list decoding of polar codes
play

List-Decoding of Polar Codes Ido Tal and Alexander Vardy University - PowerPoint PPT Presentation

Nov 20, 2023 •454 likes •1.53k views

List-Decoding of Polar Codes Ido Tal and Alexander Vardy University of California San Diego 9500 Gilman Drive, La Jolla, CA 92093, USA Problem and goal Channel polarization is slow. For short to moderate code lengths, polar codes have

  1. A closer look at successive cancellation ( P ( y 0 y 1 | u 0 = 0 ) , P ( y 0 y 1 | u 0 = 1 )) ( P ( y 0 | x 0 = 0 ) , P ( y 0 | x 0 = 1 )) x 0 → y 0 u 0 u 0 � x 0 � ( P ( y 0 y 1 � u 0 | u 1 = 0 ) , P ( y 0 y 1 � u 0 | u 1 = 1 )) ( P ( y 1 | x 1 = 0 ) , P ( y 1 | x 1 = 1 )) x 1 → y 1 u 1 � u 1 x 1 � probability pair variable boolean variable (bit)

  2. A closer look at successive cancellation ? ? ( P ( y 0 y 1 | u 0 = 0 ) , P ( y 0 y 1 | u 0 = 1 )) ( P ( y 0 | x 0 = 0 ) , P ( y 0 | x 0 = 1 )) x 0 → y 0 u 0 u 0 � ? ? x 0 � ? ? ( P ( y 0 y 1 � u 0 | u 1 = 0 ) , P ( y 0 y 1 � u 0 | u 1 = 1 )) ( P ( y 1 | x 1 = 0 ) , P ( y 1 | x 1 = 1 )) x 1 → y 1 u 1 � u 1 ? ? x 1 � probability pair variable boolean variable (bit)

  3. A closer look at successive cancellation ? � ( P ( y 0 y 1 | u 0 = 0 ) , P ( y 0 y 1 | u 0 = 1 )) ( P ( y 0 | x 0 = 0 ) , P ( y 0 | x 0 = 1 )) x 0 → y 0 u 0 u 0 � ? ? x 0 � ? � ( P ( y 0 y 1 � u 0 | u 1 = 0 ) , P ( y 0 y 1 � u 0 | u 1 = 1 )) ( P ( y 1 | x 1 = 0 ) , P ( y 1 | x 1 = 1 )) x 1 → y 1 u 1 � u 1 ? ? x 1 � probability pair variable boolean variable (bit)

  4. A closer look at successive cancellation � � ( P ( y 0 y 1 | u 0 = 0 ) , P ( y 0 y 1 | u 0 = 1 )) ( P ( y 0 | x 0 = 0 ) , P ( y 0 | x 0 = 1 )) x 0 → y 0 u 0 u 0 � ? ? x 0 � ? � ( P ( y 0 y 1 � u 0 | u 1 = 0 ) , P ( y 0 y 1 � u 0 | u 1 = 1 )) ( P ( y 1 | x 1 = 0 ) , P ( y 1 | x 1 = 1 )) x 1 → y 1 u 1 � u 1 ? ? x 1 � probability pair variable boolean variable (bit)

  5. A closer look at successive cancellation � � ( P ( y 0 y 1 | u 0 = 0 ) , P ( y 0 y 1 | u 0 = 1 )) ( P ( y 0 | x 0 = 0 ) , P ( y 0 | x 0 = 1 )) x 0 → y 0 u 0 u 0 � � ? x 0 � ? � ( P ( y 0 y 1 � u 0 | u 1 = 0 ) , P ( y 0 y 1 � u 0 | u 1 = 1 )) ( P ( y 1 | x 1 = 0 ) , P ( y 1 | x 1 = 1 )) x 1 → y 1 u 1 � u 1 ? ? x 1 � probability pair variable boolean variable (bit)

  6. A closer look at successive cancellation � � ( P ( y 0 y 1 | u 0 = 0 ) , P ( y 0 y 1 | u 0 = 1 )) ( P ( y 0 | x 0 = 0 ) , P ( y 0 | x 0 = 1 )) x 0 → y 0 u 0 u 0 � � ? x 0 � ? � ( P ( y 0 y 1 � u 0 | u 1 = 0 ) , P ( y 0 y 1 � u 0 | u 1 = 1 )) ( P ( y 1 | x 1 = 0 ) , P ( y 1 | x 1 = 1 )) x 1 → y 1 u 1 � u 1 ? ? x 1 � probability pair variable boolean variable (bit)

  7. A closer look at successive cancellation � � ( P ( y 0 y 1 | u 0 = 0 ) , P ( y 0 y 1 | u 0 = 1 )) ( P ( y 0 | x 0 = 0 ) , P ( y 0 | x 0 = 1 )) x 0 → y 0 u 0 u 0 � � ? x 0 � � � ( P ( y 0 y 1 � u 0 | u 1 = 0 ) , P ( y 0 y 1 � u 0 | u 1 = 1 )) ( P ( y 1 | x 1 = 0 ) , P ( y 1 | x 1 = 1 )) x 1 → y 1 u 1 � u 1 ? ? x 1 � probability pair variable boolean variable (bit)

  8. A closer look at successive cancellation � � ( P ( y 0 y 1 | u 0 = 0 ) , P ( y 0 y 1 | u 0 = 1 )) ( P ( y 0 | x 0 = 0 ) , P ( y 0 | x 0 = 1 )) x 0 → y 0 u 0 u 0 � � ? x 0 � � � ( P ( y 0 y 1 � u 0 | u 1 = 0 ) , P ( y 0 y 1 � u 0 | u 1 = 1 )) ( P ( y 1 | x 1 = 0 ) , P ( y 1 | x 1 = 1 )) x 1 → y 1 u 1 � u 1 ? ? x 1 � probability pair variable boolean variable (bit)

  9. A closer look at successive cancellation � � ( P ( y 0 y 1 | u 0 = 0 ) , P ( y 0 y 1 | u 0 = 1 )) ( P ( y 0 | x 0 = 0 ) , P ( y 0 | x 0 = 1 )) x 0 → y 0 u 0 u 0 � � ? x 0 � � � ( P ( y 0 y 1 � u 0 | u 1 = 0 ) , P ( y 0 y 1 � u 0 | u 1 = 1 )) ( P ( y 1 | x 1 = 0 ) , P ( y 1 | x 1 = 1 )) x 1 → y 1 u 1 � u 1 � ? x 1 � probability pair variable boolean variable (bit)

  10. A closer look at successive cancellation � � ( P ( y 0 y 1 | u 0 = 0 ) , P ( y 0 y 1 | u 0 = 1 )) ( P ( y 0 | x 0 = 0 ) , P ( y 0 | x 0 = 1 )) x 0 → y 0 u 0 u 0 � � ? x 0 � � � ( P ( y 0 y 1 � u 0 | u 1 = 0 ) , P ( y 0 y 1 � u 0 | u 1 = 1 )) ( P ( y 1 | x 1 = 0 ) , P ( y 1 | x 1 = 1 )) x 1 → y 1 u 1 � u 1 � ? x 1 � probability pair variable boolean variable (bit)

  11. A closer look at successive cancellation � � ( P ( y 0 y 1 | u 0 = 0 ) , P ( y 0 y 1 | u 0 = 1 )) ( P ( y 0 | x 0 = 0 ) , P ( y 0 | x 0 = 1 )) x 0 → y 0 u 0 u 0 � � � x 0 � � � ( P ( y 0 y 1 � u 0 | u 1 = 0 ) , P ( y 0 y 1 � u 0 | u 1 = 1 )) ( P ( y 1 | x 1 = 0 ) , P ( y 1 | x 1 = 1 )) x 1 → y 1 u 1 � u 1 � � x 1 � probability pair variable boolean variable (bit)

  12. A closer look at successive cancellation � � ( P ( y 0 y 1 | u 0 = 0 ) , P ( y 0 y 1 | u 0 = 1 )) ( P ( y 0 | x 0 = 0 ) , P ( y 0 | x 0 = 1 )) x 0 → y 0 u 0 u 0 � � � x 0 � � � ( P ( y 0 y 1 � u 0 | u 1 = 0 ) , P ( y 0 y 1 � u 0 | u 1 = 1 )) ( P ( y 1 | x 1 = 0 ) , P ( y 1 | x 1 = 1 )) x 1 → y 1 u 1 � u 1 � � x 1 � probability pair variable boolean variable (bit)

  13. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 Key point u 5 y 5 u 6 y 6 The memory u 7 y 7 needed to hold u 8 y 8 the variables at u 9 y 9 level t is O ( n /2 t ) . u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  14. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 Key point u 5 y 5 u 6 y 6 The memory u 7 y 7 needed to hold u 8 y 8 the variables at u 9 y 9 level t is O ( n /2 t ) . u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  15. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 Key point u 5 y 5 u 6 y 6 The memory u 7 y 7 needed to hold u 8 y 8 the variables at u 9 y 9 level t is O ( n /2 t ) . u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  16. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 Key point u 5 y 5 u 6 y 6 The memory u 7 y 7 needed to hold u 8 y 8 the variables at u 9 y 9 level t is O ( n /2 t ) . u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  17. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 Key point u 5 y 5 u 6 y 6 The memory u 7 y 7 needed to hold u 8 y 8 the variables at u 9 y 9 level t is O ( n /2 t ) . u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  18. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 Key point u 5 y 5 u 6 y 6 The memory u 7 y 7 needed to hold u 8 y 8 the variables at u 9 y 9 level t is O ( n /2 t ) . u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  19. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 Key point u 5 y 5 u 6 y 6 The memory u 7 y 7 needed to hold u 8 y 8 the variables at u 9 y 9 level t is O ( n /2 t ) . u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  20. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 Key point u 5 y 5 u 6 y 6 The memory u 7 y 7 needed to hold u 8 y 8 the variables at u 9 y 9 level t is O ( n /2 t ) . u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  21. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 Key point u 5 y 5 u 6 y 6 The memory u 7 y 7 needed to hold u 8 y 8 the variables at u 9 y 9 level t is O ( n /2 t ) . u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  22. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 Key point u 5 y 5 u 6 y 6 The memory u 7 y 7 needed to hold u 8 y 8 the variables at u 9 y 9 level t is O ( n /2 t ) . u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  23. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 Key point u 5 y 5 u 6 y 6 The memory u 7 y 7 needed to hold u 8 y 8 the variables at u 9 y 9 level t is O ( n /2 t ) . u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  24. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 Key point u 5 y 5 u 6 y 6 The memory u 7 y 7 needed to hold u 8 y 8 the variables at u 9 y 9 level t is O ( n /2 t ) . u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  25. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 Key point u 5 y 5 u 6 y 6 The memory u 7 y 7 needed to hold u 8 y 8 the variables at u 9 y 9 level t is O ( n /2 t ) . u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  26. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 Key point u 5 y 5 u 6 y 6 The memory u 7 y 7 needed to hold u 8 y 8 the variables at u 9 y 9 level t is O ( n /2 t ) . u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  27. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 Key point u 5 y 5 u 6 y 6 The memory u 7 y 7 needed to hold u 8 y 8 the variables at u 9 y 9 level t is O ( n /2 t ) . u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  28. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 Key point u 5 y 5 u 6 y 6 The memory u 7 y 7 needed to hold u 8 y 8 the variables at u 9 y 9 level t is O ( n /2 t ) . u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  29. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 Key point u 5 y 5 u 6 y 6 The memory u 7 y 7 needed to hold u 8 y 8 the variables at u 9 y 9 level t is O ( n /2 t ) . u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  30. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 Key point u 5 y 5 u 6 y 6 The memory u 7 y 7 needed to hold u 8 y 8 the variables at u 9 y 9 level t is O ( n /2 t ) . u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  31. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 Key point u 5 y 5 u 6 y 6 The memory u 7 y 7 needed to hold u 8 y 8 the variables at u 9 y 9 level t is O ( n /2 t ) . u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  32. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 Key point u 5 y 5 u 6 y 6 The memory u 7 y 7 needed to hold u 8 y 8 the variables at u 9 y 9 level t is O ( n /2 t ) . u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  33. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 Key point u 5 y 5 u 6 y 6 The memory u 7 y 7 needed to hold u 8 y 8 the variables at u 9 y 9 level t is O ( n /2 t ) . u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  34. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 Key point u 5 y 5 u 6 y 6 The memory u 7 y 7 needed to hold u 8 y 8 the variables at u 9 y 9 level t is O ( n /2 t ) . u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  35. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 Key point u 5 y 5 u 6 y 6 The memory u 7 y 7 needed to hold u 8 y 8 the variables at u 9 y 9 level t is O ( n /2 t ) . u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  36. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 Key point u 5 y 5 u 6 y 6 The memory u 7 y 7 needed to hold u 8 y 8 the variables at u 9 y 9 level t is O ( n /2 t ) . u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  37. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 Key point u 5 y 5 u 6 y 6 The memory u 7 y 7 needed to hold u 8 y 8 the variables at u 9 y 9 level t is O ( n /2 t ) . u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  38. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 Key point u 5 y 5 u 6 y 6 The memory u 7 y 7 needed to hold u 8 y 8 the variables at u 9 y 9 level t is O ( n /2 t ) . u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  39. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 Key point u 5 y 5 u 6 y 6 The memory u 7 y 7 needed to hold u 8 y 8 the variables at u 9 y 9 level t is O ( n /2 t ) . u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  40. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 Key point u 5 y 5 u 6 y 6 The memory u 7 y 7 needed to hold u 8 y 8 the variables at u 9 y 9 level t is O ( n /2 t ) . u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  41. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 Key point u 5 y 5 u 6 y 6 The memory u 7 y 7 needed to hold u 8 y 8 the variables at u 9 y 9 level t is O ( n /2 t ) . u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  42. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 Key point u 5 y 5 u 6 y 6 The memory u 7 y 7 needed to hold u 8 y 8 the variables at u 9 y 9 level t is O ( n /2 t ) . u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  43. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 Key point u 5 y 5 u 6 y 6 The memory u 7 y 7 needed to hold u 8 y 8 the variables at u 9 y 9 level t is O ( n /2 t ) . u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  44. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 Key point u 5 y 5 u 6 y 6 The memory u 7 y 7 needed to hold u 8 y 8 the variables at u 9 y 9 level t is O ( n /2 t ) . u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  45. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 u 5 y 5 Key point u 6 y 6 Level t is written u 7 y 7 to once every u 8 y 8 O ( 2 m − t ) stages. u 9 y 9 u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  46. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 u 5 y 5 Key point u 6 y 6 Level t is written u 7 y 7 to once every u 8 y 8 O ( 2 m − t ) stages. u 9 y 9 u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  47. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 u 5 y 5 Key point u 6 y 6 Level t is written u 7 y 7 to once every u 8 y 8 O ( 2 m − t ) stages. u 9 y 9 u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  48. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 u 5 y 5 Key point u 6 y 6 Level t is written u 7 y 7 to once every u 8 y 8 O ( 2 m − t ) stages. u 9 y 9 u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  49. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 u 5 y 5 Key point u 6 y 6 Level t is written u 7 y 7 to once every u 8 y 8 O ( 2 m − t ) stages. u 9 y 9 u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  50. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 u 5 y 5 Key point u 6 y 6 Level t is written u 7 y 7 to once every u 8 y 8 O ( 2 m − t ) stages. u 9 y 9 u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  51. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 u 5 y 5 Key point u 6 y 6 Level t is written u 7 y 7 to once every u 8 y 8 O ( 2 m − t ) stages. u 9 y 9 u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  52. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 u 5 y 5 Key point u 6 y 6 Level t is written u 7 y 7 to once every u 8 y 8 O ( 2 m − t ) stages. u 9 y 9 u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  53. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 u 5 y 5 Key point u 6 y 6 Level t is written u 7 y 7 to once every u 8 y 8 O ( 2 m − t ) stages. u 9 y 9 u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  54. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 u 5 y 5 Key point u 6 y 6 Level t is written u 7 y 7 to once every u 8 y 8 O ( 2 m − t ) stages. u 9 y 9 u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  55. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 u 5 y 5 Key point u 6 y 6 Level t is written u 7 y 7 to once every u 8 y 8 O ( 2 m − t ) stages. u 9 y 9 u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  56. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 u 5 y 5 Key point u 6 y 6 Level t is written u 7 y 7 to once every u 8 y 8 O ( 2 m − t ) stages. u 9 y 9 u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  57. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 u 5 y 5 Key point u 6 y 6 Level t is written u 7 y 7 to once every u 8 y 8 O ( 2 m − t ) stages. u 9 y 9 u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  58. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 u 5 y 5 Key point u 6 y 6 Level t is written u 7 y 7 to once every u 8 y 8 O ( 2 m − t ) stages. u 9 y 9 u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  59. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 u 5 y 5 Key point u 6 y 6 Level t is written u 7 y 7 to once every u 8 y 8 O ( 2 m − t ) stages. u 9 y 9 u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  60. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 u 5 y 5 Key point u 6 y 6 Level t is written u 7 y 7 to once every u 8 y 8 O ( 2 m − t ) stages. u 9 y 9 u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  61. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 u 5 y 5 Key point u 6 y 6 Level t is written u 7 y 7 to once every u 8 y 8 O ( 2 m − t ) stages. u 9 y 9 u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  62. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 u 5 y 5 Key point u 6 y 6 Level t is written u 7 y 7 to once every u 8 y 8 O ( 2 m − t ) stages. u 9 y 9 u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  63. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 u 5 y 5 Key point u 6 y 6 Level t is written u 7 y 7 to once every u 8 y 8 O ( 2 m − t ) stages. u 9 y 9 u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  64. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 u 5 y 5 Key point u 6 y 6 Level t is written u 7 y 7 to once every u 8 y 8 O ( 2 m − t ) stages. u 9 y 9 u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  65. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 u 5 y 5 Key point u 6 y 6 Level t is written u 7 y 7 to once every u 8 y 8 O ( 2 m − t ) stages. u 9 y 9 u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  66. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 u 5 y 5 Key point u 6 y 6 Level t is written u 7 y 7 to once every u 8 y 8 O ( 2 m − t ) stages. u 9 y 9 u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  67. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 u 5 y 5 Key point u 6 y 6 Level t is written u 7 y 7 to once every u 8 y 8 O ( 2 m − t ) stages. u 9 y 9 u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  68. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 u 5 y 5 Key point u 6 y 6 Level t is written u 7 y 7 to once every u 8 y 8 O ( 2 m − t ) stages. u 9 y 9 u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  69. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 u 5 y 5 Key point u 6 y 6 Level t is written u 7 y 7 to once every u 8 y 8 O ( 2 m − t ) stages. u 9 y 9 u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  70. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 u 5 y 5 Key point u 6 y 6 Level t is written u 7 y 7 to once every u 8 y 8 O ( 2 m − t ) stages. u 9 y 9 u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  71. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 u 5 y 5 Key point u 6 y 6 Level t is written u 7 y 7 to once every u 8 y 8 O ( 2 m − t ) stages. u 9 y 9 u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  72. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 u 5 y 5 Key point u 6 y 6 Level t is written u 7 y 7 to once every u 8 y 8 O ( 2 m − t ) stages. u 9 y 9 u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

  73. A larger example 4 3 2 1 0 u 0 y 0 u 1 y 1 u 2 y 2 u 3 y 3 u 4 y 4 u 5 y 5 Key point u 6 y 6 Level t is written u 7 y 7 to once every u 8 y 8 O ( 2 m − t ) stages. u 9 y 9 u 10 y 10 y 11 u 11 u 12 y 12 u 13 y 13 u 14 y 14 u 15 y 15

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

Partitioned Successive-Cancellation List Decoding of Polar Codes Seyyed Ali Hashemi , Alexios

Partitioned Successive-Cancellation List Decoding of Polar Codes Seyyed Ali Hashemi , Alexios

Partitioned Successive-Cancellation List Decoding of Polar Codes Seyyed Ali Hashemi , Alexios Balatsoukas-Stimming , Pascal Giard , Claude Thibeault , Warren J. Gross McGill University, Montr eal, Qu ebec, Canada

523 views • 14 slides
Partitioned Successive-Cancellation List Decoding of Polar Codes Seyyed Ali Hashemi McGill

Partitioned Successive-Cancellation List Decoding of Polar Codes Seyyed Ali Hashemi McGill

Partitioned Successive-Cancellation List Decoding of Polar Codes Seyyed Ali Hashemi McGill University, Montr eal, Qu ebec, Canada Southeast University, Nanjing, China March 22, 2016 1/14 Seyyed Ali Hashemi (McGill) PSCL Decoding of

870 views • 14 slides
List Decoding for Universal Polar Codes Boaz Shuval and Ido Tal 1/15 Overview Universal

List Decoding for Universal Polar Codes Boaz Shuval and Ido Tal 1/15 Overview Universal

List Decoding for Universal Polar Codes Boaz Shuval and Ido Tal 1/15 Overview Universal polarization: memoryless setting: o S as glu & Wang, ISIT 2011 settings with memory: Shuval & Tal, ISIT 2019 Error

801 views • 53 slides
List Decoding of Universal Polar Codes Boaz Shuval and Ido Tal 1/15 Overview Universal

List Decoding of Universal Polar Codes Boaz Shuval and Ido Tal 1/15 Overview Universal

List Decoding of Universal Polar Codes Boaz Shuval and Ido Tal 1/15 Overview Universal polarization: memoryless setting: o S as glu & Wang, ISIT 2011 settings with memory: Shuval & Tal, ISIT 2019 Error

689 views • 53 slides
Simplified Successive-Cancellation List Decoding of Polar Codes Seyyed Ali Hashemi , Carlo Condo,

Simplified Successive-Cancellation List Decoding of Polar Codes Seyyed Ali Hashemi , Carlo Condo,

Simplified Successive-Cancellation List Decoding of Polar Codes Seyyed Ali Hashemi , Carlo Condo, Warren J. Gross Department of Electrical and Computer Engineering McGill University Montr eal, Qu ebec, Canada July 12, 2016 Seyyed Ali

554 views • 22 slides
Practical Design and Decoding of Polar Codes Vera Miloslavskaya Saint-Petersburg State

Practical Design and Decoding of Polar Codes Vera Miloslavskaya Saint-Petersburg State

Practical Design and Decoding of Polar Codes Vera Miloslavskaya Saint-Petersburg State Polytechnic University veram@dcn.icc.spbstu.ru January 2015 Polar Codes Polar codes can achieve the capacity of 1 0 0 0 0 0 0 0 an arbitrary

323 views • 4 slides
CRC-Aided Belief Propagation List Decoding of Polar Codes M. Geiselhart, A. Elkelesh, M. Ebada

CRC-Aided Belief Propagation List Decoding of Polar Codes M. Geiselhart, A. Elkelesh, M. Ebada

.inue.uni-stuttgart.de CRC-Aided Belief Propagation List Decoding of Polar Codes M. Geiselhart, A. Elkelesh, M. Ebada S. Cammerer, S. ten Brink www University of Stuttgart ISIT 2020 21. - 26. June 2020 Institute of Telecommunications

545 views • 41 slides
List Decoding of Algebraic Codes Peter Beelen, Kristian Brander and Johan S.R. Nielsen DTU

List Decoding of Algebraic Codes Peter Beelen, Kristian Brander and Johan S.R. Nielsen DTU

Contents List decoding of error-correcting codes Fast list decoding of ReedSolomon codes Fast list decoding of certain AG codes List Decoding of Algebraic Codes Peter Beelen, Kristian Brander and Johan S.R. Nielsen DTU Mathematics

1.33k views • 81 slides
An Efficient, Portable and Generic Library for Successive Cancellation Decoding of Polar Codes

An Efficient, Portable and Generic Library for Successive Cancellation Decoding of Polar Codes

An Efficient, Portable and Generic Library for Successive Cancellation Decoding of Polar Codes Adrien Cassagne 1 , 2 Bertrand Le Gal 1 Camille Leroux 1 Olivier Aumage 2 Denis Barthou 2 1 IMS, Univ. Bordeaux, INP, France 2 Inria / Labri, Univ.

559 views • 20 slides
List decoding of RM(1,m) codes and Multi-linear Power Analysis attacks (MLPA) Ilya Dumer , Rafael

List decoding of RM(1,m) codes and Multi-linear Power Analysis attacks (MLPA) Ilya Dumer , Rafael

List decoding of the First order Reed-Muller codes Application to cryptanalysis PA Attacks overview Ideal Countermeasure MLPA List decoding of RM(1,m) codes and Multi-linear Power Analysis attacks (MLPA) Ilya Dumer , Rafael Fourquet , Grigory

675 views • 33 slides
On List Decoding of Alternant Codes in the Hamming and Lee metrics Ido Tal Ron M. Roth Computer

On List Decoding of Alternant Codes in the Hamming and Lee metrics Ido Tal Ron M. Roth Computer

On List Decoding of Alternant Codes in the Hamming and Lee metrics Ido Tal Ron M. Roth Computer Science Department, Technion, Haifa 32000, Israel. 1 Previous Work Berlekamp, 1968: Negacyclic codes for the Lee metric. Roth and Siegel, 1994:

850 views • 19 slides
Linear-Time Erasure List-Decoding of Expander Codes Noga Ron-Zewi (University of Haifa) Mary

Linear-Time Erasure List-Decoding of Expander Codes Noga Ron-Zewi (University of Haifa) Mary

Linear-Time Erasure List-Decoding of Expander Codes Noga Ron-Zewi (University of Haifa) Mary Wootters (Stanford) Gilles Zmor (Universit de Bordeaux) ISIT 2020 Linear-Time 3 Erasure List-Decoding of 1 Expander Codes 2 1. Erasure

559 views • 18 slides
1 Hello Hi! My name is Ido, and we are going to talk about polar codes As you may know,

1 Hello Hi! My name is Ido, and we are going to talk about polar codes As you may know,

1 Hello Hi! My name is Ido, and we are going to talk about polar codes As you may know, polar codes were invented in 2009 by Erdal Arkan. When presenting them, Im going to try and strike a good balance between a simple explanation

675 views • 20 slides
Decoding Reed-Muller and Polar Codes by Successive Factor Graph Permutations Seyyed Ali Hashemi a

Decoding Reed-Muller and Polar Codes by Successive Factor Graph Permutations Seyyed Ali Hashemi a

Decoding Reed-Muller and Polar Codes by Successive Factor Graph Permutations Seyyed Ali Hashemi a , Nghia Doan a , Marco Mondelli b , Warren J. Gross a a McGill University, Canada b Stanford University, USA ISTC 2018 Hong Kong December 4, 2018.

511 views • 34 slides
Recursive Trellis Decoding Techniques of Polar Codes Peter Trifonov ITMO University, Russia June

Recursive Trellis Decoding Techniques of Polar Codes Peter Trifonov ITMO University, Russia June

Recursive Trellis Decoding Techniques of Polar Codes Peter Trifonov ITMO University, Russia June 18, 2020 Peter Trifonov ( ITMO University, Russia) Recursive Trellis Decoding Techniques of Polar Codes June 18, 2020 1 / 18 Outline Polar

525 views • 21 slides
A Fast Polar Code List Decoder Architecture Based on Sphere Decoding Seyyed Ali Hashemi , Carlo

A Fast Polar Code List Decoder Architecture Based on Sphere Decoding Seyyed Ali Hashemi , Carlo

A Fast Polar Code List Decoder Architecture Based on Sphere Decoding Seyyed Ali Hashemi , Carlo Condo, Warren J. Gross Department of Electrical and Computer Engineering McGill University Montr eal, Qu ebec, Canada May 31, 2017 Seyyed

268 views • 26 slides
Falconieri: Remote Provisioning Service as a Service A new, modern, open source and cloud native

Falconieri: Remote Provisioning Service as a Service A new, modern, open source and cloud native

Falconieri: Remote Provisioning Service as a Service A new, modern, open source and cloud native remote provisioning service gateway. Matteo Valentini @_Amygos Intro: Remote Provisioning Service Theory Intro: What is it a Remote

476 views • 29 slides
Pique curiosity, not diabetic fingers Axelle Apvrille (Fortinet) Travis Goodspeed July 2020

Pique curiosity, not diabetic fingers Axelle Apvrille (Fortinet) Travis Goodspeed July 2020

Pique curiosity, not diabetic fingers Axelle Apvrille (Fortinet) Travis Goodspeed July 2020 Hello! Travis Goodspeed Axelle Apvrille Digital watchmaker and Studebaker Principal Security Researcher at enthusiast, @travisgoodspeed Fortinet ,

433 views • 31 slides
2013 Smart Services CRC Participants and Showcase Forum Meeting Innovation reflections 5

2013 Smart Services CRC Participants and Showcase Forum Meeting Innovation reflections 5

2013 Smart Services CRC Participants and Showcase Forum Meeting Innovation reflections 5 years on from the Review of the National Innovation System 4 December 2013 Mary OKane, NSW Chief Scientist and Engineer 5 years on from Review of

285 views • 27 slides
Horn Binary Serialization Analysis HCVS 2016 3rd Workshop on Horn Clauses for Verification

Horn Binary Serialization Analysis HCVS 2016 3rd Workshop on Horn Clauses for Verification

Horn Binary Serialization Analysis HCVS 2016 3rd Workshop on Horn Clauses for Verification and Synthesis Gabriele Paganelli https://gapag.noblogs.org/ gapag@distruzione.org Length Type Data CRC 0 3 4 7 8 N N+1 N+4 Type

502 views • 33 slides
Understanding SSD Reliability in Large-Scale Cloud Systems Erci Xu Mai Zheng Feng Qin Yikang

Understanding SSD Reliability in Large-Scale Cloud Systems Erci Xu Mai Zheng Feng Qin Yikang

Understanding SSD Reliability in Large-Scale Cloud Systems Erci Xu Mai Zheng Feng Qin Yikang Xu Jiesheng Wu Ohio State Iowa State Ohio State Aliyun Aliyun University University University Alibaba Alibaba Flash-Based Solid-Stata

709 views • 23 slides
The BLIS Approach to Skinny Matrix Multiplication Field G. Van Zee Science of High Performance

The BLIS Approach to Skinny Matrix Multiplication Field G. Van Zee Science of High Performance

The BLIS Approach to Skinny Matrix Multiplication Field G. Van Zee Science of High Performance Computing The University of Texas at Austin September 19, 2019 Science of High Performance Computing (SHPC) research group Led by Robert A. van

1.21k views • 83 slides
CREAM CE Certification and CREAM CE Certification and Testing Di Qing SA3 Academia Sinica

CREAM CE Certification and CREAM CE Certification and Testing Di Qing SA3 Academia Sinica

Enabling Grids for E sciencE Enabling Grids for E-sciencE CREAM CE Certification and CREAM CE Certification and Testing Di Qing SA3 Academia Sinica & CERN Academia Sinica & CERN Geneva, 2008 www eu egee org www.eu-egee.org EGEE

215 views • 7 slides
Geographic Data Science - Lecture IX Causal Inference Dani Arribas-Bel Today Correlation Vs

Geographic Data Science - Lecture IX Causal Inference Dani Arribas-Bel Today Correlation Vs

Geographic Data Science - Lecture IX Causal Inference Dani Arribas-Bel Today Correlation Vs Causation Causal inference Why/when causality matters Hurdles to causal inference & strategies to overcome them Correlation Vs Causation

741 views • 45 slides

More recommend