May

  • Implementation of linear form decoding algorithms. Algorithm B seems quite promising but requires a lot of operations.
  • The linear form paper is accepted for ISIT and is being updated.
  • Starting some research with Satish on Polar codes. The idea is to use ideas from coded modulation for the rate-distorion compression of sources. This could be very interesting for e.g. image compression.
  • Implemented Blahut-Arimoto like algorithm for the computation of the rate-distortion function of arbitrary sources.
  • Analyzing the linear form decoding algorithm. The questions is if one can say something from a theoretical point of view.
  • It could be that the linear form decoding algorithm leads to a capacity that is the same as the BICM capacity. This should be proved.
  • Implemented the linear form decoding algorithms to verify Bertrand's simulations. So far I had only implemented the full BP non-binary algorithms.
  • Full ISIT paper finished and submitted ISIT 2009

June

  • Working on simulations for linear form decoding
  • Founds several alternatives for algorithm B. The downside is that a lot of iterations are required to make the algorithm converge.
  • Investigated how density evolution can be used to design codes for linear form decoding..
  • Started discussing polar codes with Satish. Maybe polarization is possible for different input alphabets. The idea is to use superposition of real random variables to create a near-Gaussian distribution. Polarization might happen in this case also which would provide an interesting coding scheme for the AWGN channel.

July

  • Continuing research on linear form decoding.
  • Helping Bertrand in preparing the presentation for ISIT in Seoul.
  • Starting thinking about a full paper for linear form decoding and seeing what needs to be done for that.
  • Polar codes for Gaussian sources have the problem that after a polar transform the independent assumption does not hold. One would probably not get full mutual information.
  • Idea to setup up a collaboration with UT in Enschede in the area of probe storage. This is a whole new area where we could contribute. Collected and read some initial papers on this topic.

August

  • Theoretical foundation of linear form decoding is still missing. Working on this.
  • Full paper for linear form decoding has to be written. Reimplementing simulations of Bertrand to have a second check.
  • Looking into Reed-Solomon codes as an alternative for Raptor codes.
  • Polar codes for lossless source coding are very interesting. One can actually get a good finite length performance. Initial write-up Polar codes lossless source coding
  • Working on polar codes for rate-distortion coding of non-binary sources. Inital write up: Polar codes rate-distortion

September

  • Algorithm II for linear form decoding can be improved by continuing instead of resetting after a pass.
  • Some work summarized in slides for ALGO workshop: Slides algo workshop 30-01-2009

October

  • Continuing to write linear form full paper. Somewhat difficult since some theoretical foundation is missing.
  • Fred's algorithm for decoding RS codes on the erasure channel is fast. However, field multiplication is still an issue. Looking into this.

November

  • Looking into Fourier methods for decoding Reed-Solomon erasure codes.
  • Extending Polar codes to non-binary setting.
  • Found a nice algorithm for source coding with polar codes. Finite length performance can easily be computed.

December