Specifically, n pc parity-check bits are appended to the information payload.
The polar-code structure selected in NR relies on the addition of a more general, yet hardware friendly, outer code than just a CRC. Xiaoming Chen, in 5G Physical Layer, 2018 Parity-Check Coding Let’s investigate an example using our Hamming (7,4) code.
It is at once astonishing to the novice and inevitable to the mathematician. If we overlap these XORs cleverly, not only can we detect the error, but we can find out where in the string of bits the XOR has gone wrong and set the offending bit back to the proper value. If it’s “one or the other but not both” then a bit-flipping error to either component reverses the outcome (the XOR’d 0 result becomes 1, or 1 becomes 0). How can a series of XORT operations reveal whether received bits are different than the ones sent and, moreover, which bits they are? I don’t claim to be a mathematical theorist, but way to look at it is to consider how XOR works. Either we can “shut up and calculate” and follow the rules because they work, or we can wonder what the numbers are telling us about the way reality works at a more fundamental level. As soon as mathematics rears its ugly head, in fields as diverse as quantum physics to relativity, we can take one of two attitudes. That means according to the rule t < d, that this code can detect only a t-bit error, which means 1 ( but that's not true, because it can detect 3 bit erros).With these simple rules, we can formulate three rules for determining the value of the parity bits:ĭon’t be thrown by the “double XOR” operation: just take the result of the first XOR and use it as one of the values for the second XOR.Īt this point, it might be a good idea to tackle the issue of what the numbers mean. The numbers behind the 'bars/underscores' are the parity-check bits, it means that in each column/row is even count of number 1. T < d (and d stands for hamming distance, its minimum distance between the 2 code words / t stands for t-bit errors). The second thing is, we were learning about hamming distance and there is a rule, which says that block code finds t-bit error when this equation is right: I think the two-dimensional parity check does finds 3-bit erros, but it can't (in every case) correct it. I was given a homework, in which I should explain how does the two dimensional parity check finds 3-bit errors. I am little bit confused right now, in the school we were learning about Hamming's code, Block codes etc. Firstly, I would like to apologize if I misplaced this topic / i think the theory of coding is close to CS /
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