Fire Code in GSM

Nabil Magdy Hassan, sec :(8), B.N:19

Electronics & Electrical Communications Department, Cairo University

1. GSM codes

The codes used in GSM are: Block Convolutional Codes: these codes

are only used for correction purposes. They achieve tremendous efficiency when they are combined with likelihood estimation such as that coming from the demodulator,

Fire Code: this code is dedicated to the detection and correction of 'bursty' errors, i.e., errors that occur in a short time interval. It is used in concatenation after a block convolutional code, for which residual errors often appear in short time intervals.

Parity Codes: used for error detection.

2. Fire Code

A Fire code is a conventional linear binary block code, i.e., it consists in transmitting, in addition to the information bits, k a number or redundant bits computed by exclusive-or manipulations on the information bits. Moreover Fire codes derive from codes belonging to the 'cyclic' code family. In this case, the redundancy computation formulas can be expressed as follows. The original sequence can be used to build a polynomial, whose coefficients are the bits of the sequence. The redundancy can be expressed as the coefficients of another polynomial obtained as the remainder of the division of the polynomial representing the sequence by a pre-defined polynomial, characteristic of the code and called the generator polynomial. 3. Fire Code Properties

A Fire code has a generator polynomial designed to allow good detecting and/or correcting performance when errors happen in groups. The GSM Fire code uses the following generator polynomial:

This polynomial, being of degree 40, gives a remainder having 40 coefficients, and thus there are 40 redundancy bits. The properties of this code are

such that error groups of 11 bits can be detected and corrected.

4. Channel coding for the GSM control channels

In GSM the signaling information is just contained in 184 bits. Forty parity bits, obtained using a fire code, and four zero bits are added to the 184 bits before applying the convolution code (r = 1/2 and K = 5). The output of the convolution code is then a block of 456 bits, which does not need to be punctured.

5. Fire Code algorithm approach

A Fire code is capable of correcting bursts of length τ, is constructed using the generator polynomial.

G ( D ) = ( D2τ-2 – 1 ) P ( D )P (D): is a degree – m polynomial such that m is greater than or equal to τ & P (D) & (D2τ-2 – 1) are relatively prime that is P(D) does not divide (D2τ-2 – 1). The block length N of this code is:

N= l (2τ -1)l :is the smallest integer such that P(D) divides(D1-1).