### thomastak's Home Project

```Hello,

I would like to introduce my idea from the University. It is about speeding up the internet. What it is all about is that if we combine in a good way my suqqestion that was developped in matlab and I gained 25% of speed with it and also gained deans price. Lets talk about it in more details.

Telecommunications system is composed of source of data, encoder of the source of data, encoder of the channel, modulator, multiplexer, noisy channel, demultiplexer, demodulator, decoder of the channel, decoder of the source and receiver.

Bits that are comming into the Reed Solomon (RS) encoder are first transformed into integer number (Representation of Galois field) that is an input for RS encoder with integer input output (I/O), that is being transformed back to bits. The size of Galois field and so number of bits, that are part of symbol of the same field is being computed from the size of frame for modulator, that was determined within iniciliasation (size of frame). Since it is possible, that the number of bits after the information was encoded was lower than the size of the frame for modulator, it is necessary to add 6 bits to every code word and from this vector then we chose the same number of bits like size of frame for modulator.

The same analogy works for RS decoder in which we choose from the frame from demodulator at the beginning exact number of bits that we can decode.

Analysis and Simulation:

The simulation was based on deciding the number of sub-channels of DMT modulator.  This number was changed in tha discrete interval 128, 256, 512 and 1024 (always power of 2), but the channel width stayed unchanged. So in case of doubleing the number the number of subchannels the channel width of one subchannel was decreased to half. Subsequently the inicialisation was invoked, in which we determined the characteristics of the channel in certain subchannels and based on initialisation it is possible to realise computation of bits assigned to certain subchannels of the frame. After the computation of bits I tried to send 200 frames and was checking the BER while transmission occured. In case the BER was high, I made the correction of bits, in which the number of bits was lowered to the subchannels with high number of errors. This process was repeated until the maximum number of bits that hapenned in one frame was equal to 1 and so we could use RS code for correction of one error. Depending on fould number of bits of the frame where maximally one error occured I computed the parameters for RS code. First of all I found out what Galoisse field is necessary to apply and then I computed N and K for the number of errors (here equal to 1), that the RS code was able to correct. This procedure was applied on 4 lenghts of the physical line: 300 meters (m), 400m, 500m, 600m (these were also required) for all the subchannels mentioned above.

Next step was to keep settings assigning the number of bits to subchannels according to one of the transmission distance, (that means just one error occured in the frame) and I extended the physical line of length 100m, what served me to get from 300m to 400m thanks to the redundancy of RS codes. This way I got two values of transmission speed for transmission distances 400, 500 and 600m. First value was tied to the best accomodation  od the modulation to required distance, when in one frame only one error occured and the second value was tied to condition, when I got to required distance by increasing the transmission distance by 100m thanks to higher redundancy of RS code, that can correct more errors.

In case of any questions regarding this let me please know.

Ing. Tomas Pajda, CCNA.```

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