Re: QAM constellation script

[Daniel Estévez]

On 03/05/2023 18:20, Marcus Müller wrote:

> ¹ this is the standard situation for me to start a flamewar on the 
> nature of DSSS: from a coding perspective, DSSS is just a repetition 
> code. Repetition codes are what we call "bad", so instead of 
> concatenating a r = 1/F DSSS-repetition-code after a r=4/5 Turbo code, 
> we'd be much much better off just using a r=b/R "proper" code to begin 
> with. I guess the thing is that decoding complexites of very low rate 
> code decoders are usually not fun at bad input SNRs.

Hi Marcus,

Not to start a flamewar, since I can see what you mean here, but I'm 
wondering: is DSSS the same as repetition code? A commonly used 
technique to transmit data with DSSS is to use 2^m quasi-orthogonal 
codes to transmit m bits per "symbol". These 2^m codes may be different 
codes drawn from the same pool (Gold codes, etc.), or circular shifts of 
the same code (this concept is being explored for future GNSS signals 
under the name of CSK, code shift keying). The uncoded BER performance 
is pretty similar to m-FSK, since the "symbols" are nearly orthogonal.

I might be misremembering things, but I think that for large m the BER 
performance of uncoded m-FSK is better than uncoded BPSK, simply because 
the BER curve falls off more steeply. In this sense, using different 
DSSS codes actually achieves some coding gain that justifies bandwidth 
expansion, whereas the alternative approach of using a single PN 
sequence modulated in BPSK is as you say a repetition code and doesn't 
provide any coding gain.

Surely this idea is very far from getting us a capacity-achieving code 
(any simple FEC beats uncoded m-FSK even if m is pretty large). But on 
the other hand, the typical bandwidth expansions of a DSSS system are on 
the order of 100x or more. I would be curious to know if there's an 
r=1/100 code that is good and can be implemented in practice. Probably 
there are diminishing returns when r -> 0, and decoding cost blows up. 
Hence the usual idea of concatenating a DSSS-repetition-code and an 
outer usual FEC (maybe not an r=4/5 Turbo, but r=1/6).

Best,
Daniel.

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