0. Modeling of Digital Communication Systems using Simulink
Chap10. Digital Communications BER Performance in AWGN (Block Coding and Fading)
Chap11. Digital Communications BER Performance in AWGN and Fading (Convolution Coding)

1. 목차
Chap10. Digital Communications BER Performance in AWGN (Block Coding and Fading)
10.1 Digital Communications with Block Coding in Fading
10.2 BER Performance of BPSK in Rayleigh Fading with Interleaving and a BCH Block Code
10.3 BER Performance of BFSK in Rayleigh Fading with Interleaving and a Golay(24,12) Block Code
10.4 BER Performance of 32-FSK in Rayleigh Fading with Interleaving and a Reed-Solomon(31,15) Block Code
10.5 BER Performance of 16-QAM in Rayleigh Fading with Interleaving and a Reed-Solomon(15,7) Block Code
10.6 BER Performance of 16-QAM in Rayleigh and Rician Fading with Interleaving and a Reed-Solomon(15,7) Block Code
10.7 BER Performance of BPSK in Rayleigh Fading with Interleaving and a BCH Block Code and Alamouti STBC
10.8 BER Performance of BFSK in Rayleigh Fading with Interleaving and a Golay(24,12) Block Code and Alamouti STBC
10.9 BER Performance of 32-FSK in Rayleigh Fading with Interleaving and a Reed-Solomon(31,15) Block Code and Alamouti STBC
10.10 BER Performance of 16-QAM in Rayleigh Fading with Interleaving and a Reed-Solomon (15,7) Block Code and Alamouti STBC

2. Chap11. Digital Communications BER Performance in AWGN and Fading (Convolutional Coding)
11.1 Digital Communications with Convolutional Coding
11.2 BER Performance of Convolutional Coding and BPSK in AWGN
11.3 BER Performance of Convolutional Coding and BPSK in AWGN and Rayleigh Fading with Interleaving (Soft- and Hard-Decision Decoding)
11.4 BER Performance of Convolutional Coding and BPSK and Alamouti STBC in Rayleigh Fading with Interleaving

3. 10.4 BER Performance of 32-FSK in Rayleigh Fading with Interleaving and a Reed-Solomon(31,15) Block Code
32-FSK in Rayleigh Fading with Interleaving and a RS (31,15) Block Code

4. 10.4 BER Performance of 32-FSK in Rayleigh Fading with Interleaving and a Reed-Solomon(31,15) Block Code
BER 성능

5. 10.5 BER Performance of 16-QAM in Rayleigh Fading with Interleaving and a Reed-Solomon(15,7) Block Code
16-QAM in Rayleigh Fading with Interleaving and a RS (15,7) Block Code

6. 10.5 BER Performance of 16-QAM in Rayleigh Fading with Interleaving and a Reed-Solomon(15,7) Block Code
BER 성능

7. 10.5 BER Performance of 16-QAM in Rayleigh Fading with Interleaving and a Reed-Solomon(15,7) Block Code
Rayleigh Fading Channel 의 Maximum Doppler shift 0.1 Hz 및 0.01 Hz 인 경우

8. 10.6 BER Performance of 16-QAM in Rayleigh and Rician Fading with Interleaving and a Reed-Solomon(15,7) Block Code
16-QAM in Rayleigh and Rician Fading with Interleaving and a RS(15,7) Block Code

9. 10.6 BER Performance of 16-QAM in Rayleigh and Rician Fading with Interleaving and a Reed-Solomon(15,7) Block Code
BER 성능

10. 10.7 BER Performance of BPSK in Rayleigh Fading with Interleaving and a BCH Block Code and Alamouti STBC
BPSK in Rayleigh Fading with Interleaving and a BCH Block Code and Alamouti STBC

11. 10.7 BER Performance of BPSK in Rayleigh Fading with Interleaving and a BCH Block Code and Alamouti STBC
BER 성능

12. 10.8 BER Performance of BFSK in Rayleigh Fading with Interleaving and a Golay(24,12) Block Code and Alamouti STBC
BFSK in Rayleigh Fading with Interleaving and a Golay(24,12) Block Code and Alamouti STBC

13. 10.8 BER Performance of BFSK in Rayleigh Fading with Interleaving and a Golay(24,12) Block Code and Alamouti STBC
BER 성능

14. 10.9 BER Performance of 32-FSK in Rayleigh Fading with Interleaving and a Reed-Solomon(31,15) Block Code and Alamouti STBC
32-FSK in Rayleigh Fading with Interleaving and a RS (31,15) Block Code and Alamouti STBC

15. 10.9 BER Performance of 32-FSK in Rayleigh Fading with Interleaving and a Reed-Solomon(31,15) Block Code and Alamouti STBC
BER 성능

16. 10.10 BER Performance of 16-QAM in Rayleigh Fading with Interleaving and a Reed-Solomon (15,7) Block Code and Alamouti STBC
16-QAM in Rayleigh Fading with Interleaving and a RS(15,7) Block Code and Alamouti STBC

17. 10.10 BER Performance of 16-QAM in Rayleigh Fading with Interleaving and a Reed-Solomon (15,7) Block Code and Alamouti STBC
BER 성능

18. 11.1 Digital Communications with Convolutional Coding
11장의 내용은 AWGN 채널 및 Fading channel 에 convolutional error control coding 을 적용하는 방법을 소개한다.
BPSK 의 BER 성능을 아래 세 가지 환경에서 알아본다.
AWGN 에서 convolutional coding 을 적용한 경우 - Hard & Soft-decision decoding
AWGN 및 Rayleigh fading channel 일 때 convolutional coding 을 적용한 경우 - Hard & Soft-decision decoding
Rayleigh fading channel 일 때 convolutional coding 및 Alamouti STBC 적용한 경우 - Hard & Soft-decision decoding

19. 11.2 BER Performance of Convolutional Coding and BPSK in AWGN
Convolutional Code 란? Block code 방식에서는 데이터 비트에 패리티 비트를 추가하는 방식으로 code 를 생성하였으나 Convolutional Code 방식에서는 이전의 데이터와 현재의 데이터를 이용하여 패리티 비트를 생성.
Block code 방식 (n, k) – memoryless - 코드 길이 n 비트 중 k 비트가 데이터이고 n-k 비트는 패리티 비트로 구성됨.
Convolutional code 방식 (n, k, m) – contains memory - 입력 비트 수 k, 출력 비트 수 n, 메모리 레지스터 수 m

20. 11.2.1 Hard-Decision Decoding
Simulink 의 convolutional encoder 및 decoder 는 trellis (격자) 구조를 이용하여 8진수로 표현된 다항식 및 피드백 탭 정보를 구현함.
매트랩 함수 poly2trellis(7, [171, 133]) 7: shift register 에 저장되는 비트 수, 171 : , 133 :

21. State Diagram / Trellis Diagram

22. 11.2.1 Hard-Decision Decoding (cont’d)
Convolutional coding 을 적용한 BPSK 의 BER 특성을 보기 위한 시뮬링크 모델 ✔ ✔

23. 11.2.1 Hard-Decision Decoding (cont’d)
Convolutional Encoder

24. 11.2.1 Hard-Decision Decoding (cont’d)
Viterbi Decoder
복호 시 지연 : code rate ½ 인 경우
보통 constraint length의 다섯배 정도의 값을 씀.

25. Decode 원리 (에러가 없음, 현재 상태가 00 임을 가정할 때)
If ip=0
If ip=1
Current state
Next state (op) 00
00 (00)
10 (11) 01
00 (11)
10 (00) 10
01 (10)
11 (01) 11
01 (01)
11 (10) 00
00/2
00/X : op/hamming distance
11/0 10
11/2
10/2
10/2
00/0 01
01/0
01/0
01/0 11
10/2
Rx data 11 01 01 00 01
Tx data 1 1 1 1

26. Decode 절차 (에러가 있는 경우, Hard-decision)
If ip=0
If ip=1
Current state
Next state (op) 00
00 (00)
10 (11) 01
00 (11)
10 (00) 10
01 (10)
11 (01) 11
01 (01)
11 (10) 00
00/2
00/1
00/1
00/X : op/hamming distance
11/0
11/1
11/1 10
11/1
11/0
10/2
00/2
10/2
00/1 01
01/0
01/0
01/0 11
10/2
Rx data 11 01 01 10 01
Tx data 1 1 1 1 1

27. Decode 절차
Hard – decision decoding
Hamming distance 를 계산하여 그 거리가 최소인 경로로 결정. ex.)
010→111 해밍거리: 2
100→011 해밍거리: 3
0110→1110 해밍거리: 1
0100→1001 해밍거리: 3

28. Soft – decision decoding
Decode 절차
Soft – decision decoding
Euclidean distance 를 계산하여 그 거리가 최소인 경로로 결정. ex.)
(a) Hard-decision plane (b) 8-level by 8-level soft-decision plane (c) Example of soft code symbols (d) Encoding trellis section (e) Decoding trellis section.

29. 11.2.1 Hard-Decision Decoding (cont’d)
Viterbi Decoder – Decision Type - decoder 입력 데이터 타입이 달라짐. Unquantized: 실수를 받으며 양의 실수: logic 0, 음의 실수: logic 1 로 인식 Hard-Decision: 0, 1 을 받으며 0: logic 0, 1: logic 1로 인식 Soft-Decision: 0 ~ 2b-1 의 정수를 받으며 b 는 soft decision 비트의 개수.
Input Value
Interpretation
Most confident zero 1
Second most confident zero 2
Third most confident zero 3
Least confident zero 4
Least confident one 5
Third most confident one 6
Second most confident one 7
Most confident one

30. 11.2.1 Hard-Decision Decoding (cont’d)
BER 성능

31. 11.2.2 Soft-Decision Decoding
Convolutional coding 을 적용한 BPSK 의 BER 특성을 보기 위한 시뮬링크 모델

32. 11.2.2 Soft-Decision Decoding (cont’d)
Scalar Quantizer Encoder
boundary points 에 정해진 양자화 범위로 (index) 입력값을 대응시켜줌.
partitioning ex.) Bounded:
[ ]
Unbounded: 1 4 1 2 5 6

33. 11.2.2 Soft-Decision Decoding (cont’d)
BER 성능