1. Progress Report for the UCLA OCDMA Project
UCLA Graduate School of Engineering - Electrical Engineering Program
Communication Systems Laboratory
Progress Report for the UCLA OCDMA Project
Miguel Griot
Andres
Vila-Casado
Wen-Yen Weng
Herwin Chan
Richard Wesel

2. Progress during this period
Conference Presentations
Journal Paper preparation
Dissertation Preparation
Expanding into related problems

3. Conference Presentations
H. Chan, M. Griot, A. Vila Casado, R. Wesel, I. Verbauwhede "High Speed Channel Coding Architectures for the Uncoordinated OR Channel". IEEE 17th INTERNATIONAL CONFERENCE ON Application-specific Systems, Architectures and Processors (ASAP), Steamboat Springs, Colorado, September 2006.
M.Griot, A. I. Vila Casado and R. D. Wesel "Non-linear Turbo Codes for Interleaver-Division Multiple Access on the OR Channel". Globecom 2006, 27 Nov. - 1 Dec., San Francisco, USA.

4. Journal Paper Preparation
Journal paper on Trellis Codes nearly complete (attached).
Miguel is working towards new results for higher-order modulations before finalizing manuscript for journal paper on Turbo Codes.

5. Dissertation Preparation
During this reporting period Wen-Yen Weng completed his dissertation.

6. Expanding into related areas
An improvement in the Bhattacharya Bound
A technique for handling the broadcast Z channel
A new technique for turbo codes using higher order modulations

7. Factor of ½ improvement in Bhattacharya BER bound
Miguel Griot
Wen-Yen Weng
Richard Wesel

8. Bound so far (n,k) linear code over a symmetric channel (BSC, AWGN).
Denote u the input words, and x = x(u) the codeword.
The all-zero codeword can be assumed to be transmitted. Denote it
Union bound:

9. Bhattacharyya Bound
Upper bound for :

10. But…

11. Hence…

12. The Z-Broadcast Channel
UCLA Electrical Engineering Department-Communication Systems Laboratory
The Z-Broadcast Channel
Andres I. Vila Casado
Miguel Griot
Richard Wesel

13. The 2-User Broadcast Z-Channel1 1 ? 1 1

14. Degraded Broadcast Z-Channel
The broadcast Z-channel is a stochastically degraded broadcast channel 1 1 1 1 ?
The capacity region is given by

15. Capacity Region
Theoretically the capacity region is calculated by allowing any possible combination (joint distribution) of the messages (X1 and X2).
We conjecture that if chose to combine the messages with an OR gate we can still achieve every point of the capacity region. 1 1 1 1 OR

16. Capacity Region
A numerical computation of the capacity regions show that our conjecture is correct
The equations then become:
Where p1 and p2 are the density of ones of X1 and X2 respectively

17. Capacity Region
For  =0.1 and  =0.6 the capacity region was numerically computed:

18. Coding solution
The capacity region can be achieved using non-linear codes with the appropriate density of ones
Our solution is to use a Z-capacity achieving nonlinear code with density of ones p2 for X2 and a Z-capacity achieving nonlinear code with density of ones p1 for X1 transmitted only when X2 is zero

19. Parallel concatenated TCM for high-order modulations
Miguel Griot
Andres Vila Casado
Richard Wesel

20. Applications for non-linear codes
The new family of non-linear codes we proposed for the Z-Channel:
their basic structure…
their design…
and the analytical BER bounds…
can be applied, with little modification, to other channels.
In general, over any asymmetric channel requiring non-linear codes.

21. High-order modulations
So far, for high-order modulations, a linear code with a bits-to-constellation point mapper has been used
However, in some constellations, the mapper must be nonlinear.
Using a linear code + a mapper could be a limitation.
Trellis coded
modulation CC
Mapper
Interleaver CC
Mapper

22. Parallel Concatenated TCM
Structure of PC-TCM:
Codeword : a set of constellation points
Rate :
Using directly a TCM there could be a gain in performance.
TCM
Interleaver

23. Uniform Interleaver Analysis for AWGN
The extension of Benedetto’s uniform interleaver analysis shown for PC-NLTC over the Z-Channel [GlobeCom’06], can be applied to any system in which non-linear codes are required (or used).
In particular, it can be applied to high-order modulations over the AWGN.
Changes:
Use squared Euclidean distance instead of directional distance for Z-Channel.
Evaluate final expression in instead of

24. BER bounding analysis

25. Comments
We have a very general bounding technique under ML decoding for parallel concatenated non-linear (block or trellis) codes.
Still more work to do on the code design.
We believe we can improve the performance of previous works, using this more general approach.