40 am
content: So it doesn't look like I'll have much success here.Does anyone know of other forums that are more aimed at communication systems?

author: rs20
author_rank: Super Contributor
timestamp: October 25, 2015, 10:32:49 am
content: a) You only gave it 4 hours?b) You haven't asked an actual question.

author: crispy_tofu
author_rank: Super Contributor
timestamp: October 25, 2015, 10:35:59 am
content: Quote from: rs20 on October 25, 2015, 10:32:49 amhttps://www.eevblog.com/forum/beginners/channel-coding-probability-of-error/msg784344/#msg784344

author: tec5c
author_rank: Frequent Contributor
timestamp: October 25, 2015, 10:47:10 am
content: Quote from: rs20 on October 25, 2015, 10:32:49 amHow does the probability of error at the demodulator output differ from the probability of error at the decoder output?

author: rs20
author_rank: Super Contributor
timestamp: October 25, 2015, 11:23:21 am
content: By "decoder", do you mean the error corrector? Because clearly, if the error corrector is any good, some errors in the demodulated stream will be detected and corrected by it, and so won't be errors anymore by the time the data makes it to the decoded output? Hence the error rate is lower after the error corrector.I feel I may have misunderstood, that seems too easy.

author: tec5c
author_rank: Frequent Contributor
timestamp: October 25, 2015, 12:24:22 pm
content: Well the decoder cannot correct an error, right.Here's a block diagram which is taken from a textbook chapter on channel coding...I understand the concept behind what you said, however I should have been clearer in that I don't understand how to calculate the probability of error at the decoder output. My apologies for any misconceptions, I am severely under the hammer with Uni work as the end of the (Uni) year is less than 4 weeks away.

author: TheUnnamedNewbie
author_rank: Super Contributor
timestamp: October 25, 2015, 01:11:00 pm
content: Let Si be a codeword that enters the decoder. This codeword can be written as Si=Mi+Ei, where Mi represents the message, and Ei is the error on said message. Depending on the EC coding used, there will be a range of functions Ei that can be filtered out. However, there will always be values for Ei that cannot be filtered out. The probability of error in the decoder is the probability that Ei is a function we cannot filter out, and the output of the decoder is not equal to the encoded data. To find this probability you will need to look for a way to determine which error can and cannot be corrected.

author: tec5c
author_rank: Frequent Contributor
timestamp: October 25, 2015, 01:50:16 pm
content: Thanks for the reply. If I now understand correctly, I need to be using conditional probability density functions... which makes sense now I think about it.It seems like you've deceitfully named yourself on this forum...

author: coppice
author_rank: Super Contributor
timestamp: October 25, 2015, 04:21:14 pm
content: If you want an indignant rant, you can have an answer in a few seconds. If you want a real engineering question answered you need to give it 24 hours, just to let it wash through the time zones.Shannon's channel capacity theorem tells us that its conceptually possible to send a certain amount of data through a channel every second (termed the channel capacity) with an arbitrarily low error rate, but doesn't give us a clue how. I find this total separation of an easily derived theoretical boundary and implementation quite intriguing.Nobody has figured out a modulation scheme that will get really close to the channel's capacity. Things like OFDM perform pretty well, but it you want to get within a fraction of a dB of capacity you need to code the data. Quite a few effective coding techniques exist, from early ones like trellis coding, through turbo codes, to the most recent codes like Polar codes. After coding there will be more bits than before, so the channel actually carries a higher bit rate. However, the effectiveness of good coding is such than it overcomes the effects of those extra bits, and gives you the effect of several dBs of extra SNR. Coming out of the demodulator will be the output of the coder with some bad bits. After decoding there will be the original number of bits, and hopefully a lot less bad bits. The patterns for what gets fixed and what doesn't varies enormously with the actual coding scheme. TheUnnamedNewbie gave a good generalised why of looking at it, but there is an important caveat. The modulator/demodulator path is carrying a higher bit rate because it is carrying a coded bit stream. Depending on the type of coding and modulation, this may adversely affect the BER out of the demodulator. You need to consider this when trying to make a fair comparison of the BER before and after the decoder.

author: tec5c
author_rank: Frequent Contributor
timestamp: October 26, 2015, 01:16:51 am
content: Right, things are making sense now.The BER is higher at the demodulator output for the coded system, though the probability of message error is lower at the decoder output for the coded system...This is what I've concluded for the probability of bit error at the decoder output, along with an example of how it's implemented:Criticism is welcomed.Also, thanks coppice for your reply.