Chapter 4. Channel Coding and Error Control

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1 Chapter 4 Channel Coding and Error Control Adapted from class notes by Prof. Leszek T. Lilien, CS, Western Michigan University and Prof. Dharma P. Agrawal & Qing-An Zeng, University of Cincinnati Most slides based on publisher s slides for 1 st and 2 nd edition of: Introduction to Wireless and Mobile Systems by Agrawal & Zeng 2003, 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved. Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 1 Protocol: an agreement between the communicating parties on how communication is to proceed. 1. 工作站 5. 印表機通訊傳輸媒介 4. 工作站 3. 工作站 2. 工作站 Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 3 1

2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 4 Protocol Hierarchies (cont.

2 Open System Interconnection (OSI) Model-- Seven Layers 應用層 (Application Layer) 表達層 (Presentation Layer) 會議層 (Session Layer) 傳輸層 (Transport Layer) 網路層 (Network Layer) 鏈結層 (Data Link Layer) 實體層 (Physical Layer) Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 4 Protocol Hierarchies (cont.) 對等式通訊 (Peer-to-Peer) 網際網路 TCP IP Ethernet (IEEE 802.3) Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 5 2

3 An exchange using the OSI model Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 6 OSI Model TCP/IP Model OSI Model Application layer: http, telnet, snmp, smtp, nfs, ftp TCP, UDP IPv4, IPv6 Host-to-Network layer Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 7 3

Relationship of layers and addresses in TCP/IP

Channel: 必經之道 Noise: 有馬賊 Channel coding: 請保鑣 Copyright http://images.

5 Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 10 Channel/ Channel coding A B Information: 金銀財寶 Channel: 必經之道 Noise: 有馬賊 Channel coding: 請保鑣 Copyright , Dharma P. Agrawal and Qing-An Zeng. All rights reserved 11 5

4.1. Introduction Why need channel coding for radio communication?

Low S/N (signal-to-noise) ratio = SNR Copyright 2007 by Leszek 2006, Dharma T.

All rights reserved 12 S/N Ratio (SNR), SIR 訊號與雜訊比 (Signal to Noise Ratio; Signal to

6 4.1. Introduction Why need channel coding for radio communication? Severe transmission problems In terrestrial mobile communications due to: Multipath fading E.g., reflections / diffractions / scattering in cellular wireless communications Low S/N (signal-to-noise) ratio = SNR Copyright 2007 by Leszek 2006, Dharma T. LilienP. Agrawal and Qing-An Zeng. All rights reserved 12 S/N Ratio (SNR), SIR 訊號與雜訊比 (Signal to Noise Ratio; Signal to Interference Ratio) 雜訊 (Noise) 對訊號 (Signal) 的干擾程度 S/N 或 S/I: 通常以 db 來表示比值 S/N 值愈高, 訊號品質愈好必須使 S/N > 1 ( 其 db 值 >0) 提高發射功率, 可使 S/N 值提高, 但須規範 S/N = 10 log(s/n) db Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 13 6

7 4.1. Introduction (cont.) In satellite communications due to: Limited xmitting power for forward channels (downlink ) Limited satellite energy resources => Need means to improve transmissions Channel coding and error control are such means Copyright 2007 by Leszek 2006, Dharma T. Lilien P. Agrawal and Qing-An Zeng. All rights reserved 14 For example, mobile phone A B Speaker Ch.4 Ch.3 Ch.4 Copyright Source: 禹帆, 2006, 無線通訊網路概論 Dharma P. Agrawal, 文魁 and Qing-An Zeng. All rights reserved 15 7

http://image.slidesharecdn.com/gsmreviewnote-100825014815-phpapp02/95/gsm-review-note-by-zemaryali-40-728.jpg?

1 => Need channel coding and error control to improve transmissions 10,000 1,000?

on enhanced reliability http://pansci.asia/wp-content/uploads/2014/04/pp1-560x286.png http://us.etherwan.

8 Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved Introduction cont. 1 => Need channel coding and error control to improve transmissions 10,000 1,000? Channel coding (CC) = coding (discrete digital) information into a form suitable for transmission, with emphasis on enhanced reliability Copyright 2007 by Leszek 2006, Dharma T. LilienP. Agrawal and Qing-An Zeng. All rights reserved 17 8

transmission quality Measured by Bit error quality (BER) / Frame error quality (FER) http://www.pipecogroup.com/wp-content/uploads/2015/12/quality.

9 4.1. Introduction cont. 1 Channel coding (CC) CC adds redundancy that allows for info restoration or recovery when needed Price paid: need broader bandwidth 代價 ; 運費 ; 押鏢金 CC ensures proper transmission quality Measured by Bit error quality (BER) / Frame error quality (FER) Copyright 2007 by Leszek 2006, Dharma T. LilienP. Agrawal and Qing-An Zeng. All rights reserved 18 Channel Coding Bit Error Rate (BER): 數位系統訊號受干擾的程度 BER 過高通話品質下降 Error Detection / Error Correction Channel Coding GSM TCH channel coding 保鑣一保鑣二沒有保鑣 Copyright Source: 禹帆, 2006, 無線通訊網路概論 Dharma P. Agrawal, 文魁 and Qing-An Zeng. All rights reserved 19 9

10 Channel Coding (cont.) GSM TCH 頻道編碼時對 260 個位元的處理方式 Need broader bandwidth Copyright Source: 禹帆, 2006, 無線通訊網路概論 Dharma P. Agrawal, 文魁 and Qing-An Zeng. All rights reserved 20 Channel Coding (cont.) GSM 語音頻道於各個階段經過訊號處理後的速率 Copyright Source: 禹帆, 2006, 無線通訊網路概論 Dharma P. Agrawal, 文魁 and Qing-An Zeng. All rights reserved 21 10

11 4.1. Introduction cont. 2 Channel coding/decoding in a wireless communication system Information to be transmitted Source coding Channel coding Modulation Transmitter Information received Source decoding Channel decoding Demodulation Receiver Channel p. 80 ( 頁 90) Fig. 4.1 Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 22 Error Control Process Single-bit error Multiple-bit error WCB/McGraw-Hill The McGraw-Hill Companies, Inc., 2001 Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 24 11

12 Error Control Process (2) Burst error WCB/McGraw-Hill The McGraw-Hill Companies, Inc., 2001 Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 25 Error Control Process (3) All transmission media have potential for introduction of errors Error control process has two components Error detection redundancy in data so that error can be detected Error correction once error detected, errors corrected or frames retransmitted Copyright 2006, 2003, Dharma Andrew P. Agrawal S. Tanenbaum, and Qing-An Vrije Zeng. Univ., All Netherlands rights reserved 26 12

13 Error Detection Parity Check odd parity or even parity make number of 1 s in character odd or even The McGraw-Hill Companies, Inc., 2001 Copyright 2006, 2003, Dharma Andrew P. Agrawal S. Tanenbaum, and Qing-An Vrije Zeng. Univ., All Netherlands rights reserved 27 Error Detection Cyclic Redundancy Check (CRC) treat frame as one long binary number divide by unique prime binary number attach remainder to frame The McGraw-Hill Companies, Inc., 2001 Copyright 2006, 2003, Dharma Andrew P. Agrawal S. Tanenbaum, and Qing-An Vrije Zeng. Univ., All Netherlands rights reserved 28 13

14 Error Correction Two types of errors Lost frame - never arrives Damaged frame - error in bits Automatic Repeat request (ARQ) Error detection (e.g. CRC) Positive acknowledgment (ACK) if received Retransmission after time-out if not ACK Negative ACK and retransmission if error Error-Correcting Codes Copyright 2006, 2003, Dharma Andrew P. Agrawal S. Tanenbaum, and Qing-An Vrije Zeng. Univ., All Netherlands rights reserved 30 Error Correction (2) WCB/McGraw-Hill The McGraw-Hill Companies, Inc., 2001 Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 31 14

15 The key EC idea: Error Correction (3) Transmit enough redundant data to allow receiver to recover from errors all by itself No sender retransmission required Major categories of EC codes ( 保護的方法與等級 ) (really: forward error correction FEC) Linear block codes Hamming code BCH code Cyclic codes Reed-Solomon codes Convolutional codes Turbo codes Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved (Modified by LTL) Linear Block Codes Information is divided into blocks of length k r parity bits or check bits are added to each block Total length: n = k + r Code rate: R = k/n = k/(k + r) Decoder looks for code word closest to received vector Received vector = code vector + error vector Tradeoffs between Efficiency Reliability Encoding/decoding complexity k k Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 33 15

All rights reserved 34 1 Hamming Code (2) 1 1 Generation of Hamming Code (Even Parity Check) 1

16 Hamming Code (1) n = 11, k = 7, r = 4, R = 7/11 Code word WCB/McGraw-Hill The McGraw-Hill Companies, Inc., 2001 Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 34 1 Hamming Code (2) 1 1 Generation of Hamming Code (Even Parity Check) 1 WCB/McGraw-Hill The McGraw-Hill Companies, Inc., 2001 Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 35 16

17 Hamming Code (4) WCB/McGraw-Hill The McGraw-Hill Companies, Inc., 2001 Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 37 Error-Detecting Codes -- CRC WCB/McGraw-Hill The McGraw-Hill Companies, Inc., 2001 Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 52 17

Hardware CRC Source: http://www.erg.abdn.ac.uk/users/gorry/course/dl-pages/crc.html Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 55

18 Hardware CRC Source: Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved Convolutional Codes 請功夫最好的保鑣 Most commonly used channel codes E.g., in GSM and IS-95 Encoding of information stream rather than information blocks Output (encoded bits) depends not only on current input bits but also on past data bits M - max. # of (past) stages (a.k.a. memory size ) affecting output Easy implementation using shift register Assuming k inputs and n outputs Decoding most often based on the Viterbi Algorithm Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved (Modified by LTL) 59 18

電動絞肉機 Source: http://att3.citysbs.com/f400x400/hangzhou/2013/04/09/11/110208_18421365476528946_fdd3a35cdf17b7ce100b676050565345.jpg Copyright 2006, Dharma P. Agrawal and Qing-An Zeng.

19 電動絞肉機 Source: Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 60 Convolutional Codes: (k=1, n=2, M=2) Encoder Coding Rate R = k/n =1/2 x Input D1 D2 y 1 Output c y 2 p. 88 ( 頁 99) Fig. 4.3 Di -- Register Input: Output: Input: Output: Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 61 19

Input p. 88 ( 頁 99) Fig. 4.3 State Diagram x D1 D2 y 1 Output 10/1 y 2 01/1 11 01/0 10/0 10 01 00/1 11/1 11/0 00 D1D2 y1y2/x 00/0 p. 88 ( 頁 100) Fig. 4.4 Copyright 2006, Dharma P.

20 Input p. 88 ( 頁 99) Fig. 4.3 State Diagram x D1 D2 y 1 Output 10/1 y 2 01/ /0 10/ /1 11/1 11/0 00 D1D2 y1y2/x 00/0 p. 88 ( 頁 100) Fig. 4.4 Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 62 GSM Channel Coding Convolutional Coding 運用 Exclusive OR 計算出更多的位元 Copyright Source: 禹帆, 2006, 無線通訊網路概論 Dharma P. Agrawal, 文魁 and Qing-An Zeng. All rights reserved 65 20

21 Example 3: recursive encoder Rate 1/2 recursive, systematic convolutional (RSC) encoder with constraint length 4 One can see that the input being encoded is included in the output sequence too (look at the output 2). Such codes are referred to as systematic; otherwise the code is called nonsystematic. Source: Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 66 Example 2: non-recursive encoder Rate 1/3 non-recursive, non-systematic convolutional encoder with constraint length 3 n1 = m1 + m0 + m-1 n2 = m0 + m-1 n3 = m1 + m-1. Source: Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 67 21

Viterbi Decoding Algorithm The Viterbi algorithm was conceived by Andrew Viterbi in 1967 as an error-correction scheme for noisy digital communication links, finding universal application in decoding

22 Viterbi Decoding Algorithm The Viterbi algorithm was conceived by Andrew Viterbi in 1967 as an error-correction scheme for noisy digital communication links, finding universal application in decoding the convolutional codes used in both CDMA and GSM digital cellular, dial-up modems, satellite, deep-space communications, and wireless LANs. Source: Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved Interleaver Interleaving is heavily used in wireless communication for protection against burst errors Recall: Burst error a contiguous sequence of symbols, received over a data transmission channel, such that: Block interleaver - most common interleaver Concept next slide Copyright 2007 by Leszek 2006, Dharma T. LilienP. Agrawal and Qing-An Zeng. All rights reserved 70 22

23 Write Concept of Interleaver 2 1 1) Sender writes row-byrow into buffer 2) Read col-by-col from buffer onto link 3 4 1) Write col-by-col from link into buffer 2) Receiver reads row-byrow from buffer p. 90 ( 頁 102) Fig. 4.7 Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 71 Interleaving (Example) Burst error Transmitting Data De-Interleaving 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0 0, 1, 0, 0 0, 1, 0, 0 1, 0, 0, 0 Read Output Data 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, Discrete error p. 91 ( 頁 102) Fig. 4.8 Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 74 23

24 Channel Interleaving 頻道編碼 (Channel Coding) 與交錯 (Interleaving) 對資料的切割方式 Copyright Source: 禹帆, 2006, 無線通訊網路概論 Dharma P. Agrawal, 文魁 and Qing-An Zeng. All rights reserved 77 Channel Coding (cont.) For example, GSM Copyright Source: 禹帆, 2006, 無線通訊網路概論 Dharma P. Agrawal, 文魁 and Qing-An Zeng. All rights reserved 79 24

25 Brief history of turbo codes: 4.7. Turbo Codes First introduced by C. Berrou et al. only in 1993 Considered as the most efficient FEC coding schemes Performance close to the (perfect) Shannon Limit at modest complexity! Turbo codes use known components Including: simple convolutional or block codes, interleaver, soft-decision decoder Turbo codes proposed for Low-power applications Such as deep-space and satellite communications, Interference-limited applications Such as 3G cellular, PCS (personal communication services), ad hoc networks and sensornets Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 81 Information Capacity Theorem Bit Rate: 單位時間內傳送的位元數目,bps Baud Rate: 載波之頻率或相位的變化率,Hertz Nyquist Theory: C = 2B (ideal channel) C: 載波最高的傳輸率,bps B: 通訊頻道的頻寬,Hz 例 :1 GSM 頻道 = 200kHz = B 載波傳輸率上限 C = 2B = 400kbps Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 82 25

26 Information Capacity Theorem (cont.) Shannon's theorem: 利用換底公式 : C = B log 2 (1+S/N) (noisy channel) C: 頻道的數據傳輸率,bps B: 通訊頻道的頻寬,Hz 例 :1 GSM 頻道 = 200kHz = B S/N = 2.56 數據傳輸率上限 C = 200k*lg(2.56) = 271 kbps S/N = 10 ( 剛好 10 db) 數據傳輸率上限 C = 200k*lg(11) = 692 kbps log( 2.56) lg( 2.56) log 2(2.56) log( 2) Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 83 Turbo Codes: Encoder Data Source X X Interleaving Convolutional Encoder 1 Convolutional Encoder 2 Y 1 Y Y 2 (Y 1, Y2) X: Information Y i : Redundancy Information p. 92 ( 頁 103) Fig. 4.9 Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 86 26

Example of Convolutional Encoder in Turbo Coding Rate 1/2 recursive, systematic convolutional (RSC) encoder with constraint length 4 Source: http://en.

All rights reserved 87 Example of Turbo-code Encoder Hardware-wise, this turbo-code encoder consists of two identical RSC coders, С1 and C2, as depicted on

27 Example of Convolutional Encoder in Turbo Coding Rate 1/2 recursive, systematic convolutional (RSC) encoder with constraint length 4 Source: Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 87 Example of Turbo-code Encoder Hardware-wise, this turbo-code encoder consists of two identical RSC coders, С1 and C2, as depicted on the figure, which are connected to each other using a concatenation scheme, called parallel concatenation Source: Copyright , Dharma P. Agrawal and Qing-An Zeng. All rights reserved 88 27

28 Turbo Codes: Decoder De-interleaving Y 1 Convolutional Decoder 1 Interleaver X Interleaving Convolutional Decoder 2 De-interleaving Y 2 X X : Decoded Information p. 92 ( 頁 104) Fig Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved Automatic Repeat Request (ARQ) [LTL] Sometimes Cyclic Code can detect but can t correct errors Must ask for retransmission Can use Automatic Repeat Request (ARQ) D sends (positive) acknowledgement ACK if received packets correct If D detects error it can t correct, D sends negative acknowledge-ment NAK this requests retransmission Source S Transmitter Channel Receiver Destination D Encoder Transmit Controller Modulation Demodulation Decoder Transmit Controller Acknowledge (ACK or NAK) x p. 93 ( 頁 104) Fig Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 90 28

29 Stop-And-Wait ARQ (SAW ARQ) Transmitting Data Retransmission Time Received Data Error Time Output Data Time ACK: Acknowledge NAK: Negative ACK p. 93 ( 頁 105) Fig Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 91 Go-Back-N ARQ (GBN ARQ) Go-back 3 Go-back 5 Transmitting Data Time Received Data Error Error Time Output Data Time p. 95 ( 頁 107) Fig Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 93 29

30 Selective-Repeat ARQ (SR ARQ) Retransmission Retransmission Transmitting Data Time Received Data Error Error Time Buffer Time Output Data Time p. 96 ( 頁 108) Fig Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 95 The End of Section 4 Copyright 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 97 30

Chapter 3 The Data Link Layer

Chapter 3 The Data Link Layer 陳瑞奇 (Rikki) 亞洲大學資訊工程學系 Adapted from Computer Networks, Andrew S. Tanenbaum, Vrije University, Netherlands & Computer Networking: A Top Down Approach, Jim Kurose, Keith Ross