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

S TAGES OF C HANNEL C ODING

BLOCK CODING FOR LOGICAL CHANNELS ChannelGenerating PolynomialNotes TCH/FS X 3 + X + 1 Cyclic Code (Pe =10 -6 ~ ) DCCH and CCCH (part) (X )(X 17 + X ） Fire Code (probability of undetected error only ) RACH X 6 + X 5 + X 3 + X 2 + X +1 P0(8)+parity(6)+tail(4)=P1(18) SCH X 10 + X 8 + X 6 + X 5 + X 4 + X 2 + 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: r GSM =1/v GSM =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.] 3 rd edition Wiley, 2009