Block Markov Superposition Transmission of Fourier Transform Pair Codes
Xiao Ma, Dian Chen, Yaping Lv · 2022
This paper proposes a new class of systematic linear codes called Fourier transform pair (FTP) codes. Given any element$\beta$of order$n$in a finite field, a codeword in the FTP code consists of an information vector of length$n$followed by its Fourier transform vector defined with$\beta$as the parity-check vector. The FTP code has length$2n$, dimension$n$, and minimum distance at least$2\sqrt{n}$. Distinguishingly, an FTP code defined with any element of order three is a maximum distance separable (MDS) code. To improve the performance of FTP codes, we turn to the block Markov superposition transmission (BMST) systems. Simulation results show that BMST-FTP codes have good performances in the water-fall region (within 0.5$\mathbf{dB}$away from the corresponding Shannon limits) and reach the corresponding genie-aided (GA) bounds in the error-floor region. Compared with BMST of other short codes, the BMST-FTP codes require shorter encoding memory to achieve comparable performance, potentially leading to low decoding complexity and low latency.