Non-binary coded CCSK and Frequency-Domain Equalization with simplified LLR generation

Abstract

In this paper, we investigate the performance of Single-Carrier (SC) transmission with Non-Binary Low-Density Parity-Check (NB-LDPC) coded Cyclic Code-Shift Keying (CCSK) signaling in a multipath environment and we show that the combination of CCSK signaling and non-binary codes results in two key advantages, namely, improved Log-Likelihood Ratio (LLR) generation via correlations and reduced implementation complexity. We demonstrate that Maximum Likelihood (ML) demodulation can be expressed by two circular convolution operations and thus it can be processed in the frequency domain. Then, we propose a joint Frequency-Domain Equalization (FDE) and LLR generation scheme that aims at reducing the complexity of the receiver. Finally, we demonstrate through Monte-Carlo simulations and histogram analysis that this proposed CCSK signaling scheme gives more robustness to SC-FDE systems than commonly employed Hadamard signaling schemes (a gap of ≈ 1.5dB in favor of CCSK signaling is observed at BER = 10 −5 , assuming perfect Channel State Information).

Non-Binary Polar Codes for Spread-Spectrum Modulations

“…, q − 1. (1) The CCSK modulation maps an element u ∈ U to the sequence P u . The ratio p/q is referred to as the spreading factor of the modulation.…”

“…where P (0) (h) and P (1) (h) denote the polarizing parameters of W (0) and W (1) channels, respectively, assuming that the channel combining coefficient is equal to h. We numerically estimate the values of P (0) (h) and P (1) (h), for all h ∈ GF(q)\ {0}, based on Monte Carlo simulation (see also Section IV-C).…”

“…Once the value of h 0 is determined, we can optimize the kernel coefficients for the second (middle) polarization 1 We assume here that the mutual information is normalized (expressed in terms of symbols per channel use), thus taking values between 0 and 1. ) , or two copies of W (1) . Therefore, two coefficients need to be optimized, denoted by h 1 and h 2 in Fig.…”

Time-Synchronization of CCSK Short Frames

“…This "preamble-less frame" is hereby referred to as a Quasi-Cyclic Short Packet (QCSP) frame. It is based on the use of a Cyclic Code Shift Keying (CCSK) modulation scheme [11] jointly associated with powerful Non-Binary (NB) forward error correction codes defined over a Galois Field GF(q), where q > 2, such as NB-Low Density Parity Check (NB-LDPC) codes [12], NB-Turbo [13], NB Turbo Product Codes [14], and NB-Polar codes [15]. In this paper, we will focus only on the NB-LDPC code.…”

Rate-adaptive Inner Code for Non-Binary Decoders

“…Without loss of generality, the NB-encoder is in this article an NB-LDPC encoder. This concatenation allows to target efficiently very low SNRs and gives advantages in both modulation and synchronization [12]. The Truncated CCSK (TCCSK) described in [10] consists of not transmitting consecutive bits of the CCSK sequence to obtain code rate flexibility.…”