1. Interleaver-Division Multiple Access on the OR Channel
UCLA Electrical Engineering Department-Communication Systems Laboratory
Interleaver-Division Multiple Access on the OR Channel
Miguel Griot, Andres Vila Casado, Wen-Yen Weng, Herwin Chan, Juthika Basak, Eli Yablanovitch, Ingrid Verbauwhede, Bahram Jalali, Rick Wesel

2. The OR Multiple Access Channel (OR-MAC)
User 1
User 2
Receiver
User N
If all users transmit zeros, receiver sees a zero.
UCLA Electrical Engineering
Communication Systems Laboratory

3. The OR Multiple Access Channel (OR-MAC)
User 1 1
User 2 1
Receiver
User N
If any user transmits a one, receiver sees a one.
UCLA Electrical Engineering
Communication Systems Laboratory

4. OR-MAC Capacity Region1
Can achieve with joint decoding using random codes.
Successive decoding is also optimal if rate-splitting is used at the encoders with jointly optimized ones densities [Grant 01].
Rate of User 2
Rate of User 1
All n-tuples with sum-rate ≤1 form the capacity region.
UCLA Electrical Engineering
Communication Systems Laboratory

5. Interleaver Division Multiple Access (IDMA)
User 1
Encoder
Interleaver 1
User 2
Same Encoder
Interleaver 2
User N
Still Same Encoder
Interleaver N
Interleaver-Division Multiple Access [Ping 02] allows a single encoder/decoder pair to work for all users.
Introduced for CDMA channels, but easily generalizes to most memoryless MAC channels.
UCLA Electrical Engineering
Communication Systems Laboratory

6. Communication Systems Laboratory
Ways to use IDMA...
IDMA plus an optimal code (or codes if we have various rates) can achieve optimal sum-rate with joint decoding.
IDMA plus optimal codes and jointly optimized ones densities can achieve the optimal sum-rate with successive decoding.
IDMA plus a short block length code and single-user decoding treating all other users as noise is pretty silly…
No, it’s very practical for gigabit decoding rates.
UCLA Electrical Engineering
Communication Systems Laboratory

7. Single-User Decoding produces a Z-Channel1
N users, all transmitting with the same ones density p:
P(X=1)=p
P(X=0)=1-p
Focus on a desired user
If desired user transmits a 1, a 1 will be received.
A 0 will be received only if all users transmit a 0
UCLA Electrical Engineering
Communication Systems Laboratory

8. Theoretical Sum-Rate Comparison
To maximize H(Y)
Output should
Have 50% ones
Optimal ones densities:
Users
Joint Decoding
Others as noise 2
0.293
0.286 6
0.109
0.108 12
0.056
UCLA Electrical Engineering
Communication Systems Laboratory

9. What can I achieve with a latency of 35 bits?
User 1
Trellis Encoder
Interleaver 1
User 2
Trellis Encoder
Interleaver 2
Viterbi Decoder
User N
Trellis Encoder
Interleaver N
The required trellis code needs to be nonlinear at the binary level to achieve a very low ones density.
A new definition of distance is required.
A design approach is needed.
UCLA Electrical Engineering
Communication Systems Laboratory

10. Trellis Code Parameters
State at time (t+1):
Input 0
State at time t:
Input 1
Density of ones p.
Rate-1/n (1 input bit, n output bits).
S=2v states (represented by v bits).
2S branches.
UCLA Electrical Engineering
Communication Systems Laboratory

11. Controlling the ones density
Input 0
Input 1 1
There are S/2 of these sub-graphs.
In this subgraph of four branches, assign a Hamming weight of w+1 to i branches, and a Hamming weight of w to (4-i) branches.
UCLA Electrical Engineering
Communication Systems Laboratory

12. Example Hamming Weight Assignments
6-user Rate-1/20 Trellis Code
n=20, desired p=0.125
Two branches with weight 2
Two branches with weight 3
100-user rate-1/400 Trellis Code
n=400, desired p=0.0069
One branch with weight 2
Three branches with weight 3
UCLA Electrical Engineering
Communication Systems Laboratory

13. Communication Systems Laboratory
Directional Distance
Define the directional Hamming distance as the number of ones that have to be added to a codeword so that all ones of the other codeword are present in the received word.
For two codewords with different Hamming weights, if the received word contains all ones from both codewords, the one with larger Hamming weight will be more likely than the codeword with smaller Hamming weight.
UCLA Electrical Engineering
Communication Systems Laboratory

14. Communication Systems Laboratory
Trellis Code Design
A trellis branch belongs to many codewords, so we don’t know which direction is the important one.
Code design branch metric chooses the smaller of the two directional distances:
UCLA Electrical Engineering
Communication Systems Laboratory

15. Communication Systems Laboratory
Ungerboeck’s Rule
split
merge
Maximize distance between all splits and merges.
All output values have Hamming distance of w or w+1.
There are at least v+1 branches in an error event.
UCLA Electrical Engineering
Communication Systems Laboratory

16. Extending Ungerboeck’s rule
One can extend Ungerboeck’s rule into the trellis. 1
Maximize split
UCLA Electrical Engineering
Communication Systems Laboratory

17. Extending Ungerboeck’s rule
One can extend Ungerboeck’s rule into the trellis. 1 1 1
Maximize
UCLA Electrical Engineering
Communication Systems Laboratory

18. Extending Ungerboeck’s rule
One can extend Ungerboeck’s rule into the trellis.
Note that by maximizing the distance between the 8 branches, coming from a split 2 trellis section before, we are maximizing all groups of 4 branches coming from a split in the previous trellis section, and all splits. 1 1
Maximize 1
UCLA Electrical Engineering
Communication Systems Laboratory

19. Designing for a very low desired ones density
For a low enough desired ones density, all the branches can be chosen to have maximum distance. The design becomes straight-forward.
It is possible to choose all branches so that there is at most 1 branch that has a 1 in a given position.
Straight-forward design:
Assign Hamming weights to branches
For each branch, add ones in positions that aren’t used in previous branches
Example: 100-user OR-MAC,
UCLA Electrical Engineering
Communication Systems Laboratory

20. Trellis Code Simulations, Bounds, FPGA Results
6-user BER 10-5
UCLA Electrical Engineering
Communication Systems Laboratory

21. Results: observations
An error floor can observed for the FPGA rate-1/20 NL-TCM.
This is mainly due to the fact that, while theoretically a 1-to-0 transition means an infinite distance, for implementation constraints those transitions are given a value of 20.
Trace-back depth of 35.
Additional coding required to lower BER to below 10-9.
UCLA Electrical Engineering
Communication Systems Laboratory

22. C-Simulation Performance Results: 6-user OR-MAC
6-user BER 10-5
UCLA Electrical Engineering
Communication Systems Laboratory

23. Could do Joint Decoding… Results for Rate-1/20 p=0.125 code.
Number of Users
Sum Rate
Trellis Code BER 6
0.3
No Errors 8
0.4
2.7e-7 10
0.5
2.0e-5 12
0.6
4.0e-4
UCLA Electrical Engineering
Communication Systems Laboratory

24. C-Simulation Performance Results: NL-TCM only, 100-user OR-MAC
Rate
Sum-rate p
BER
1/360
0.2778
1/400
0.25
UCLA Electrical Engineering
Communication Systems Laboratory

25. Reed-Solomon + NL-TCM : Results
A concatenation of the rate-1/20 NL-TCM code with (255 bytes,247 bytes) Reed-Solomon code has been tested for the 6-user OR-MAC scenario.
This RS-code corrects up to 8 erred bits.
The resulting rate for each user is (247/255).(1/20)
The results were obtained using a C program to apply the RS-code to the FPGA NL-TCM output.
Rate
Sum-rate p
BER
0.0484
0.29
0.125
0.4652
UCLA Electrical Engineering
Communication Systems Laboratory

26. Optical MAC Coding Architecture
2 Gbps
Reed Solomon
(255, 237)
Trellis Code
1/20
int
OR channel
93 Mbps
5 other tx
Correct extra errors
Separate different transmitters
Asychronous
Access code
UCLA Electrical Engineering
Communication Systems Laboratory

27. Communication Systems Laboratory
Demonstration
FPGA with both Transmitter
and Receiver (slide 29)
FPGA
Transmitters
UCLA Electrical Engineering
Communication Systems Laboratory

28. Communication Systems Laboratory
Conclusions
We presented an Interleaver Division Multiple Access system for the OR-MAC.
A relatively low ones density is essential for the OR-MAC channel.
We presented a single-user trellis coded solution.
An arbitrary number of users is supported, maintaining relatively the same efficiency (around 30%).
Joint decoding for six-users increases efficiency to 50-60%.
Although these codes are not capacity achieving,a good part of the capacity is achieved, with a suitable BER for optical needs, and a complexity feasible for optical speeds with today’s technology. An FPGA implementation has been built to prove this fact.
Turbo coded single-user implementation (week supports) 60%.
UCLA Electrical Engineering
Communication Systems Laboratory

29. Future work: Capacity achieving codes
Although they may not be feasible for optical speeds, with today’s technology, Turbo codes and LDPC codes will be feasible in the near future
Part of my immediate future’s work will be the design Turbo-Like codes, with an arbitrary ones density.
Most common Turbo-like codes are
Parallel concatenation of convolutional codes
Serially concatenated convolutional codes.
The convolutional codes will be replaced by properly designed NL-TCMs.
UCLA Electrical Engineering
Communication Systems Laboratory

30. Non-linear Turbo Like codes
Serial concatenation CC + NL-TCM:
Parallel concatenated NL-TCMs: CC
Interleaver
NL-TCM
NL-TCM
Interleaver
NL-TCM
UCLA Electrical Engineering
Communication Systems Laboratory

31. Communication Systems Laboratory
Code details
For all implementations, states were used.
6-user OR-MAC
n=20 : Sum-rate = 0.30
2 branches with Hw=2, 2 with Hw=3 (p=1/8).
h=3, g=2 :
n = 18 : Sum-rate = 1/3
3 branches with Hw=2, 1 with Hw=3 (p=1/8).
h=2,g=2 :
n = 17 : Sum-rate = 0.353
all with Hw=2 (p=2/17=0.118).
100-user OR-MAC,
n = 400 : w=2, i=3 (p = )
n = 360 : w=2, i=2 (p = )
for both cases
UCLA Electrical Engineering
Communication Systems Laboratory