Tree-Search Techniques for Joint Iterative Compressive Sensing and LDPC Decoding in Wireless Sensor Networks

Abstract

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 an 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 that 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${1}.{7} \text {dB}$ </tex-math></inline-formula> . Furthermore, the SISO schemes allow the iterations inside the CS decoding to eliminate the error floors and obtain a further <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${2}.{45}$ </tex-math></inline-formula> -dB gain.