High-Rate Fair-Density Parity-Check Codes
summary
Introduces a deterministic construction: a base matrix with two-ones columns with about 2√n rows, then stack permuted copies to get high-rate codes whose low-weight codewords are provably scarce, enabling union-type ML bounds and a predicted error floor around 10^-16. Implements a low-complexity decoder, MP-PL weighted min-sum + progressive list, that beats 5G LDPC by ≈0.5 dB at n=1024, tracks the RCU bound on BEC, and yields linear-time decoding with much lower latency and complexity than SCL polar.
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chapters (8)
- 0:00High-rate fair-density codes
- 1:54High-rate code requirements
- 5:47Fundamental limits analysis
- 13:48Motivation for sparse BP-decodable codes
- 19:10Constructing fair-density codes
- 26:19Simulation results comparison
- 32:42Progressive list decoding
- 37:49Conclusion and future work
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