# ADSL throughput loss from Reed-Solomon encoding

I'm reading about ADSL starting here and I am confused by how the Reed-Solomon encoding for ECC is limiting the available transfer rate, as much as it does (nearly half). This pdf on the same subject contains the following;

A maximum of 255 sub-carriers can be used to modulate data in the downstream direction. Sub-carrier 256, the downstream Nyquist frequency, and sub-carrier 64, the downstream pilot frequency, are not available for user data, thus limiting the total number of available downstream sub-carriers to 254. Each of these 254 sub-carriers can support the modulation of 0 to 15 bits. Since the ADSL DMT data frame rate is 4000 frames per second, the maximum theoretical downstream data rate of an ADSL system is 15.24Mbps. Due to limitations in system architecture, specifically the maximum allowable Reed-Solomon codeword size (255 bytes), the maximum achievable downstream data rate is 8.16Mbps.

How is this nearly halving the throughput? Is all that extra bandwidth overhead of the RS encoding? 15240000 bps (15.24Mbps) - 8160000 bps (8.12Mbps) = 7080000 bps (7.08Mbps). Where has that 7Mbps of throughput gone?

EDIT: I tried to read the wiki page on Reed-Soloman but it's all crazy maths and algerbra, which I don't understand. I can understand that data is split into 255 byte codewords, because that maybe the max codeword size whilst still maintaining accuracy during transmission; But I don't understand why that means less data is sent?

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Yeah, it says that theoretical bandwidth is 15 but practically because of word size 255 bytes its really only 8.12Mbps. I dont understand your substraction, this value 8 is computed from the actual size of word, so nobody ever said, that this is somewhat halved or something. – Andrew Smith Jun 30 '12 at 17:31
hmm, I am clearly missing something here in my understanding. Where does the RS codewords fit in the transmission stack for DSL? Data is split into 53 byte ATM frames, are these then encoded on the wire with RS codwords? – jwbensley Jun 30 '12 at 18:56
This diagram shows is how I imagine data is placed onto the wire for DSL, is that remotely correct? (books.google.co.uk/…) – jwbensley Jun 30 '12 at 19:00