Page 1248 - 5G Basics - Core Network Aspects

2 Transport aspects

Transmission order within FEC code word

1 2 3 4 238 239 240 241 254 255

FEC sub-row D 254 D 253 D 252 D 251 D j D 17 D 16 R 15 R 14 R j R 1 R 0

1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8
d 7j d 6j d 5j d 4j d 3j d 2j d 1j d 0j r 7j r 6j r 5j r 4j r 3j r 2j r 1j r 0j

G.709/Y.1331_FA.2

Figure A.2  FEC code word

Information bytes are represented by:

I (z )  D 254 . z 254  D 253 . z 253  ... D 16 . z 16

Where Dj (j = 16 to 254) is the information byte represented by an element out of GF(256) and:

D  d j 7   7  d j 6   6  ... d j 1   1  d j 0
j
Bit d j 7 is the MSB and d j 0 the LSB of the information byte.

D 254 corresponds to byte 1 in the FEC sub-row and D 16 to byte 239.

Parity bytes are represented by:

1
R (z ) R  15 z 15  R 14 z  14  ... R  1 z  R 0
Where Rj (j = 0 to 15) is the parity byte represented by an element out of GF(256) and:

R  r j 7   7  r   6  ... r   1  r j 0
j
j 6
j 1
Bit r 7 j is the MSB and r 0 j the LSB of the parity byte.
R 15 corresponds to the byte 240 in the FEC sub-row and R0 to byte 255.

R(z) is calculated by:

R(z) = I(z) mod G(z)
where "mod" is the modulo calculation over the code generator polynomial G(z) with elements out of the
GF(256). Each element in GF(256) is defined by the binary primitive polynomial x 8 x 4 x 3 x 2  . 1

The Hamming distance of the RS(255,239) code is dmin = 17. The code can correct up to 8 symbol errors in
the FEC code word when it is used for error correction. The FEC can detect up to 16 symbol errors in the
FEC code word when it is used for error detection capability only.

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