FORWARD ERROR CORRECTION (FEC) CODING IN THE GLOBAL SYSTEM FOR MOBILE COMMUNICATIONS (GSM)

Dai, Shuai (Jason)

Sun, Chang (Fred)

Zhuang, Fuxin (Henry)

March 17, 2011

STAGES OF CHANNEL CODING

BLOCK CODING FOR LOGICAL CHANNELS

Channel Generating Polynomial Notes

TCH/FS X3 + X + 1 Cyclic Code (Pe =10-6 ~ 10-5)

DCCH and CCCH (part)

(X23 + 1)(X17 + X3 + 1） Fire Code (probability of undetected error only 2-40)

RACH X6 + X5 + X3 + X2 + X +1 P0(8)+parity(6)+tail(4)=P1(18)

SCH X10 + X8 + X6 + X5 + X4 + X2 + X +1 P0(25)+parity(10)+tail(4)=P1(39)

CONVOLUTIONAL CODING• Block coding has supplemented the data with redundancy bits (parity bits) for error detection• Convolutional coding is to calculate additional redundancy for error correction• A convolutional code is described by three integers:, v, k and K.• Code rate = k/v; in GSM: rGSM=1/vGSM=1/2;

INTERLEAVING

Errors tend to occur in bursts. Distributing errors evenly in time improve the

efficiency of error detection and correction.

Interleaving Depth:the number of bursts over which a codeword is spread.

Reference: GSM : architecture, protocols and services / Jörg Eberspächer ... [et al.] 3rd edition Wiley, 2009