Systematic BMST-FTP Codes and Their Application to q-ary Erasure Channels

In this paper, q-ary Fourier Transform Pair (FTP) codes over q-ary erasure channels are investigated. To improve the performance of FTP codes, we propose an encoding and decoding scheme based on block Markov superposition transmission. Specifically, the information symbols of FTP codes are transmitted directly, while the check symbols are transmitted in a superposition way. To analyze the performance, we present a Genie-Aided (GA) lower bound, which serves as a tool to set properly the encoding memory. Simulation results show that the proposed scheme can improve the performance of FTP codes, approaching the Shannon limit within 0.06 at the symbol erasure rate of 10⁻⁴. Particularly, the simulated performance matches the GA lower bounds in the low erasure probability region. With the same code rate and similar code length, the proposed scheme performs better than the non-binary low density parity check code.