The document discusses Reed-Solomon FEC coding. It explains that Reed-Solomon RS(n,k) encoding takes k data bytes and calculates n-k parity bytes to create an n-byte codeword. A Reed-Solomon decoder can correct up to t byte errors, where t=(n-k)/2. ITU G.975 and G.709 recommend Reed-Solomon RS(255,239) coding, which can correct up to 8 byte errors and provides a coding gain of around 6dB with a 7% overhead. The document also provides examples of calculating RS(n,k) parameters for an OTN frame.

1. RS(n,k):Exploring "n" and "k" in Reed-Solomon FEC code
FEC codes in optical communications are based on a class of codes know as .Reed-Solomon
A code is specified as , which means that the and aReed-Solomon RS ( , )n k encoder takes data bytesk dds parity bytes to make an n bytes
. A Reed-Solomon decoder can correct up to bytes in the codeword, where .codeword t 2t=n - k
ITU recommendation G.975 proposes a . In this case 16 extra bytes are appended to 239 information-bearing bytes.Reed-Solomon (255, 239)
The bit rate increase is about , the code can correct up to and the coding gain can be7% [(255-239)/239 = 0.066] 8 byte errors [255-239/2 =8]
demonstrated to be about .6dB
The same Reed-Solomon coding (RS (255,239)) is recommended in ITU-T G.709. The coding overhead is again about 7% for a 6dB coding
gain. Both G.975 and G.709 improve the efficiency of the Reed-Solomon by interleaving data from different codewords. The interleaving
technique carries an advantage for burst errors, because the errors can be shared across many different codewords. In the interleaving approach
lies the main difference between G.709 and G.975: G.709 interleave approach is fully standardized,while G.975 is not.
The actual G.975 data overhead includes also one bit for framing overhead, therefore the bit rate exp ansion is . In G.709[(255-238)/238 = 0.071]
the frame overhead is higher than in G.975, hence an even higher bit rate expansion. One byte error occurs when 1 bit in a byte is wrong or
. Example: RS (255,239) can correct 8 byte errors. In the worst case, 8 bit errors may occur, each in awhen all the bits in a byte are wrong
separate byte so that the decoder corrects 8 bit errors. In the best case, 8 complete byte errors occur so that the decoder corrects 8 x 8 bit errors.
There are other, more powerful and complex RS variants (like for example concatenating two RS codes) capable of Coding Gain 2 or 3 dB higher
than the ITU-T FEC codes, but at the expense of an increased bit rate (sometimes as much as 25%).
FOR OTN FRAME: Calculation of RS( n,k) is as follows:-
*OPU1 payload rate= 2.488 Gbps (OC48/STM16)
*Add OPU1 and ODU1 16 bytes overhead:
3808/16 = 238, (3808+16)/16 = 239
ODU1 rate: 2.488 x 239/238 ~ 2.499Gbps
*Add FEC
OTU1 rate: ODU1 x 255/239 = 2.488 x 239/238 x 255/239
=2.488 x 255/238 ~2.667Gbps
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2. NOTE:4080/16=(255)
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