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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

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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
Progress during this period
  • Conference Presentations
  • Journal Paper preparation
  • Dissertation Preparation
  • Expanding into related problems
conference presentations
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 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
Dissertation Preparation
  • During this reporting period Wen-Yen Weng completed his dissertation.
expanding into related areas
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 improvement in bhattacharya ber bound

Factor of ½ improvement in Bhattacharya BER bound

Miguel Griot

Wen-Yen Weng

Richard Wesel

bound so far
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
Bhattacharyya Bound
  • Upper bound for :
the z broadcast channel

UCLA Electrical Engineering Department-Communication Systems Laboratory

The Z-Broadcast Channel

Andres I. Vila Casado

Miguel Griot

Richard Wesel

degraded broadcast z channel

1

1

1

1

0

0

0

0

Degraded Broadcast Z-Channel
  • The broadcast Z-channel is a stochastically degraded broadcast channel

?

  • The capacity region is given by
capacity region

1

1

1

1

0

0

0

0

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.

OR

capacity region16
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 region17
Capacity Region
  • For =0.1 and  =0.6 the capacity region was numerically computed:
coding solution
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

Parallel concatenated TCM for high-order modulations

Miguel Griot

Andres Vila Casado

Richard Wesel

applications for non linear codes
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
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

Mapper

CC

Interleaver

CC

Mapper

parallel concatenated tcm

TCM

Interleaver

TCM

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.
uniform interleaver analysis for awgn
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 .
comments
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.