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

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 ) .

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))

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

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 10.6428 10.2706 5.5250e-004 13.3035 11.2397 1.3246e-004 15.9642 12.0315 3.2276e-005 18.6249 12.7009 7.9564e-006 21.2856 13.2809 1.9785e-006 23.9463 13.7924 4.9530e-007 26.6070 14.2500 1.2467e-007

Finding the parameters of the RS code by iteration Power table

Code construction The generator polynom

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

Encoder implementation + 1

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

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 10.6428 10.2706 5.5250e-004 13.3035 11.2397 1.3246e-004 15.9642 12.0315 3.2276e-005 18.6249 12.7009 7.9564e-006 21.2856 13.2809 1.9785e-006 23.9463 13.7924 4.9530e-007 26.6070 14.2500 1.2467e-007

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

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 ??

Improving SE with coding If a Service Provider launches an 1 Mbps dataspeed wireless service then it requires B= 2.825 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 !!!

Standard cyclic odes applied in the MAC sublayer ARQ = Automatic Repeat reQuest CRC = Cyclic Redundancy Check CCITT 16 bit code INTEL 82586 (Local communication controller) Ethernet chip