Spatially Coupled LDPC Codes and Cooperative Communication

In this dissertation we focus on three topics in wireless communication: 1) design of spatially coupled low-density parity-check (SC-LDPC) codes over GF(q) for windowed decoding (WD), 2) cooperative communication in the context of bandwidth-efficient modulation, and 3) the use of rate-compatible SC-LDPC codes in binary coded cooperation.

As for the first topic, we consider the generalization of binary SC-LDPC codes to finite fields GF(q), q>=2, and discuss design rules for q-ary SC-LDPC code ensembles based on their iterative belief propagation (BP) decoding thresholds, with particular emphasis on low-latency 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 q-ary 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; we also show that these gains increase as the finite field size q=2^m increases. Moreover, we demonstrate that our design rules provide WD thresholds that are close to capacity, even when both m and W are relatively small (thereby reducing complexity and latency). Analysis 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.

Regarding the second topic, we consider a communication scenario in which a pair of cooperating partners (i.e., two source nodes) convey their data to a common destination. To mitigate fading, each partner transmits its own local data and acts as a relay for the other partner. Specifically, relaying is incorporated into the channel coding function: local data (originating at the transmitting node) and relayed data (originating at the partner of the transmitting node) are encoded separately, and the resulting bitstreams are then multiplexed together prior to bandwidth-efficient modulation (e.g., 8-PSK, 16-QAM, etc.) in such a way that the relayed coded bits partition the signal constellation into sparse subsets, as in Ungerboeck's set partitioning approach to coded modulation. The partner, having knowledge of the relayed bits, is able to demodulate each block-faded and noise-corrupted symbol using the appropriate sparse sub-constellation, improving the partner-to-partner link. The destination benefits in two ways: indirectly from the increased diversity made possible by the enhanced partner-to-partner link, and directly by exploiting the set-partition labeling. Outage results and frame error rate simulations using low-density parity-check codes demonstrate substantial performance gain, fundamentally and practically, over the conventional 'time-sharing' approach to cooperation.

Finally, for the third topic, we investigate the use of rate-compatible SC-LDPC codes for binary coded cooperation. In the same 'two sources, one destination' model as described above, one source node relays additional parity-check bits for its partner's latest transmission to provide cooperative diversity at the destination. Different families of SC-LDPC code ensembles are generated by applying the edge spreading technique to several good rate-compatible protograph-based LDPC-BC ensembles from the literature. Simulation of the outage behavior shows that, using SC-LDPC code ensembles, system performance approaches the theoretical limit, regardless of whether the original uncoupled LDPC-BC ensembles were designed specifically for coded cooperation or not. The same result holds when WD is used to reduce decoding latency.