Construction algorithm for network error-correcting codes attaining the Singleton bound

We give a centralized deterministic algorithm for constructing linear network error-correcting codes that attain the Singleton bound of network error-correcting codes. The proposed algorithm is based on the algorithm by Jaggi et al. We give estimates on the time complexity and the required symbol size of the proposed algorithm. We also estimate the probability of a random choice of local encoding vectors by all intermediate nodes giving a network error-correcting codes attaining the Singleton bound. We also clarify the relationship between the robust network coding and the network error-correcting codes with known locations of errors.Comment: To appear in IEICE Trans. Fundamentals (http://ietfec.oxfordjournals.org/), vol. E90-A, no. 9, Sept. 2007. LaTeX2e, 7 pages, using ieice.cls and pstricks.sty. Version 4 adds randomized construction of network error-correcting codes, comparisons of the proposed methods to the existing methods, additional explanations in the proo

S-PRAC: Fast Partial Packet Recovery with Network Coding in Very Noisy Wireless Channels

Well-known error detection and correction solutions in wireless communications are slow or incur high transmission overhead. Recently, notable solutions like PRAC and DAPRAC, implementing partial packet recovery with network coding, could address these problems. However, they perform slowly when there are many errors. We propose S-PRAC, a fast scheme for partial packet recovery, particularly designed for very noisy wireless channels. S-PRAC improves on DAPRAC. It divides each packet into segments consisting of a fixed number of small RLNC encoded symbols and then attaches a CRC code to each segment and one to each coded packet. Extensive simulations show that S-PRAC can detect and correct errors quickly. It also outperforms DAPRAC significantly when the number of errors is high

Passive network tomography for erroneous networks: A network coding approach

Passive network tomography uses end-to-end observations of network communication to characterize the network, for instance to estimate the network topology and to localize random or adversarial glitches. Under the setting of linear network coding this work provides a comprehensive study of passive network tomography in the presence of network (random or adversarial) glitches. To be concrete, this work is developed along two directions: 1. Tomographic upper and lower bounds (i.e., the most adverse conditions in each problem setting under which network tomography is possible, and corresponding schemes (computationally efficient, if possible) that achieve this performance) are presented for random linear network coding (RLNC). We consider RLNC designed with common randomness, i.e., the receiver knows the random code-books all nodes. (To justify this, we show an upper bound for the problem of topology estimation in networks using RLNC without common randomness.) In this setting we present the first set of algorithms that characterize the network topology exactly. Our algorithm for topology estimation with random network errors has time complexity that is polynomial in network parameters. For the problem of network error localization given the topology information, we present the first computationally tractable algorithm to localize random errors, and prove it is computationally intractable to localize adversarial errors. 2. New network coding schemes are designed that improve the tomographic performance of RLNC while maintaining the desirable low-complexity, throughput-optimal, distributed linear network coding properties of RLNC. In particular, we design network codes based on Reed-Solomon codes so that a maximal number of adversarial errors can be localized in a computationally efficient manner even without the information of network topology.Comment: 40 pages, under submission for IEEE Trans. on Information Theor