1. Improving the quality of digital communication by error correcting codes – communication engineerig

2. Error Trapping on LFBSR
Full coding scheme
LFFSR
Error Trapping on LFBSR
LFBSR
Design of the code:
Given the channel quality which determines d_min or “t” ( number f errors to be corrected ) .

3. Advantages – the communication engineering context
RS codes – optimal performance ( error correction with minimal decrease in data speed)
Real Time operation – shift register based implementation supporting high data speed
Binary transmission – codes over GF(2ˆm), each symbol is translated into a binary sequence ( best utilization of signal tansmission power))

4. A design problem
Given a radio channel with SNR= 4.25dB over which reliable data communication is to be implemented. The message is sent by using BPSK modulation and the QoS requierement specifies that the block error rate cannot exceed 2*10–4.
The objective is to construct an error-correcting code, which can achieve this QoS.
Compare the spectral efficiency of the system with and without coding!
Solution :
Given :
1. SNRdB=4.25dB
2. The desired block errror rate : ~2*10–4

5. Solution by Reed-Solomon codes
d_min 1 2 3 4 5 6 7 8 9 11
SNR
SNR[dB]
P_bit error
2.6607
4.2500
0.0514
5.3214
7.2603
0.0105
7.9821
9.0212
0.0024
5.5250e-004
1.3246e-004
3.2276e-005
7.9564e-006
1.9785e-006
4.9530e-007
1.2467e-007

6. Finding the parameters of the RS code
by iteration
Power table

7. Code construction
The generator polynom

8. Error Trapping on LFBSR
The coding scheme
Error Trapping on LFBSR
LFFSR
LFBSR T + 1

9. Encoder implementation+ 1

10. Encoder implementation
SRC
SRC
SRC 1
SRC
SRC 1 +
VLSI implementáció nehézkes !!!

11. The solution (cont’) d_min 1 2 3 4 5 6 7 8 9 11 SNR SNR[dB]
P_bit error
2.6607
4.2500
0.0514
5.3214
7.2603
0.0105
7.9821
9.0212
0.0024
5.5250e-004
1.3246e-004
3.2276e-005
7.9564e-006
1.9785e-006
4.9530e-007
1.2467e-007

12. ALGORITHMS CAN EXTEND RESOURCES !!!
Physical domain
Algorithmic domain
ALGORITHMS CAN EXTEND RESOURCES !!!

13. Wireless communication technologies
Radiospectrum expensive
High utilization of narrowband channels
Spectral efficiency [bit/sec/Hz]: what is the required bandwidth for a given dataspeed?
Presently SE=0.48 bit/sec/Hz
High speed services are costly !!!
HOW TO IMPROVE SE WITH ERROR CONTROL CODING ??

14. Improving SE with coding
If a Service Provider launches an 1 Mbps dataspeed wireless service then it requires
B= MHz in case of no coding
B= 1.5 MHz in case of coding
Roughly half of the bandwidth is required – TREMENDOUS IMPROVEMENT!!!
ALGORITHMS (HUMAN MIND) CAN EXTEND RESOURCES !!!

16. Standard cyclic odes applied in the MAC sublayer
ARQ = Automatic Repeat reQuest
CRC = Cyclic Redundancy Check
CCITT 16 bit code
INTEL (Local communication controller)
Ethernet chip