4
|L
OF F
i
| = max(
d
min
i
|l
j
| − β, 0), β > 0
2. layered scheduling for updating rule
Ref
PK19
claim they used layered scheduling, which helped to eliminate the oscillating
errors caused by the trapping sets. The criteria for how to choose the schedule is unclear
for me yet.
3. enhanced feedback
Ref
WSBW12
developed an optimization called Enhanced Feedback iterative BP decoder. In
the second round of BP decoding, he locate the frustrated checks and some common qubits
connected with them, then use the output probability to replace the input probability for
those qubits. This approach is very similar to what I tried ( in the codeword-based LLR-
simpliﬁed BP decoder for toric codes). The diﬀerence is that, I simply use the output
probability (LLR vector) to replace the input probability for all qubits. I saw it ﬁx all
double errors on large-size (about 35x35) toric codes, but only tiny improvement in the
numerics of small size (5, 7, 9, 11, 13). I am not sure about the reason on small size. there
may be a bug in the program as well.
CTJL05
Jinghu Chen, R Michael Tanner, Christopher Jones, and Yan Li. Improved min-sum decod-
ing algorithms for irregular ldpc codes. In Proceedings. International Symposium on Information
Theory, 2005. ISIT 2005., pages 449–453. IEEE, 2005.
Fil09
Tom Filler. Simpliﬁcation of the belief propagation algorithm. online lecture note, 2009.
FT10
Bill Freeman and Antonio Torralba. Lecture 7: graphical models and belief propagation,
February 2010. MIT EECS course 6.869.
LP18
Ye-Hua Liu and David Poulin. Neural belief-propagation decoders for quantum error-
correcting codes. arXiv preprint arXiv:1811.07835, 2018.
MMK03
David JC MacKay and David JC Mac Kay. Information theory, inference and learning
algorithms. Cambridge university press, 2003.
PK19
Pavel Panteleev and Gleb Kalachev. Degenerate quantum ldpc codes with good ﬁnite length
performance. arXiv preprint arXiv:1904.02703, 2019.
ROJ19
Alex Rigby, JC Olivier, and Peter Jarvis. Modiﬁed belief propagation decoders for quantum
low-density parity-check codes. Physical Review A, 100(1):012330, 2019.
WSBW12
Yun-Jiang Wang, Barry C Sanders, Bao-Ming Bai, and Xin-Mei Wang. Enhanced feed-
back iterative decoding of sparse quantum codes. IEEE Transactions on Information Theory,
58(2):1231–1241, 2012.