In this paper, we study spatially coupled lowdensity parity-check (SC-LDPC) codes over finite fields GF(q), q ≥ 2, and develop design rules for q-ary SC-LDPC code ensembles based on their iterative belief propagation 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 the protograph versions of q-ary density evolution (for the BEC) and the q-ary extrinsic information transfer analysis (for the BIAWGNC). We show that the WD of q-ary SC-LDPC codes provides significant threshold gains compared with 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 = 2m 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 with standard flooding-schedule decoding, the WD of q-ary SC-LDPC code ensembles results in significant reductions in both the decoding complexity and the decoding latency and that these reductions increase as m increases. For the 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.

In this paper, we compare the finite-length performance of protograph-based spatially coupled low-density paritycheck (SC-LDPC) codes and LDPC block codes (LDPC-BCs) over GF(q). To reduce computational complexity and latency, a sliding window decoder with a stopping rule based on a soft belief propagation (BP) estimate is used for the q-ary SC-LDPC codes. Two regimes are considered: one when the constraint length of q-ary SC-LDPC codes is equal to the block length of q-ary LDPC-BCs and the other when the two decoding latencies are equal. Simulation results confirm that, in both regimes, (3,6)-, (3,9)-, and (3,12)-regular non-binary SC-LDPC codes can significantly outperform both binary and non-binary LDPC-BCs and binary SC-LDPC codes. Finally, we present a computational complexity comparison of q-ary SC-LDPC codes and q-ary LDPC-BCs under equal decoding latency and equal decoding performance assumptions.

In this paper, we compare the finite-length performance of non-binary spatially coupled low-density parity-check (NB SC-LDPC) codes constructed from protographs to non-binary LDPC block codes (NB LDPC-BCs). A sliding window decoding architecture with a stopping rule based on a soft bit-error-rate (BER) estimate for the NB SC-LDPC codes is considered. It is demonstrated that NB SC-LDPC codes with sliding window decoding outperform NB LDPC-BCs with no increase in decoding complexity when the decoding latency of the SC-LDPC codes equals the block length of the LDPC-BCs. We also investigate the relationship between the protograph lifting factor, the decoding window size, and the decoding performance of NB SC-LDPC codes when the decoding latency is fixed. Simulation results for several (3,6)-regular NB code examples confirm that NB SC-LDPC codes can significantly outperform both binary LDPC-BCs and binary SC-LDPC codes with the same decoding latency.

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 near-capacity performance for a sufficiently large window size W on both the BEC and the BIAWGNC. Also, we show that NBSC-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.

This paper investigates the use of rate-compatible spatially-coupled codes for coded cooperation. Transmitting to the same destination, two source nodes cooperate to combat block fading; using rate-compatible spatially-coupled codes, one source node relays additional parity-check bits for its partner's latest transmission to provide cooperative diversity at the destination. Different families of spatially-coupled codes are generated by applying the edge spreading technique to several rate-compatible protograph-based block LDPC codes from the literature. Simulation of the outage behavior shows that, using spatially-coupled codes, system performance approaches the theoretical limit, regardless of whether the original underlying block LDPC codes were designed specifically for coded cooperation or not. The same result holds when windowed decoding, instead of decoding across the entire graph, is used to reduce decoding latency.

This paper considers cooperative diversity in the context of bandwidth-efficient modulation. Specifically, it analyzes a scenario in which high-order modulation - 16-QAM is used for illustration - is used in a way that enables two partners to cooperatively convey their data to a common destination. This approach uses set partitioning so that “relayed” data selects a sparse subset while “local” data selects the transmitted symbol from that subset. An outage probability analysis is presented that illustrates the advantage of this technique over the conventional time-sharing approach to cooperative diversity; for 16-QAM, coding gains range from 1.5 dB (for a spectral efficiency of η = 0.5 bits/symbol) to 3.2 dB (for η = 1.5). Then, a variation on this approach - in which codewords are spread out over multiple frames (and multiple channel realizations) - is examined and shown to provide a substantial gain at the cost of delay.

This paper presents two new techniques employing bandwidth-efficient modulation to enable two partners to cooperatively convey their data to a common destination. Both approaches integrate relaying and channel coding, exploiting the fact that each partner knows the data relayed by the other partner to enhance the partner-to-partner link. The first approach is based on bit-interleaved coded modulation (BICM); a key innovation is the use of set-partition (SP) labelling that enables the receiving partner to demodulate and decode based on a sparse subset of the original constellation. The second approach is based on trellis coded modulation (TCM); the local and relayed data are multiplexed together prior to encoding, and the receiving partner prunes the trellis edges inconsistent with the known relayed data. In both approaches, the receiver at the common destination benefits in two ways - indirectly from the increased diversity made possible by the enhanced partner-to-partner link, and directly by exploiting the SP-labeling/trellis-pruning in its decoding protocol. Simulations indicate that the new techniques offer significant performance gain over conventional cooperation based on time-sharing - a gain of 2.50 dB for the 16-QAM BICM system and a gain of 3.0 dB for the 8-PSK TCM system, both at a frame error rate of 10-2.