In this paper we consider the generalization of binary spatially coupled low-density parity-check (SC-LDPC) codes to finite fields GF(q), q ≥ 2, and develop design rules for q-ary SC-LDPC code ensembles based on their iterative belief propagation (BP) decoding thresholds, with particular emphasis on low-latency windowed decoding (WD). We consider transmission over both the binary erasure channel (BEC) and the binary-input additive white Gaussian noise channel (BIAWGNC) and present results for a variety of (J, K)-regular SC-LDPC code ensembles constructed over GF(q) using protographs.Thresholds are calculated using protograph versions of q-ary density evolution (for the BEC) and qary extrinsic information transfer analysis (for the BIAWGNC). We show that WD of q-ary SC-LDPC codes provides significant threshold gains compared to corresponding (uncoupled) q-ary LDPC block code (LDPC-BC) ensembles when the window size W is large enough and that these gains increase as the finite field size q = 2 m increases. Moreover, we demonstrate that the new design rules provide WD thresholds that are close to capacity, even when both m and W are relatively small (thereby reducing decoding complexity and latency). The analysis further shows that, compared to standard flooding-schedule decoding, WD of q-ary SC-LDPC code ensembles results in significant reductions in both decoding complexity and decoding latency, and that these reductions increase as m increases.For applications with a near-threshold performance requirement and a constraint on decoding latency, we show that using q-ary SC-LDPC code ensembles, with moderate q > 2, instead of their binary counterparts results in reduced decoding complexity.
Abstract-In this paper we study the iterative decoding threshold performance of non-binary spatially-coupled low-density parity-check (NB-SC-LDPC) code ensembles for both the binary erasure channel (BEC) and the binary-input additive white Gaussian noise channel (BIAWGNC), with particular emphasis on windowed decoding (WD). We consider both (2, 4)-regular and (3, 6)-regular NB-SC-LDPC code ensembles constructed using protographs and compute their thresholds using protograph versions of NB density evolution and NB extrinsic information transfer analysis. For these code ensembles, we show that WD of NB-SC-LDPC codes, which provides a significant decrease in latency and complexity compared to decoding across the entire parity-check matrix, results in a negligible decrease in the nearcapacity performance for a sufficiently large window size W on both the BEC and the BIAWGNC. Also, we show that NB-SC-LDPC code ensembles exhibit gains in the WD threshold compared to the corresponding block code ensembles decoded across the entire parity-check matrix, and that the gains increase as the finite field size q increases. Moreover, from the viewpoint of decoding complexity, we see that (3, 6)-regular NB-SC-LDPC codes are particularly attractive due to the fact that they achieve near-capacity thresholds even for small q and W . I. INTRODUCTIONNon-binary low-density parity-check (NB-LDPC) block codes constructed over finite fields of size q > 2 outperform comparable binary LDPC block codes [1], in particular when the blocklength is short to moderate; however, this performance gain comes at the cost of an increase in decoding complexity. A direct implementation of the belief-propagation (BP) decoder [1] has complexity O(q 2 ) per symbol. More recently, an implementation based on the fast Fourier transform [2] was shown to reduce the complexity to O(q log q). Beyond that, a variety of simple but sub-optimal decoding algorithms have been proposed in the literature [3] [4]. As for computing iterative decoding thresholds, a non-binary extrinsic information transfer (NB-EXIT) analysis was proposed in [5] and was later developed into a corresponding version P-NB-EXIT [6] suitable for protograph-based codes.A protograph [7] is a small Tanner graph, which can be used to produce a structured LDPC code ensemble by applying a graph lifting procedure, such that every code in the ensemble maintains the structure of the protograph, i.e., it has the same degree distribution and the same type of edge connections. Figure 1 illustrates a (3, 6)-regular protograph,
In this paper, a decode-and-forward (DF) shortpacket relaying model is developed to achieve timely status updates for intelligent monitoring within the Internet of Things (IoT), where the status updates generated at an IoT device are delivered to a remote server with the aid of a relay in both halfduplex (HD) and full-duplex (FD) modes. To characterise the data freshness of status updates, we exploit the age of information (AoI) as a metric, which is defined as the time elapsed since the generation of the latest successfully decoded status update. The average AoI is formulated and minimised for both HD-DF and FD-DF relaying IoT networks in finite blocklength regime. For the HD-DF relaying, we introduce a perfect approximation of the average AoI to solve the problem of average AoI minimisation with the optimal blocklengths in two phases. For the FD-DF relaying, we propose an iterative algorithm to solve the problem of average AoI minimisation by optimising the relay's transmit power and the blocklength. Illustrative numerical results not only substantiate the validity of our proposed algorithms, but also provide useful references for the IoT monitoring network design, specifically for the transmit power thresholds at the IoT device and the relay.Index Terms-Age of information (AoI), decode-and-forward (DF), finite blocklength regime, full duplex (FD), half duplex (HD), short-packet relaying, status updates.
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