Concatenated Irregular Variable Length Coding and Irregular Unity - PowerPoint PPT Presentation

Concatenated Irregular Variable Length Coding and Irregular Unity Rate Coding R. G. Maunder and L. Hanzo Communications Research Group School of Electronics and Computer Science, University of Southampton, SO17 1BJ, UK. http://www-mobile.ecs.soton.ac.uk School of ECS, Univ. of Southampton, UK. http://www-mobile.ecs.soton.ac.uk 1/ 14 ⇒ |

Outline ❏ Serial concatenations of regular and irregular codes ❏ EXIT chart matching ❏ BER and complexity performance results ❏ Summary School of ECS, Univ. of Southampton, UK. http://www-mobile.ecs.soton.ac.uk 2/ 14 ⇒ |

VLC-URC η = 2 . 12 E b /N 0 = 5 . 97 dB 1 0.8 Concatenation of b a ; b ) 0.6 regular codes c e ; c ), I (˜ 0.4 I (˜ a b c d 0.2 VLC URC π encoder encoder 0 0 0.2 0.4 0.6 0.8 1 ˜ b a c e ˜ c a ; c ), I (˜ b e ; b ) I (˜ π − 1 VLC-URC η = 2 . 12 10 0 10 6 bits 10 5 bits ˜ ˆ a d VLC URC 10 − 1 decoder decoder 10 − 2 BER E b /N 0 = 4 . 28 dB E b /N 0 = 4 . 57 dB 10 − 3 ˜ b e c a ˜ π 10 − 4 10 − 5 4 5 6 7 E b /N 0 [dB] School of ECS, Univ. of Southampton, UK. http://www-mobile.ecs.soton.ac.uk 3/ 14 ⇒ |

IrVLC-URC η = 2 . 12 E b /N 0 = 5 . 11 dB 1 0.8 Concatenation of irregular b a ; b ) 0.6 and regular codes c e ; c ), I (˜ 0.4 I (˜ a 1 b 1 0.2 a b c d N VLC URC π a N b N encoders encoder 0 0 0.2 0.4 0.6 0.8 1 ˜ c a ; c ), I (˜ b a c e ˜ I (˜ b e ; b ) π − 1 IrVLC-URC η = 2 . 12 ˜ ˜ b a b a 10 0 10 6 bits 1 N ˆ a 1 10 5 bits ˜ ˆ a d N VLC URC 10 − 1 ˆ a N decoders decoder ˜ ˜ b e b e 10 − 2 N 1 BER E b /N 0 = 4 . 28 dB E b /N 0 = 4 . 57 dB 10 − 3 ˜ b e ˜ c a π 10 − 4 10 − 5 4 5 6 7 E b /N 0 [dB] School of ECS, Univ. of Southampton, UK. http://www-mobile.ecs.soton.ac.uk 4/ 14 ⇒ |

IrVLC-IrURC η = 2 . 12 E b /N 0 = 4 . 61 dB 1 0.8 Concatenation of b a ; b ) 0.6 irregular codes c e ; c ), I (˜ 0.4 I (˜ a 1 b 1 c 1 d 1 0.2 a b c d N VLC M URC π a N b N c M d M encoders encoders 0 0 0.2 0.4 0.6 0.8 1 ˜ c a ; c ), I (˜ b a c e ˜ I (˜ b e ; b ) π − 1 IrVLC-IrURC η = 2 . 12 ˜ ˜ b a b a c e c e ˜ ˜ 10 0 10 6 bits ˜ N M 1 1 ˆ a 1 d 1 10 5 bits ˜ ˆ a d N VLC M URC ˜ 10 − 1 ˆ a N d M decoders decoders ˜ ˜ b e b e c a c a ˜ ˜ 10 − 2 N M 1 1 BER E b /N 0 = 4 . 28 dB E b /N 0 = 4 . 57 dB 10 − 3 ˜ b e c a ˜ π 10 − 4 10 − 5 4 5 6 7 E b /N 0 [dB] School of ECS, Univ. of Southampton, UK. http://www-mobile.ecs.soton.ac.uk 5/ 14 ⇒ |

GA for designing component VLC codebooks N = 30 1 0.8 ❏ Arbitrary EXIT curve 0.6 n ; b n ) ❏ Near-unity VLC-encoded bit b a I (˜ entropy 0.4 ❏ Low decoding complexity 0.2 0 0 0.2 0.4 0.6 0.8 1 I (˜ b e n ; b n ) School of ECS, Univ. of Southampton, UK. http://www-mobile.ecs.soton.ac.uk 6/ 14 ⇒ |

Full search for selecting component URC codes M = 10, E b /N 0 = 4 . 74 dB 1 0.8 0.6 m ; c m ) c e I (˜ 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1 c a I (˜ m ; c m ) School of ECS, Univ. of Southampton, UK. http://www-mobile.ecs.soton.ac.uk 7/ 14 ⇒ |

EXIT chart matching x e ; x ) = f x [ I (˜ x a ; x )] I (˜ IrVLC EXIT function... IrURC EXIT function... f b = � N f c = � M n =1 α n f b n , m =1 α m f c m , where where � N � M n =1 α n = 1 , m =1 α m = 1 , α n ≥ 0 ∀ n ∈ [1 . . . N ] , α m ≥ 0 ∀ m ∈ [1 . . . M ] . R = � N n =1 α n R n . School of ECS, Univ. of Southampton, UK. http://www-mobile.ecs.soton.ac.uk 8/ 14 ⇒ |

Joint EXIT chart matching algorithm 1 URC EXIT IrURC EXIT function function N VLC Match with M URC EXIT incremental Match EXIT functions coding rate functions IrVLC EXIT function School of ECS, Univ. of Southampton, UK. http://www-mobile.ecs.soton.ac.uk 9/ 14 ⇒ |

EXIT chart matching accuracy 4 3.5 3 η = 4 R 2.5 η = 2 . 12 2 Channel capacity Attainable capacity 1.5 IrVLC-IrURC IrVLC-URC VLC-URC 1 2 4 6 8 10 12 14 E b /N 0 [dB] School of ECS, Univ. of Southampton, UK. http://www-mobile.ecs.soton.ac.uk 10/ 14 ⇒ |

EXIT charts VLC-URC η = 2 . 12 E b /N 0 = 5 . 97 dB IrVLC-URC η = 2 . 12 E b /N 0 = 5 . 11 dB IrVLC-IrURC η = 2 . 12 E b /N 0 = 4 . 61 dB 1 1 1 0.8 0.8 0.8 b a ; b ) b a ; b ) b a ; b ) 0.6 0.6 0.6 c e ; c ), I (˜ c e ; c ), I (˜ c e ; c ), I (˜ 0.4 0.4 0.4 I (˜ I (˜ I (˜ 0.2 0.2 0.2 0 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 c a ; c ), I (˜ c a ; c ), I (˜ b e ; b ) I (˜ c a ; c ), I (˜ I (˜ b e ; b ) b e ; b ) I (˜ School of ECS, Univ. of Southampton, UK. http://www-mobile.ecs.soton.ac.uk 11/ 14 ⇒ |

BER performance 10 0 IrVLC-IrURC 1 000 000 bits IrVLC-IrURC 100 000 bits 10 − 1 IrVLC-URC 1 000 000 bits IrVLC-URC 100 000 bits VLC-URC 1 000 000 bits 10 − 2 VLC-URC 100 000 bits BER E b /N 0 = 4 . 28 dB E b /N 0 = 4 . 57 dB 10 − 3 10 − 4 10 − 5 5 6 7 E b /N 0 [dB] School of ECS, Univ. of Southampton, UK. http://www-mobile.ecs.soton.ac.uk 12/ 14 ⇒ |

Decoding complexity 10 6 Average ACS per source symbol IrVLC-IrURC 1 000 000 bits IrVLC-IrURC 100 000 bits IrVLC-URC 1 000 000 bits IrVLC-URC 100 000 bits VLC-URC 1 000 000 bits VLC-URC 100 000 bits 10 5 E b /N 0 = 4 . 28 dB E b /N 0 = 4 . 57 dB 10 4 5 6 7 E b /N 0 [dB] School of ECS, Univ. of Southampton, UK. http://www-mobile.ecs.soton.ac.uk 13/ 14 ⇒ |

Summary ❏ Serial concatenations of regular and irregular codes ❏ EXIT chart matching ❏ BER and complexity performance results School of ECS, Univ. of Southampton, UK. http://www-mobile.ecs.soton.ac.uk 14/ 14 ⇒ |