Short Non-Binary Low-Density Parity-Check Codes for Phase Noise Channels

Abstract

This work considers the design of short non-binary low-density parity-check (LDPC) codes over finite fields of order m, for channels with phase noise. In particular, m-ary differential phase-shift keying (DPSK) modulated code symbols are transmitted over an additive white Gaussian noise (AWGN) channel with Wiener phase noise. At the receiver side, noncoherent detection takes place, with the help of a multi-symbol detection algorithm, followed by a non-binary decoding step. Both the detector and decoder operate on a joint factor graph. As a benchmark, finite length bounds and information rate expressions are computed and compared with the codeword error rate (CER) performance, as well as the iterative threshold of the obtained codes. As a result, performance within 1.2 dB from finite-length bounds is obtained, down to a CER of 10 −3 .

Approximate ML Decoding of Short Convolutional Codes Over Phase Noise Channels

“…The code polynomials were taken from [7] and chosen to optimize the CC code free distance. 5 They are specified in octal notation as [515, 677] (for m = 8) and [5537, 6131] (for m = 11). The information word length is 64 bits, while the codeword length is 128 bits.…”

“…However, whenever blocks in the range of a few hundred bits or less are considered, the aforementioned schemes may show a loss in performance, since the employed channel codes and decoding algorithms were not explicitly tailored to short blocks. An exception is the work in [5] that focuses on M2Mtype communications with block lengths of a few hundreds of bits. In absence of pilots, [5] derives an approach based on non-binary low-density parity-check (LDPC) codes with differential phase-shift keying (PSK).…”

“…An exception is the work in [5] that focuses on M2Mtype communications with block lengths of a few hundreds of bits. In absence of pilots, [5] derives an approach based on non-binary low-density parity-check (LDPC) codes with differential phase-shift keying (PSK). The authors show that an iterative joint detection and decoding algorithm can be employed to achieve results within 1.2 dB from finite-length performance bounds.…”

Non-binary codes approach on the performance of short-packet full-duplex transmissions

“…It has been proved by many researches that NB-LDPC outperforms their binary counterpart in the case of short code length and higher order of modulation [17], [18]. In the present era, NB-LDPC codes are increasingly seen as a promising coding method for mMTC devices within 5G networks or sensors used in IoT applications that handle limited data transmission [19]. However, it is important to address and mitigate the issue of excessive complexity and latency during the decoding process.…”

SISO Decoding of ℤ4 Linear Kerdock and Preparata Codes

“…More recently, nonlinear codes are often used as components of product codes in order to achieve better reliability and security [19,20]. Codes over rings have also found application in coding for the phase noise channel [21] and network-coded bidirectional relaying systems [22].…”