Performance Analysis and Design of LT Codes Under the Gaussian Elimination Algorithm in Wireless Sensor Networks

With the growing demand, wireless sensor networks (WSNs) play an increasingly important role in many fields. The focus has been on deploying Luby transform (LT) codes in WSNs because of their inherent advantages in erasure channels. Since most data transmitted by WSNs are small, the Gaussian elimination (GE) decoding algorithm is highly attractive. In this paper, we investigate the performance analysis and code design methods for LT codes under the GE algorithm. First, the analytical expressions of the data erasure probability are detailed for two simple kinds of LT codes. Then, a characteristic indicator of the data erasure probability is introduced to evaluate the performance of general LT codes. Finally, we propose novel design methods by optimizing degree distributions from three goals based on the characteristic indicator. The numerical results validate the proposed performance analysis and code design methods in comparison with the conventional method.