1. 林茂昭 教授 台大電機系 96.2.15 個人專長 錯誤更正碼 數位通訊
大學部專題介紹
林茂昭 教授
台大電機系
個人專長
錯誤更正碼
數位通訊

2. Basic Coded Communication System
Source
Source
Encoder
Channel
Encoder
Channel
User
Source
Decoder
Channel
Decoder
Source encoder/decoder: For reducing redundancy without
distortion or with distortion
Channel encoder/decoder: for increasing transmission reliability
by adding redundancy

3. Importance of Error-Control Coding (ECC)
ECC can be used to increase the transmission rate and reliability in the digital communication (either wireless or wired communication) and digital storage system.
Most powerful system can be obtained by integrating, ECC, modulation, channel information and synchronization.

4. Repetition Codes (I) Let C={(000),(111)} Received vector
0 0 0
0 0 1
0 1 0
1 0 0
Coding rate R=1/3
Minimum distance d=3
Error correcting capability
decoding
0 0 0
0 1 1
1 0 1
1 1 0
1 0 0
1 1 1

5. Repetition Codes (II) Let c={(00000),(11111)}. Then d=5,R=1/5 and
Let c={(00…0),(11…1)} and n=2t+1. Then d=2t+1 R=1/(2t+1)
Apparently, as Is it necessary that to achieve zero error probability, we can only have zero coding rate!

6. (7,4) Hamming code n=7 , k=4 , d=3, R=4/7. 0000 1000 0100 1100 0010
1010
0110
1110
0001
1001
0101
1101
0011
1011
0111
1111

7. Nearest-Neighbor Decoding:
Let be the transmitted codeword, be the received vector and be the error vector. The codeword can be correctly recovered if Equivalently

8. Error Control Coding (I)
For any (n,k,d) code C, up to errors can always be corrected, or up to d-1 errors can always be detected.
An (n,k,d) code C is a subset of with size , for which the minimum distance between any two codewords is d.

9. Error Control Coding (II)
For a given d, it is desired to find a subset C of such that is as large as possible. For a given k, it is desired to find a subset C of such that and d is as large as possible
Code construction
Low decoding complexity

10. Binary Symmetric Channel (BSC)
transition probabilities:

11. Additive White Gaussian Noise Channel (AWGN Channel)
: one-side power spectral density of the AWGN Channel
: Bandwidth

12. Hard Decision and Soft Decision
Consider an AWGN channel with binary input A and –A. if hard decision in the output is made, then the AWGN channel is reduced to a BSC channel
Example
let C={(-1,-1),(1,1)}. Suppose that If hard decoding is used, no decision on the decoded codeword can be made. If soft decoding is used, (-1,-1) will be decoded.

13. Integrated Coding and Modulation
Each signal point in the 8PSK signal set (or constellation) is labeled by 3 bits (a,b,c)
(2)
010
(3) 110
100 (1)
(4) 001
000 (0) 1
(5) 101
111 (7)
011
(6)

14. Trellis Coded MPSK over Rayleigh Fading Channel
Let be the transmitted MPSK
sequence. Let be the received sequence, where
: zero mean complex Gaussian noise with variance
: normalized random variable with Rayleigh distribution
,ie.

15. Current Topics Convolutional coding Coded OFDM Coded Equalization
Noncoherent Coded Modulation
Space-time coding
Coding for Memory systems

16. Topics for Beginners
Viterbi Decoder
Turbo Decoder

17. Recent Publications (I)
“Minimal Trellis Modules and Equivalent Convolutional Codes ,” IEEE Transactions on Information Theory, Vol. 52, No. 8, pp , August 2006.
“Recursive Clipping and Filtering with Bounded Distortion for PAPR Reduction,” IEEE Transactions on Communications, Vol. 55, No. 1, pp , January 2007

18. Recent Publications (II)
“Coded MIMO Using Interblock Memory,” IEEE Vehicular Technology Conference, Spring 2006, Melbourne, Australia, May 7-10, 2006.
“Improved Decoding for Trellis Coded Modulation with A Delay Processor,” International Symposium on Information Theory and Its Applications, Seoul Korea, October 29-November 1, 2006
“Binary Turbo Coding with Interblock Memory,” IEEE Wireless Communications and Network Conference (WCNC 2007), March 11-15, Hong Kong.