Long, powerful soft detection forward error correction codes are typically constructed by concatenation of shorter component codes that are decoded through iterative Soft-Input Soft-Output (SISO) procedures. The current gold-standard is Low Density Parity Check (LDPC) codes, which are built from weak single parity check component codes that are capable of producing accurate SO. Due to the recent development of SISO decoders that produce highly accurate SO with codes that have multiple redundant bits, square product code constructions that can avail of more powerful component codes have been shown to be competitive with the LDPC codes in the 5G New Radio standard in terms of decoding performance while requiring fewer iterations to converge. Motivated by applications that require more powerful low-rate codes, in the present paper we explore the possibility of extending this design space by considering the construction and decoding of cubic tensor codes.

翻译：长码、高性能的软检测前向纠错码通常通过级联较短的组件码来构造，这些组件码通过迭代的软输入软输出（SISO）过程进行译码。当前的金标准是低密度奇偶校验（LDPC）码，它由较弱的单奇偶校验组件码构建而成，这些组件码能够产生准确的软输出。由于近期SISO译码器的发展，能够为具有多个冗余位的码产生高度准确的软输出，可利用更强大组件码的方形乘积码构造已被证明在译码性能上与5G新空口标准中的LDPC码具有竞争力，同时需要更少的迭代次数收敛。受需要更强大低码率码的应用驱动，本文通过考虑立方张量码的构造与译码，探索扩展这一设计空间的可能性。