Motorola Pro FLX Manuel d'utilisateur télécharger pdf (Page 37)

Design and Implementation of a Practical FLEX Paging Decoder

Grayson Wireless 29

what would be implemented in hardware with taps at each location. After all 31 bits pass

through these two shifting registers, the resulting m1 and m3 are used to calculate S1 and S3.

Syndrome 1 is simply the result in m1 (S1=m1). The calculation for Syndrome 3 which uses m3

is given below. The notation of S3.0 means Syndrome 3 bit location 0. All addition with m3 bit

location is modulo 2.

S3.0 = m3.0

S3.1 = m3.2+ m3.3+ m3.4

S3.2 = m3.4

S3.3 = m3.1+ m3.2+ m3.3+ m3.4

S3.4 = m3.3

The error-location polynomial,

(z) will be one of the following based on S1 and S3 [Mac 77].

i) If S1=S3=0,

(z) = 0. (No errors)

ii) If S1 != 0, S3 = S1

(z) = 1+S1z. (1 bit error)

iii) If S1 != 0, S3 != S1

(z) = 1 + S1z + ((S3/S1 + S1

. (2 bit errors)

A table look up of the Galois Field (GF) for the minimum polynomial m1(x) is given in [Lin 83].

An inverse table to the GF is also used so that multiplication of values can be done using the GF

index or power so that addition can be used. The error-location polynomial is evaluated for each

bit

(

) and if the result is zero then that bit is in error. The overall even parity bit was also used

to help determine the number of bits in error. An incorrect received even parity means that there

are an odd number of bits in error, and a correct received even parity means there is an even

number of bits in error. The parity bit itself might be a bit in error and it is not included in the

BCH error encoding.

3.4 BER Measurements

The number of bits required for a valid BER measurement is determined by the method

“bounded binomial sampling” which is used as one of the method in [Fun 91]. Bounded

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Motorola Pro FLX Manuel d'utilisateur Page 37