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

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

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.

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.

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

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

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

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:

Bhattacharyya Bound Upper bound for :

But…

Hence…

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

The 2-User Broadcast Z-Channel 1 1 ? 1 1

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

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

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

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

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

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

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.

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

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

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 .

BER bounding analysis

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.