The essence of Reed-Solomon coding

I think Reed-solomon should be considered in future network protocols designs to combat censorship. Every byte should be demuxed into bits and transferred in independent data streams, so MITM boxes can only intercept incomplete streams, and aggregate streams back to original would be insanely difficult. Let transport layers do only one job and no distinguish whatever the content might be inside.

Currently H2 does support M:N stream muxing but popular browsers only support N:1 mode.

Some additions, as "exercise for the reader":

1. The finite field you choose has a minimum size. What is the minimum size field 2^bits for an RS(N,K) coding system? What happens when you try to construct a Reed-Solomon code with a finite field that is too small?

2. Consider a Reed-Solomon coding system which uses a lookup table for the finite field multiplication operation that fits in L1 cache. Given that the table already fits in L1 cache, how could you make the encoder/decoder faster, if you had a smaller finite field?

I've found that, just as with CRCs, there's an abundance of articles that show the theoretical explanation of RS, but aren't much help for those wanting to actually implement it. Here's a good practical explanation of implementing RS, including the GF operations: https://en.wikiversity.org/wiki/Reed%E2%80%93Solomon_codes_f...

I really wish physical and OS network stacks would be able to give you the ability to send uncorrected bit streams. That way you can tune the error rate at the application level that makes sense. For example, with video streaming, you probably don’t need much error correction on the data stream as periodic i-frames would correct any transient glitches (you’d only bother to EC the control headers for the video). Then WiFi networks maybe wouldn’t have to be as careful about time multiplexing all the coex streams and some noise due to conflicts would be fine and not require retransmission (because the application layer could handle it).

This does come with tradeoffs (eg it may take your application longer to recover from the noise than a quick retransmit at the physical layer).

From a cost perspective it’s also maybe impractical because the computer industry gets efficiency gains by solving a problem for everyone at some quality threshold by giving up optimality for applications that could do something with it. Also you would still need to correct the control layer of the network (IP + MAC) just to make it work at all so it may be a wash (ie the incremental cost of correcting the data vs control + data may be insignificant).

Still, at least having the option as a switch that could be flipped for experimentation purposes would be quite neat to allow the curious to find new techniques / layers of abstractions vs what’s orthodoxy today.

Using Reed-Solomon coding to recover from erasures (at known positions) is relatively straightforward. It can be understood with a basic knowledge of linear algebra and finite field arithmetic.

Using RS for error correction (at initially unknown positions) is quite difficult. I wrote a step-by-step guide on it including demo code, and it doesn't even cover the most efficient decoding algorithm (I used PGZ instead of Berlekamp-Massey): https://www.nayuki.io/page/reed-solomon-error-correcting-cod...