Hi all, I'd just like to share a status of how my LDPC implementation project is going. When the summer started, Manu and I made a list of the LDPC-related algorithms for encoding, decoding, and parity check matrix construction that we had found in our literature review. We then divided them up such that there would be no overlap in our efforts. The algorithms that I put on my list were: 1. Regular and irregular parity check matrix construction functions 2. Generating a code that is optimized for PSK 3. Constructing quasi-cyclic codes which are especially efficient for encoding 4. Performing encoding as described by Richardson & Urbanke in Appendix A of 'Modern Coding Theory' (manipulating the parity-check matrix into an approximate upper triangulation form which reduces complexity during the real-time encoding steps) 5. Bit-flip decoding, a hard decision algorithm 6. Min-sum algorithm for decoding So far, I've written prototype functions for these methods in python, using numpy: #1/regular, #4, and #5. Right now, I'm at the stage where I'm trying to link them all together and confirm that the processes perform as expected before moving on to converting them to C++. The challenge that I'm facing is that the parity check matrices being created by my function are not full rank, and so they don't work with the encoding algorithm. I have tried a method to manipulate them into being full rank before encoding but it was not successful. This is my top priority right now - to be able to have the parity-check matrices that I am creating work with the encoding algorithm that I've written up. Then I'd like to finish testing the chain of processes before moving on to creating classes that inherit from those in the FEC API. My GitHub repo is here: https://github.com/tracierenea/GNU-Radio-GSoC2013 Any questions or comments, just let me know. Thanks, Tracie Perez

on 2013-07-22 01:38

on 2013-08-29 22:49

Hello all once again, I'd like to thank everyone who has given me helpful feedback since my last status. I really appreciate the thoughtful comments. I solved the issue regarding getting my matrices to work with the encoder algorithm. For the parity check matrices, I'm constructing regular LDPC parity check matrices per a simple algorithm described in Gallager's original 1963 thesis on this topic. However, per design, the matrices are never full rank, so I then process them to be so. Then, the matrices are ran through a pre-processing algorithm to set them up for efficient, low complexity encoding per a process described by Richardon and Urbanke. I call the resulting matrix an "encoding-ready" parity check matrix, and it takes days to generate each one (bigger = more days). I would like to build up to matrices for n=5000 because I believe this is the ballpark for codeword lengths used in industry. As my scripts create these matrices, I am pushing them to a library of sorts on my github repo. Of course the idea is that the time is invested in creating them once, and then they can be used as needed after that. There are regular parity check matrices already available on the web by Dr. MacKay, but they are not full rank, so they won't work with my encoder. By the time I reduce them to be full rank, the information rate that they offer is unacceptably low. So, this is why I have gone the route of generating my own matrices that are compatible with Richardson and Urbanke's encoding algorithm. Next, I ran into an issue with my decoder failing for large size codewords. That tied me up for a few weeks. After much troubleshooting, I discovered that the issue stemmed from rounding errors from numpy doing mod 2 operations. I won't go into to much detail since I will be porting this algorithm out of python to C++ anyway. After manually correcting this rounding issue, my hard decision bit-flip decoding algorithm performed really well in the prototype python tests that I did. To simulate errors, I manually introduced bit flips and checked that the decoder could detect and correct them. I have tested codewords up to 2400 bits in length, and the algorithm can correct a few errors in 1 or 2 iterations, which is actually much faster than I anticipated. I will be testing larger codewords as I construct larger and larger parity check matrices. Now I am at the point where I am converting my python code into C++. After thinking about how best to do this, we (Jens, Nick and I) agreed that it made sense to fork Nick McCarthy's fecapi repo. So, I have done this, and I will create classes that inherit from and use the FEC API classes that he has already written. This will hopefully allow me to eventually use the BER curve generator to do final tests of my implementation. Because there are so many matrix operations, I am using the GNU Scientific Library (GSL) in my C++ code. I thought that this would be a reasonable approach since GSL is a required dependency for gr-wavelet, and, if I am not mistaken, a user would get the GSL as part of the standard install via pybombs. I do think that there will be many opportunities to increase efficiency by using VOLK, but I don't think that will fall within the scope of this summer's project. I will be flagging potential VOLK code replacements with something like "FIXME - consider replacing this with VOLK library functions." As always, I welcome any feedback that you have! Thanks, Tracie Perez

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