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

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.

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.

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

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

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.

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.

Working on finalizing the linear form paper. Submitted to tcom: Linear form paper

Working on the paper for ISIT about lossless source coding with polar codes: ISIT 2010 submission