New Forward Error Correction Codes

Thanks to the work of the last GSoC and the researchers at Virginia Tech, we now have an implementation of LDPC and turbo product code (TPC). These classes of codes have a number of possibilities for their setup and runtime behavior. LDPC in particular has a pretty good selection of techniques to compute them, and we're working on adding at least a second way of doing things -- again, coming from last year's GSoC projects.

GNU Radio contains a BER curve generator called ber_curve_gen.grc and installed as a gr-fec example. We can easily add new FEC codes to this test, the output of which is plotted below, truncated after some time so the curves haven't all been smoothed out, yet.

First, we're plotting BER vs Es/N0 and not Eb/N0, so this is showing performances at different code rates. The TPC and LDPC codes are using the default parameters, which could be improved upon. In fact, there is still probably lots to learn about all of this. In this case, the LDPC was using the default alist that comes with GNU Radio (found in gr-fec examples directory) and the only change from the default TPC encoder and decoder was to use the MAX LOG-MAP decoder.

To see the differences in just the TPC decoder modes available, I plotted all five against each other. These are the same codes and rates with just different approaches to decoding them. What was not analyzed here, however, is the computational cost of each, and I would suspect we'd see a direct trade-off between BER performance and required compute power.

And if you haven't seen the new FEC-API, this is a way to easily use encoders and decoders of varying styles and requirements in both streaming and bursty communications. It makes using and reusing FEC blocks very easy between GNU Radio applications as well as allows us to easily use and replace the FEC being used in any given application. GNU Radio installs many examples for how to use the encoders and decoders in streaming, tagged stream, and PDU message modes into the digital examples directory.

Finally, these codes are not greatly optimized for speed. We felt it was important to provide access to the codes now so they can start being utilized in real systems. Hopefully, this is intriguing enough that one or more serious coders takes this as an opportunity to improve things.