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Cyclically Equivariant Neural Decoders for Cyclic Codes
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the cyclically equivariant neural decoder instead of N18 | Neural decoding of cyclic codes · BCH and punctured RM codes | negative natural logarithm of BER: 0.7dB | Helped |
| Use the cyclically equivariant decoder instead of the hyper-graph-network decoder | Neural decoding of BCH codes · BCH(63,36) and BCH(63,45) | decoding performance: 0.3dB | Helped |
| Add boosting by repeatedly feeding decoder output LLRs back as inputs | Neural decoder · BCH and punctured RM codes | negative natural logarithm of BER | Helped |
| Increase list size from ℓ=1 to ℓ=n+1 | List decoder · BCH and punctured RM codes | negative natural logarithm of FER: up to 3dB | Helped |
| Use list size ℓ=8 rather than no list decoding | Neural list decoder · BCH and punctured RM codes | decoding performance: 0.7∼0.9dB | Helped |
| Use list size ℓ=n+1 | List decoder · High-rate codes (rate ≥ 0.7) | gap to ML decoder: no larger than 0.1dB | Helped |
| Use list size ℓ=n+1 | List decoder · Codes with rate ≤ 0.5 | gap to ML lower bound: larger than 1dB | Hurt |
| Replace the (n-k)×n parity matrix with a randomly extended n×n matrix (ablation) | N18 feed-forward neural decoder · BCH(63,24), BCH(63,36), BCH(63,45), and PRM(63,22) | negative natural logarithm of BER: 3.24 -> 3.27; 4.36 -> 4.38; 5.80 -> 5.78; 3.97 -> 3.97; 5.27 -> 5.28; 7.05 -> 7.07; 4.37 -> 4.49; 5.71 -> 5.81; 7.45 -> | No clear effect |
| Add cyclic structure to the n×n parity matrix (ablation) | N18 feed-forward neural decoder · BCH and punctured RM codes | negative natural logarithm of BER: 0.45dB | Helped |
| Use the proposed cyclically equivariant decoder instead of N18 with the same n×n cyclic matrix (ablation) | Neural decoding with n×n cyclic parity matrix · BCH and punctured RM codes | negative natural logarithm of BER: 0.25dB | Helped |
| Use a cyclic n×n matrix instead of a randomly extended n×n matrix (ablation) | N18 feed-forward neural decoder · BCH and punctured RM codes | negative natural logarithm of BER: 3.27 -> 3.67; 4.38 -> 5.08; 5.78 -> 6.78; 3.97 -> 4.42; 5.28 -> 5.93; 7.07 -> 7.84; 4.49 -> 4.87; 5.81 -> 6.19; 7.47 -> | Helped |
| Use a cyclically equivariant decoder rather than the N18 FF decoder with the same cyclic parity matrix (ablation) | Neural decoding of cyclic codes · BCH(63,24), BCH(63,36), BCH(63,45), and PRM(63,22) | negative natural logarithm of BER: 3.67 -> 3.78; 5.08 -> 5.11; 6.78 -> 7.07; 4.42 -> 4.63; 5.93 -> 6.48; 7.84 -> 8.86; 4.87 -> 5.12; 6.19 -> 6.97; 7.76 -> | Helped |
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