LT codes are the first practical rateless codes whose reception overhead totally depends on the degree distribution adopted. The capability of LT codes with a particular degree distribution named robust soliton has been theoretically analyzed; it asymptotically approaches the optimum when the message length approaches infinity. However, real applications making use of LT codes have finite number of input symbols. It is quite important to refine degree distributions because there are distributions whose performance can exceed that of the robust soliton distribution for short message length. In this work, a practical framework that employs evolutionary algorithms is proposed to search for better degree distributions. Our experiments empirically prove that the proposed framework is robust and can customize degree distributions for LT codes with different message length. The decoding error probabilities of the distributions found in the experiments compare well with those of robust soliton distributions. The significant improvement of LT codes with the optimized degree distributions is demonstrated in the paper.

Single-packet attack can be tracked with logging-based IP traceback approaches, whereas DDoS attack can be tracked with marking-based approaches. However, both approaches have their limits. Logging-based approaches incur heavy overhead for packet-digest storage as well as time overhead for both path recording and recovery. Marking-based approaches incur little traceback overhead but are unable to track single packets. Simply deploying both approaches in the same network to deal with single-packet and DDoS attacks is not an efficient solution due to the heavy traceback overhead. Recent studies suggest that hybrid approaches are more efficient as they consume less router memory to store packet digests and require fewer attack packets to recover attack paths. Thus, the hybrid single packet traceback approach is more promising in efficiently tracking both single-packet and DDoS attacks. The major challenge lies in reducing storage and time overhead while maintaining single-packet traceback capability. We present in this paper a new hybrid approach to efficiently track single-packet attacks by designing a novel path fragment encoding scheme using the orthogonality of Walsh matrix and the degree distribution characteristic of router-level topologies. Compared to HIT (Hybrid IP Traceback), which, to the best of our knowledge, is the most efficient hybrid approach for single-packet traceback, our approach has three advantages. First, it reduces the overhead by 2/3 in both storage and time for recording packet paths. Second, the time overhead for recovering packet paths is also reduced by a calculatable amount. Finally, our approach generates no more than 2/3 of the false-positive paths generated by HIT.

Internet behavior is becoming more complex due to ever-changing networking technologies and applications. Thus, understanding and controlling the complex behavior of the Internet are important for designing future networks. One of the complex behaviors of the Internet is traffic dynamics. Previous studies revealed that flow control in the transport layer affects the traffic dynamics of the Internet. However, it is not clear how the topological structure impacts traffic dynamics. In this paper, we investigate packet delay dynamics and traffic fluctuation in ISP router-level topologies where the degree distribution exhibits a power-law nature, and the nodes interact via end-to-end feedback control functionality. We show the packet delay dynamics of the BA topologies generated by the Barabasi-Albert (BA) model and the ISP router-level topologies. Simulation results show that the end-to-end delay distributions exhibit a heavy tail in the TCP model. Moreover, the number of links with highly fluctuating queue length increases dramatically compared to that in the stop-and-wait model. Even in this case, the high-modularity structures of the ISP topologies reduce the number of highly fluctuating links compared with the BA topologies.

Luby et al. derived evolution of degree distributions in residual graphs for irregular LDPC code ensembles. Evolution of degree distributions in residual graphs is important characteristic which is used for finite-length analysis of the expected block and bit error probability over the binary erasure channel. In this paper, we derive detailed evolution of degree distributions in residual graphs for irregular LDPC code ensembles with joint degree distributions.

Irregular Repeat-Accumulate (IRA) codes, introduced by Jin et al., have a linear-time encoding algorithm and their decoding performance is comparable to that of irregular low-density parity-check (LDPC) codes. Meanwhile the authors have introduced detailedly represented irregular LDPC code ensembles specified with joint degree distributions between variable nodes and check nodes. In this paper, by using density evolution method [7],[8], we optimize IRA codes specified with joint degree distributions. Resulting codes have higher thresholds than Jin's IRA codes.