11/13/2022 0 Comments 2d parity check program c![]() ![]() ![]() The same shift-register architecture can be used by the successive-cancellation list decoder to prune all paths that result in an erroneous parity-check bit. Empirical evidence suggests that enforcing such spacing makes the resulting scheme robust against error propagation. ![]() Specifically, the parity bits are computed through a length 5 shift register that evaluates the F 2-sum of information bits that are five positions apart see for details. To aid the intermediate steps of the successive-cancellation list-decoding algorithm, each parity-check bit is designed to depend only on preceding information bits. This improves the distance spectrum of the resulting concatenated code. Some of them are assigned to the unfrozen-bit positions in the vector u that correspond to the rows in the polar transform matrix G with smallest Hamming weights. This improves the error performance of the code. Some of them are assigned to the k + n pc unfrozen synthetic channels with lowest polarization weight. 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. 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. ![]()
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