## 1 Introduction  
Wireless Sensor Networks (WSN) suffer many constraints such as limited battery energy, low transmission rate and poor-quality links [1]. How to provide a reliable data transmission in WSN in order to prolong the network lifetime as long as possible is an important and challenging issue. A new attractive technique named network coding goes especially well with WSN due to the broadcast nature and diversity of the links in WSN [2]. Network coding will reduce the number of transmissions and receptions in network nodes which results in the reduction of energy consumption. Network coding is a technique where relay nodes mix and combine packets using mathematical operations, which reduces the number of transmitted packets. Network coding was firstly proposedin [3]. The traditional architecture of networks is storing-and-forwarding, and it was once believed that switch and router would not bring any benefit. However, it turns out that network coding can increase the network throughput dramatically which results in a high packets delivery ratio. Even in the application, network coding also has a good performance [4]. Some works also intend to reach the lower bound of the theory bandwidth as far as possible, for example, by constructing new codes [5]. In summary, network coding has already seen tremendous advancement in both theory and application. Although network coding can dramatically improve the performance of WSN, it suffers a serious disturbance from propagated errors due to its inherent mixture characteristic. In network coding, its very nature of combining information in the relay nodes makes the network very susceptible to transmission errors. A single error will be propagated by every node further downstream in the networks. This will thus prevent the reconstruction of the file in the sink. The poor-quality links in WSN further intensify the crisis of error propagation in network coding. There are fruitful works about network error correction coding for network coding (NEC) [6; 7; 8; 9]. However, none of the existing works thoroughly solved the error propagation problem in network coding. Most of the pre-existing works about NEC have apparent drawbacks. Homomorphic signature scheme which is based on Cryptographic approaches has high complexity and intolerable delay [10]. NEC which is based on information theoretic approaches has low complexity, but they cannot cope with the dense propagated errors which exceed \(C/2\) where \(C\) is the max flow min cut of the multicast network. Some works are based on hamming distance [11; 12; 13; 14] is based on hamming distance and other works are based on rank distance [15] is based on rank distance; Neither escapes the above rule. [PERSON]'s works increase the information rate as far as possible, the effectiveness of such improvements is also limited [16; 17]. [PERSON] and [PERSON] present a seminal idea of subspace codes without having to consider the randomness of the random network, and it is a huge progress [18]. However, subspace codes still cannot correct errors which exceed \(C/2\)[18]. Due to the nature of the linear block codes from which NECs are developed, \(C/2\) is the upper bound of the corrected errors number. The number of corrected errors is bounded by Shannon information theory. Thus, the constraint means the number of links where an error occurs cannot exceed \(C/2\). However, it is unrealistic to assume the number of original error is less than \(C/2\). The number of links, where \"original error\" occurs, usually exceeds \(C/2\). Furthermore, the number of random errors caused by channel noise, is usually very large. Under a fixed bit error rate (BER), the more links there are, the more corrupted packets there will be. The situation will be worse where no link-layer error correction is performed, such as in wireless sensor networks of which the computational power is limited.