Aiming at the popular wireless multi-hop network, this paper proposes a concise and practical endurance network coding scheme which can nearly reach the capacity of wireless multi-hop network. In this scheme, the source node encodes a group of packets to be sent, the intermediate node expands and forwards the received coded packets by using a causal systematic upper triangular recoding matrix, and the receiver node judges a whole group of packets received and sends feedback to the sender according to whether it is decodable. These operations have three advantages: 1) Increase the probability of first transmission and reducing the number of retransmission; 2) The flow transmission and expansion on intermediate nodes ensure low latency and improve reliability respectively; 3) Feedback can further increase reliability and throughput. Through analysis and simulation results, we prove that the proposed scheme can achieve a better compromise between throughput and packet delay. Furthermore, the transmission scheme can be compatible with a variety of existing coding methods to ensure the above performance of throughput and delay while maintaining their respective advantages.

Enabling remote data integrity checking with failure recovery becomes exceedingly critical in distributed cloud systems. With the properties of a lower repair bandwidth while preserving fault tolerance, regenerating coding and network coding (NC) have received much attention in the coding-based storage field. Recently, an outstanding outsourced auditing scheme named NC-Audit was proposed for regenerating-coding-based distributed storage. The scheme claimed that it can effectively achieve lightweight privacy-preserving data verification remotely for these networked distributed systems. However, our algebraic analysis shows that NC-Audit can be easily broken due to a potential defect existing in its schematic design. That is, an adversarial cloud server can forge some illegal blocks to cheat the auditor with a high probability when the coding field is large. From the perspective of algebraic security, we propose a remote data integrity checking scheme RNC-Audit by resorting to hiding partial critical information to the server without compromising system performance. Our evaluation shows that the proposed scheme has significantly lower overhead compared to the state-of-the-art schemes for distributed remote data auditing.

We consider a unicast network with an adversary who is able to attack a proportion of edges, which is no more than p for some 0 <; p <; 1. Based on the knowledge of the adversary, three cases of attacks are considered: 1) the adversary knows nothing about the source message; 2) the adversary knows the source message but does not know the transmitted codeword; and 3) the adversary knows the transmitted codeword. Two classes of code schemes, deterministic code and stochastic code, are designed to assure reliable transmission against the adversarial attack. It is concluded that stochastic code does not provide any more benefit than the deterministic code does against the attacking cases 1 and 3. However, when the attacking case 2 is considered, stochastic code would achieve a higher capacity than the deterministic code does.

We consider a unicast network with an adversary who is able to attack a proportion of edges, which is no more than p for 0 <; p <; 1. Based on the knowledge of the adversary, three cases of attacks are considered: 1) the adversary knows nothing about the source message; 2) the adversary knows the source message but does not know the transmitted codeword; 3) the adversary knows the transmitted codeword. Two classes of code schemes, deterministic code and stochastic code, are designed to assure reliable transmission against the adversarial attack. It is concluded that stochastic code does not provide any more benefit than the deterministic code against the attacking cases 1 and 3. However, when the attacking case 2 is considered, stochastic code would achieve a higher capacity than the deterministic code.

This paper is a summary version of [4]. A new coding scheme is proposed to establish a lower bound on the strong secrecy capacity of stochastic code over the general arbitrarily varying wiretap channel. Moreover, the lower bound is the secrecy capacity when the main channel is less noisy than the wiretap channel. The main idea is to construct secure partitions over the “good” codebook by extending Csiszár's almost independent coloring scheme. This new scheme provides a fundamental tool to deal with the strong secrecy problems of wiretap channels.

The zero-error capacity of a channel is defined as the maximum rate at which it is possible to transmit information with zero probability of error. In this paper, we settle all previously unsolved cases for the zero-error capacity of binary channels with one memory.

The decoding problem is addressed in this paper for the scenario that convolutional codes are employed at the source node of the network with linear or convolutional network coding for error correction. Since network errors may disperse or neutralize due to network coding, decoding cannot be done at sink nodes merely based on the minimum Hamming distance between the received and sent sequence. Source decoding is proposed in previous work by multiplying the inverse of the network transfer matrix, where the inverse is hard to compute and sometimes the result is noncausal. Starting from the Maximum A Posteriori (MAP) decoding criterion, we find that it is equivalent to the minimum error weight under our model. Inspired by classical Viterbi algorithm, we propose a Viterbi-like decoding algorithm based on the minimum error weight of combined error vectors, which can be carried out directly at sink nodes and can correct any network errors within the capability of convolutional network error correction codes (CNECC). We then study the distributed decoding of CNECC and give a sufficient condition that is able to realize such a decoding process with the proposed algorithm.

The zero error capacity of a channel is defined as the least upper bound of rates at which it is possible to transmit information with zero probability of error. Unsolved cases are addressed in this paper to complement the table of the zero error capacity of noisy binary channels with 1-memory. All cases are classified according to the isomorphic property of their confusability graphs, and then we determine the zero error capacity of the rest binary channels with 1-memory one by one.

We consider an Adaptive Random Convolutional Network Coding (ARCNC) algorithm to address the issue of field size in random network coding for multicast, and study its memory and decoding delay performances through both analysis and numerical simulations. ARCNC operates as a convolutional code, with the coefficients of local encoding kernels chosen randomly over a small finite field. The cardinality of local encoding kernels increases with time until the global encoding kernel matrices at the related sink nodes have full rank. ARCNC adapts to unknown network topologies without prior knowledge, by locally incrementing the dimensionality of the convolutional code. Because convolutional codes of different constraint lengths can coexist in different portions of the network, reductions in decoding delay and memory overheads can be achieved. We show that this method performs no worse than block linear network codes in terms of decodability, and can provide significant gains in terms of average decoding delay or memory in combination, shuttle and random geometric networks.

We propose an efficient Adaptive Random Convolutional Network Coding (ARCNC) algorithm to address the issue of field size in random network coding. ARCNC operates as a convolutional code, with the coefficients of local encoding kernels chosen randomly over a small finite field. The lengths of local encoding kernels increase with time until the global encoding kernel matrices at related sink nodes all have full rank. Instead of estimating the necessary field size a priori, ARCNC operates in a small finite field. It adapts to unknown network topologies without prior knowledge, by locally incrementing the dimensionality of the convolutional code. Because convolutional codes of different constraint lengths can coexist in different portions of the network, reductions in decoding delay and memory overheads can be achieved with ARCNC.We show through analysis that this method performs no worse than random linear network codes in general networks, and can provide significant gains in terms of average decoding delay in combination networks.