Minimum weight distribution (MWD) is an important metric to calculate the first term of union bound called minimum weight union bound (MWUB). In this paper, we first prove the maximum likelihood (ML) performance approaches MWUB as signal-to-noise ratio (SNR) goes to infinity and provide the deviation when MWD and SNR are given. Then, we propose a nested reliability sequence, namely MWD sequence, to construct polar codes independently of channel information. In the sequence, synthetic channels are sorted by partial MWD which is used to evaluate the influence of information bit on MWD and we prove the MWD sequence is the optimum sequence evaluated by MWUB for polar codes obeying partial order. Finally, we introduce an entropy constraint to establish a relationship between list size and MWUB and propose a heuristic construction method named entropy constraint bit-swapping (ECBS) algorithm, where we initialize information set by the MWD sequence and gradually swap information bit and frozen bit to satisfy the entropy constraint. The simulation results show the MWD sequence is more suitable for constructing polar codes with short code length than the polar sequence in 5G and the ECBS algorithm can improve MWD to show better performance as list size increases.

This paper studies the routing problem for IP energy-efficient networks. We propose a robust routing algorithm to reach the higher network energy efficiency, which is based on optimization problem. To attain the highly energy-efficient routing for IP networks, the link of low utilization is turned into the sleeping state to save the network energy. At the same time, the low link traffic is aggregated to the link with high utilization to enhance the link utilization and to sleep the links as many as possible. We present an optimized link sleeping method to maximize the number of the sleeping links. By targeting the network robustness, a weight adaptive strategy is brought forth to reduce the link congestion and enhance the robustness of the network. Simulation results indicate that our algorithm is effective and feasible for IP energy-efficient networks.