1. {a(k)} s(t) H ch (f) w(t) + r(t) H tr (f) {a(k)} H (f) w(t) + r(t) 

2. a(k) H (f) w(t) + r(t) H * (f) kT z(k) a(k) G(z) n(k) ~N c (0, N 0 g(i-j)) + z(k) 

3. a(k) H (f) w(t) + r(t) H * (f) kT z(k) a(k) G(z) n(k) ~N c (0, N 0 g(i-j)) + z(k)  u(k) a(k) F + (z) w(k) ~N c (0, (N 0 /A 2 )  (i-j)) + u(k)  u 0 (k)

4. a(k) G(z) n(k) ~N c (0, N 0 g(i-j)) + z(k) a(k) F + (z) w(k) ~N c (0, (N 0 /A 2 )  (i-j)) + u(k) 

5. a(k)a(k-1)a(k-L) f + (1)f + (L) u 0 (k) xx + z -1...  u(k) w(k)

6. a(k)S(k)  st (.,.)  out (.,.) w(k) u 0 (k) u(k) S(k+1) z -1 +

7. k f + (k)f - (k) k 00 x1x1 11 x2x2 x3x3 x4x4 x5x5 (x 1 ) * (x 2 ) * (x 3 ) * (x 4 ) * (x 5 ) *

8. k k+1 state (1, 1) (1, -1) (-1, 1) (-1, -1) 1|2.5 -1|0.5 1|1.5 -1|-0.5 1|0.5 -1|-1.51|-0.5 -1|-2.5

9. ... kk+1k+2k+3 k’k’+1k’+2k’+3 state (1, 1) (1, -1) (-1, 1) (-1, -1)

10. (++) (+0) (0+) (+-) (0-) (00) (-0) (-+) (--) k+1k

11. (++) (+0) (0+) (+-) (0-) (00) (-0) (-+) (--) 20 8 5 2 5 13 6 14 6 6 6 6 4 7 22 14 10 15 7 7 7 k=0k=1k=2 k=3k=4k=5 9

12. 16 0 4 4 0 36 4 0 4 16 0 (1,1) (1,-1) (-1,1) (-1,-1) k=0 k=1k=2k=3k=4

13. 0 4 16 0 36 4 16 0 4 4 0 4 0 4 (1,1) (1,-1) (-1,1) (-1,-1) k=0 k=1k=2k=3k=4

14. 0 0 16 4 0 4 1 9 1 25 9 4925 81 5 9 25 49 (1,1) (1,-1) (-1,1) (-1,-1) k=0 k=1k=2k=3k=4

15. 0 0 16 4 0 5 9 25 49 16 0 4 4 0 4 36 13 25 5 41 (1,1) (1,-1) (-1,1) (-1,-1) k=0 k=1k=2k=3k=4

16. r(t) H * (f) kT z(k) H LE (z) u(k) symbol-by- symbol detector

17. a(k) G LE (z) u 0 (k) H LE (z) n(k) ~ N c (0, N 0 g(i-j)) w(t) + u(k)

18. a(k) 1/G(z) n(k) ~ N c (0, N 0 g(i-j)) + u(k)

19. a(k) G LE (z) -1 H LE (z) n(k) ~ N c (0, N 0 g(i-j)) +  (k)

20. a(k)u 0 (k) n(k) ~ N c (0, N 0 g(i-j)) + u(k)

21. r(t) H * (f) kT z(k) H FF (z) u’(k) symbol-by- symbol detector + u(k) H FB (z) -

22. a(k) G’ DFE (z) H FF (z) n(k) ~ N c (0, N 0 g(i-j)) + u’(k) symbol-by- symbol detector + u(k) H FB (z) -

23. a(k) G DFE (z) H FF (z) n(k) ~ N c (0, N 0 g(i-j)) + u(k) n’(k)

24. a(k) ~ N c (0, (N 0 /A 2 )  (i-j)) + u(k) n’(k)

25. a(k) G DFE (z) - 1 H FF (z) n(k) ~ N c (0, N 0 g(i-j)) +  (k) n’(k)

26. a(k) G(z)H’ FF (z) - 1 H’ FF (z) n(k) ~ N c (0, N 0 g(i-j)) +  ’(k) 1 - H FB (z)  (k)

27. a(k) n(k) ~ N c (0, N 0 g(i-j)) + n’(k) u(k)

28. r(t) H * (f) kT H FF (z) u’(k) r(t) H rec (f) kT u’(k) r(t) H rec (f) kT u’(k) H AA (f) r(t) h eq (n) iT s u’(k) H AA (f)  NsNs    z(k)

29. r(kN s +K FF1 ) r(kN s -K FF2 ) r(kN s +1) r(kN s ) r(kN s -1) h eq (-K FF1 )h eq (K FF2 )h eq (-1)h eq (0) h eq (1) xxxxx z -1/Ns...  z -1 xxxx...  h FB (K FB -1)h FB (K FB )h FB (2)h FB (1) + u’(k) u(k)

30. r(kN s +K FF1 ) r(kN s -K FF2 ) r(kN s +1) r(kN s ) r(kN s -1) h eq (-K FF1 ;k)h eq (K FF2 ;k)h eq (-1;k)h eq (0;k) h eq (1;k) xxxxx z -1/Ns...  z -1 xxxx...  h FB (K FB -1;k)h FB (K FB ;k)h FB (2;k)h FB (1;k) + u’(k) u(k)