Symmetric Product Codes
summary
Defines a half product code as the antisymmetric subcode of a square product code: entries on the diagonal are forced to zero so length and dimension drop about half while rate stays similar. Claims minimum distance increases (roughly a 3/2 gain for many BCH/Hamming examples), so a two‑error component can act like a three‑error one and improve iterative thresholds. Uses syndrome-based iterative algebraic decoding (store syndromes not LLRs) for large memory and latency savings versus LDPC. Benefit is clear for 2→3 error steps, marginal or negative for 3→4.
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chapters (12)
- 0:00Intro
- 3:11Prologue (3)
- 5:39Outline
- 5:50Background
- 7:29Applications
- 8:47A Note on Decoding
- 12:58Symmetric Product Codes
- 15:22Minimum Distance (1)
- 17:35Minimum Distance (2)
- 22:24Iterative Decoding Analysis (2)
- 26:55Simulation Results (3)
- 29:30Conclusions
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