Novel techniques are conceived for joint Compressive Sensing (CS) and Low-Density Parity Check (LDPC) coding in Wireless Sensor Networks (WSNs), namely a Soft-Input Soft-Output (SISO) tree search Sphere Decoding (SD) technique, and a SISO Hamming Distance (HD) based solution. Factor graphs are utilized to describe the connectivity between the signals and sensors, as well as with the LDPC codes. In the Fusion Center (FC), the factor graphs may be used for iterative joint LDPC-CS decoding, in order to recover the signals observed. However, the CS decoder of the FC suffers from high complexity, if the exhaustive Maximum A posteriori (e-MAP) technique is employed, which considers all possible combinations of source signals detected by each of the associated sensors. Hence, in the proposed SD and HD schemes only the more likely combinations of source signals are tested for reducing the CS decoding complexity. More specifically, a tree search technique is used in the first step to find the most likely combination of source signal values.Then, in the second step, the proposed SD continues the tree search to find a set of alternative hypotheses. This facilitates the generation of high quality extrinsic information, which may be iteratively exchanged with the LDPC decoder. By contrast, in the HD approach, the second step obtains the alternative hypotheses within a certain HD of the most likely source signal combination. Both our BLock Error Rate (BLER) results and Extrinsic Information Transfer (EXIT) charts show that the proposed SD and HD techniques approach the performance of the full-search e-MAP approach at a significantly reduced complexity. In particular, we show the e-MAP solution is about 56 times more complex than the SD approach and around 210 times more complex than the HD approach. Compared to a Separate Source-Channel Coding (SSCC) hard information benchmarker, the proposed SISO schemes improve the decoding performance by about 1.7 dB. Furthermore, the SISO schemes allow the iterations inside the CS decoding to eliminate the error floors and obtain a further 2.45 dB gain.

A new support identification technique based on factor graphs and belief propagation is proposed for Compressive Sensing (CS) aided Wireless Sensor Networks (WSNs), which reliably estimates the locations of non-zero entries in a sparse signal through an iterative process. Our factor graph based approach achieves a support identification error rate of 10% at an Signal to Noise Ratio (SNR) that is 6 dB lower than that required by the state-of-the-art relative frequency based support identification approach, as well as by the Orthogonal Matching Pursuit (OMP) algorithm. We also demonstrate that our support identification technique is capable of mitigating the signal reconstruction noise by as much as 4 dB upon pruning the sparse sensing matrix. Furthermore, by intrinsically amalgamating the relative frequency based and the proposed factor graph based approach, we conceived a hybrid support identification technique for reducing communication between the sensor nodes and the Fusion Center (FC), while maintaining highaccuracy support identification and simultaneously mitigating the noise contaminating signal reconstruction.

The novel concept of joint Compressive Sensing (CS) and Low Density Parity Check (LDPC) coding is conceived for Joint Source-Channel Coding (JSCC) in Wireless Sensor Networks (WSNs) supporting a massive number of signals. More explicitly, we demonstrate this concept for a specific scheme, which supports a massive number of signals simultaneously, using a small number of Internet of Things Nodes (IoTNs) based on the concept of CS. The compressed signals are LDPC coded in order to protect them from poor transmission channels. We also propose the new iterative joint source-channel decoding philosophy for exchanging soft extrinsic information, which combines CS decoding and LDPC decoding by merging their respective factor graphs. We then characterize this scheme using Extrinsic Information Transfer (EXIT) chart analysis. Our BLock Error Rate (BLER) results show that the proposed iterative joint LDPC-CS decoding scheme attains about 1.5 dB gain at a BLER of 10 −3 compared to a benchmarker, which employs separate CS and LDPC decoding. Naturally, this gain is achieved at the cost of approximately doubling the complexity of the proposed iterative joint LDPC-CS decoding scheme.

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