An effective way of improving decoding performance of an LDPC code is to extend the single-decoder decoding method to a parallel decoding method with multiple sub-decoders. To this end, this paper proposes a parallel decoding method for the LDPC codes constructed by m-sequence. In this method, the sub-decoders have two types. The first one contains only one decoding module using the original parity-check constraints to implement a belief propagation (BP) algorithm. The second one consists of a pre-decode module and a decoding module. The parity-check matrices for pre-decode modules are generated by the parity-check constraints of the sub-sequences sampled from an m-sequence. Then, the number of iterations of the BP process in each pre-decode module is set as half of the girth of the parity-check matrix, resulting in the elimination of the impact of short cycles. Using maximum a posterior (MAP), the least metric selector (LMS) finally picks out a codeword from the outputs of sub-decoders. Our simulation results show that the performance gain of the proposed parallel decoding method with five sub-decoders is about 0.4 dB, compared to the single-decoder decoding method at the bit error rate (BER) of ${10}^{-5}$.

Random linear network coding (RLNC) is a promising network coding solution when the network topology information is not fully available to all the nodes. However, in practice, nodes have partial knowledge of the network topology information. Motivated by this, we investigate the performance of RLNC and obtain different upper bounds on the failure probability of RLNC for the network constrained by different partial network topology information. These upper bounds not only improve the existing ones in the literature, but also show that the partial network topology information can bring benefits to the performance analysis of RLNC. On the other hand, it is observed that if more network topology information can be utilized, tighter upper bounds can be obtained, as expected. The upper bounds on two classical networks are compared for demonstration. To obtain a deeper understanding about the performance of RLNC, the asymptotic behavior of RLNC as the field size goes to infinity is also investigated.

Recently, network coding technique has emerged as a promising approach that supports reliable transmission over wireless loss channels. In existing protocols where users have no interest in considering the encoded packets they had in coding or decoding operations, this rule is expensive and inefficient. This paper studies the impact of encoded packets in the reliable unicast network coding via some theoretical analysis. Using our approach, receivers do not only store the encoded packets they overheard, but also report these information to their neighbors, such that users enable to take account of encoded packets in their coding decisions as well as decoding operations. Moreover, we propose a redistribution algorithm to maximize the coding opportunities, which achieves better retransmission efficiency. Finally, theoretical analysis and simulation results for a wheel network illustrate the improvement in retransmissions efficiency due to the encoded packets.

Incremental automatic modulation recognition is essential for the awareness of complex electromagnetic environments but is prone to catastrophic forgetting. This is fundamentally precipitated by shortcut learning, a phenomenon where deep models prioritize stable but non-essential channel artifacts (e.g., noise, fading) over intrinsic modulation characteristics. Consequently, models rely on spurious correlations that collapse during incremental task updates or environmental shifts, leading to representation drift. To bridge this gap, we propose the ParalIMR framework, which integrates a parallel reconstruction architecture with the segment substitution (SS) strategy to decouple modulation signatures from environmental fingerprints. Specifically, the parallel branch utilizes a Denoising AutoEncoder (DAE) as a task-agnostic structural anchor, purifying feature representations and maintaining geometric consistency across varying signal-to-noise ratios without propagating noise-overfitting to the classifier. In the meantime, the SS strategy actively disrupts the temporal coupling between class labels and hardware fingerprints through random reorganization, forcing the model to extract modulation-invariant structural cues. Experimental results on the RML2016a datasets demonstrate that in a three-stage incremental setup, our method achieves an overall accuracy of 84.32% at 0 dB SNR, representing a 2.69% improvement over the iCaRL baseline. Notably, this advantage expanded to 4.46% on RML2018, demonstrating that ParalIMR effectively arrests catastrophic forgetting. Ultimately, this research provides a robust learning paradigm tailored for cognitive radio and electronic warfare in dynamic electromagnetic landscapes.