Recently I have implemented an FPGA LDPC decoder for a commercial project. The belief propagation LDPC decoder algorithm admits many different approximations in the arithmetic, and other tricks that can be used to trade off between decoding sensitivity (BER versus Eb/N0 performance) and computational complexity. To help me benchmark the different belief propagation algorithms, I have extended my ldpc-toolbox project to implement many different LDPC decoding algorithms and perform BER simulations.
ldpc-toolbox is a Rust library and command line tool for the design of LDPC codes. I initially created this project when I was trying to design a suitable LDPC code for a narrowband 32APSK modem to be used over the QO-100 amateur GEO transponder. The tool so far supported some classical pseudorandom constructions of LDPC codes, computed Tanner graph girths, and could construct the alists for all the DVB-S2 and CCSDS LDPC codes. Extending this tool to support LDPC encoding, decoding and BER simulation is a natural step.
A couple months ago I presented my work-in-progress design for a data modem intended to be used through the QO-100 NB transponder. The main design goal for this modem is to give the maximum data rate possible in a 2.7 kHz channel at 50 dB·Hz CN0. For the physical layer I settled on an RRC-filtered single-carrier modulation with 32APSK data symbols and an interleaved BPSK pilot sequence for synchronization. Simulation and over-the-air tests of this modulation showed good performance. The next step was designing an appropriate FEC.
Owing to the properties of the synchronization sequence, a natural size for the FEC codewords of this modem is 7595 bits (transmitted in 1519 data symbols). The modem uses a baudrate of 2570 baud, so at 50 dB·Hz CN0 the Es/N0 is 15.90 dB. In my previous post I considered using an LDPC code with a rate of 8/9 or 9/10 for FEC, taking as a reference the target Es/N0 performance of the DVB-S2 MODCODs. After some performing some simulations, it turns out that 9/10 is a bit too high with 7595 bit codewords (the DVB-S2 normal FECFRAMEs are 64800 bits long, giving a lower LDPC decoding threshold). Therefore, I’ve settled on trying to design a good rate 8/9 FEC. At this rate, the Eb/N0 is 9.42 dB.