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基于 FFT 的频域 RS 译码

基于 FFT 的频域 RS 译码. 季文洁 2014.3.21. 频域译码. FFT. Prime factor Cyclostome FFT. Prime factor. e.g. GF(2 4 ) N=15=3×5. CFFT. CFFT. e.g. GF(2 3 ). polynomial. F= ALf. CFFT. 选择一组正规基 ( γ , γ 2 , γ 4 ) ， 此处取 γ = α 3 ， 满足 γ+γ 2 + γ 4 = 1 ）. F= ALf. Winograd Algorithm.

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基于 FFT 的频域 RS 译码

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  1. 基于FFT的频域RS译码 季文洁 2014.3.21

  2. 频域译码

  3. FFT • Prime factor • Cyclostome FFT

  4. Prime factor • e.g. GF(24) • N=15=3×5

  5. CFFT

  6. CFFT e.g. GF(23) polynomial F=ALf

  7. CFFT 选择一组正规基(γ, γ2, γ4)，此处取γ = α3，满足γ+γ2+γ4 = 1） F=ALf Winograd Algorithm

  8. CFFTGF(23) 3-point cyclic convolution

  9. CFFT GF(23) n=7 Lr=2 GF(25) n=31 Lr=6 GF(26) n=63 Lr=12 GF(28) n=255 Lr=34 …… GF(24) n=15 Lr=4

  10. 预估结果 F=ALf 计算n个校验子的硬件需求

  11. TF

  12. CFFT i mod m2 = 0，0≤i<m，→{0, 3} • e.g. GF(26) • m = 6=2×3 • m1 = 2, m2 = 3 [y0, y1, y2, y3, y4, y5]T = [a0, a1, a2, a3, a4,a5]C·[y0, y1, y2, y3, y4, y5]T

  13. 预估结果 • e.g. GF(26) 常数乘法器 相同的例子 如： 10=2×5 15=3×5

  14. THE END

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