* Still working on irregular product codes with Masoud and Omid. On one hand we're looking at asymptotic analysis of these codes (on erasure channels, we can give families with MDS component codes that achieve rate arbitrarily close to capacity, but at the cost of the field size growing like \sqrt(n). On the other hand we're still running simulations and we've got the best 8×8 codes, and by trial and error we have 50×50 codes that do better than all traditional product codes of similar rate.

* Starting to look at higher dimensions of product codes.

* Reviving the secure network coding project with Christina, Vinod and Yasin. We want to write up our results in a paper that we will submit to Netcod 2012.


* Working a bit on LT codes but mostly on NetCod paper with Christina, Vinod and Yasin. Our main contributions: formulating a security problem on networks; deriving necessary and sufficient conditions on the butterfly network and on canonical combination networks and giving an optimal algorithm; deriving lower bounds and giving algorithms on more general combination networks.

* Final version: Netcod paper


* Looking with Omid and Masoud at a generalization of LDPC codes, where parity checks are generalized to check membership in short codes. This has already been done, but the novel idea is to allow the short codes to be of variable rates. We find the optimal rate distribution that these short codes should come from and show that the codes constructed like this are capacity achieving, however the decoding complexity is no better than that of Forney's concatenated codes. We are also implementing an LP to derive optimal distributions.


* Working with Omid and Masoud on another application of the “rate distribution” idea: generalized LT codes where each output symbol can now correspond to a set of parity symbols obtained in an MDS fashion from a subset of the input symbols. We start by studying the simpler case of a constant number r of parity symbols. We consider the simpler case where all parity symbols are packed together, and the more complicated case where they are sent independently over the channel. We derive optimal degree distributions in both cases for r=2 and try to generalize it.

* Writing up our results on irregular product codes into a paper that we submitted to ITW 2012.


* Still working on generalized LT with Omid and Masoud. For the case where all parity symbols are packed, we derive optimal degree distribution for every fixed r. For the case where they are sent independently, we derive a differential equation, but it's not trivial to solve. Report.


* School of Information theory Cornell 19-22 * NetCod 29-30

July, August


* ITW 3-7


* Monte Verita 28-2