Re: [8023-10GEPON] [FEC] upstream lock status
Dear Glen,
Thank You for Your explanation. I was only curious as to what blocks were assumed to follow in the positions S1 ... Sx :-) Now it is more than clear.
Regarding the maximum Hamming distance sequences -> I examined in total a several tens of thousands of sequences which fit the following conditions:
- run length <= 3 for 1/0 symbols
- DC balance within 1 symbol max (that is in 66 bits we may have 33/33, 32/34 or 34/32 for 1/0 symbols, respectively).
- minimum Hamming distance of 30
Here is the updated list of 66 bits wide sequences:
000111011000110001001001110101000110110110110001101100101110011101; 3 34/32
001001011100110110111011010100111001001101110001101110001100101000; 3 34/32
010010001110001001001110100101010110001100101110100101100101101011; 3 32/34
010010001110010011001011011010110001110011000101001100100111011100; 3 32/34
011011010001000111001011010001010010110101110001000110111010001011; 3 32/34
101011010110010110001011100101011100010100100101101110110010011000; 3 33/33
101011101001010011001101101110001110101000100110100011010001010101; 3 33/33
101100110010110100101100101001110101110010001110010110010001010001; 3 32/34
101101100101011101001010111000100010100110110011101101001001001010; 3 33/33
110011011001000110100101011010011000110110101100110001110010001010; 3 32/34
110100011001010110001011010010111010100101100100100010111010111001; 3 33/33
111001001001101011010100101010101010100010001001110001011100101101; 3 32/34
All the sequences which were identified have a run length of 3 - I suspect that there may no exist a sequence with run length of 2 and Hamming distance >= 30 though I may be mistaken. I will keep the list updated ...
Regarding the searching methodology - as indicated earlier by Frank, it is virtually impossible to explore all possible combinations of 0/1 for 66 bit wide sequence. That would mean running 2^66 tests, which is 73.786.976.294.838.206.464 and that is slighly outside of the reach of my PCs. What I am doing instead, is eliminating all the sequences outside of the assumed DC balance range (there must be 32,33 or 34 1s in the sequence) and then placing the 1s in the 66 bit wide container at random, collecting only the unique solutions, that then testing the Hamming distance only for the unique sequences to lower the calculation burden. I am not aware of any other method to do this type of examination since the possible sollution space is too large to check all the possible solutions.
I hope today to have some time also to try to examine the Golden block problem in more detail.
Best wishes
Marek Hajduczenia (141238)
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-----Original Message-----
From: Glen Kramer [mailto:glen.kramer@TEKNOVUS.COM]
Sent: quinta-feira, 21 de Dezembro de 2006 1:19
To: STDS-802-3-10GEPON@listserv.ieee.org
Subject: Re: [8023-10GEPON] [FEC] upstream lock status
Marek,
> Does that mean that after the sequence G8 we expect a scrambled block with
> G1 (accidental match) ??
>
0x5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 G1 G2 G3 G4 G5 G6 G7 G8 S1 S2 S3 S4
x x x x = = = =
<-- G1 G2 G3 G4 G5 G6 G7 G8 -->
What I meant was that, following the G8 is a scrambled block (S1 S2 S3...)
which can take on any values. It may happen that S1 = G5, S2 = G6, etc. so,
the farther the comparator moves past the Golden block, the shorter the
Hamming distance it will see.
We normally should never move past the Golden block. Doing so means that the
burst is lost already (i.e., Golden Block was not found due to too many
errors.)
I think we don't need to look at codes giving 28 or 29 bit differences, if
we have 30-bit codes readily available. In my opinion, Hamming distance of
30 is plenty, though I am curious to know if blocks giving Hamming distance
>30 exist.
Glen