Understanding multipliers and divisors value in calculating OTN frame rates (255,239,238,237 etc) for OPUk,ODUk and OTUk

**Multiplicative factor is just a simple math :eg. for ODU1/OPU1=3824/3808={(239*16)/(238*16)}

Here value of multiplication factor will give the number of times for rise in the frame size after adding header/overhead.

Example:let consider y=(x+delta[x])/x; In terms of OTN frame here delta[x] is increment of Overhead.

As we are using Reed Soloman(255,239) i.e we are dividing 4080bytes in sixteen frames (The forward error correction for the OTU-k uses 16-byte interleaved codecs using a Reed- Solomon S(255,239) code. The RS(255,239) code operates on byte symbols.).Hence 4080/16=255.

Try to understand using OTN frames now. I have tried to make it legible.

As we know that OPU1 payload rate= 2.488 Gbps (OC48/STM16) and is  frame size is 4*3808 as below.

*After adding OPU1 and ODU1 16 bytes overhead: Frames could be fragmented into following number of chunks.

3808/16 = 238, (3808+16)/16 = 239

So, ODU1 rate: 2.488 x 239/238** ~ 2.499Gbps

*Now after adding  FEC bytes

OTU1 rate: ODU1 x 255/239 = 2.488 x 239/238 x 255/239

=2.488 x 255/238 ~2.667Gbps

Now let’s have a small discussion over different multiplier and divisor scenarios that will make it clearer to understand.

We know that an OTU frame 4 * 4080 bytes (= 255 * 16 * 4)

OPU representing the Payload (3824-16) * 4 * 4 = 3808 bytes (= 238 * 16 * 4) .

OPU1 is exactly the rate of STM-16.

Now,

ODU1 = (3824/3808) * OPU1 = ((16 * 239) / (238 16 *)) * OPU1 = (239/238) * STM-16

OTU1 = (4080/3808) * OPU1 = ((255 * 16) / (238 * 16)) * OPU1 = (255/238) * STM-16