1. Information-Theoretic Study of Optical Multiple Access
Jun Shi and Richard D. Wesel
UCLA
01/14/05

2. Princeton’s Scheme Princeton uses a (4,101) 2D prime code. wavelength
Time
User 1
User 2
User 3

3. The (4,101) code Asynchronous, coordinated.
Each bit takes 4 time/wavelength slots.
1’s density per user (chip level) =4/808≈0.005
1’s density per user (bit level) =1/2.
Upper bound on BER:

4. The Z-channel All other users are treated as noise.
Each user sees a Z-channel
Throughput (Sum-rate) : 1 1 Pe

5. Double-Interference
Due to asynchronism, in the worst case, a one from an interferer affects two bits of the desired users.
Asynchronous channel is very complicated. The exactly capacity is still under investigation, but here is an approximation: synchronous double-interference
User 1
User 2
User 1 p
receiver 2p 2p 2p
User 2
User 3
User 4

6. The Ideal case
Under perfect synchronism and with joint decoding (other users are not noise but information), the throughput is a constant equal to 1bit/transmission.
Let input 1’s density be 0.005, the chip density of Princeton’s scheme, we can plot throughput vs. # of users.

8. Random Codes
In Princeton’s approach, prime codes are assigned a priori, which requires coordination.
We can assign the patterns randomly.

11. Prime code constraint
Princeton’s scheme is slightly better at small number of users while random code shows advantages with large number of users.
This is due to the requirement that a prime codeword has at most one slot per wavelength, increasing the probability of collision.

12. Error Correcting Codes
Prime codes do not correct errors. To achieve capacity, error-correcting codes are required.
Encoding and decoding can be done in FPGA boards. This is an item for future work in Phase II.
Decoder
LDPC
Encoder
Data 1
User 1
Decoder
Data 2
LDPC
Encoder
User 2

13. Successive Decoding
We can decode the first user by treating others as noise, then the first user’s ones become erasures for the other users. Proceed in this way until finish decoding all the users.
This is called successive decoding. For binary OR channel, this process does not lose capacity as compared to joint decoding.

14. A 3-user example ? 1 R1 1 User 1 User 2 User 3 1 1 R3 R2 User 1 1 11
User 1 1 1
User 2
User 3
Receiver

15. A 3-user example 1 ? e R1 1 User 1 User 2 User 3 1 1 R3 R2 User 1 1 11 ? e
User 1 1 1
User 2 e
User 3
Receiver

16. A 3-user example 1 ? e R1 1 User 1 User 2 User 3 1 1 R3 R2 User 1 1 11 ? e
User 1 1 1
User 2 e
User 3
Receiver

17. A 3-user example 1 R1 1 User 1 User 2 User 3 1 1 R3 R2 User 1 User 21
User 1
User 2
User 3
Receiver

18. Density Transformer
To achieve capacity and apply successive decoding, a key thing is to get the right one’s density. This is an item for future work under Phase II.
LDPC
Encoder
Density
Transformer
Source 1 p1
LDPC
Encoder
Density
Transformer p2
Source 2 p3
LDPC
Encoder
Density
Transformer
Source 3

19. Synchronization
In successive decoding, the receiver only needs to be synchronized to one user at a time.

20. Multiple looks
To further increase the throughput, we should not treat other users as interference but as useful information.
We want the receiver to align with each of the users, not just one user.
This can be done in a star network where the receiver has all the information.

21. A 2-user example x11, x12, x13, … 2 looks User 1’s clock
y11, y12, y13, …
Receiver
x21, x22, x23, …
y21, y22, y23, …
User 2’s clock
Receiver’s clocks

22. Joint Decoding LDPC Encoder Data 1 User 1 Joint Decoder Data 2 LDPC