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.

In this letter, we consider the capacity results of network error correction coding over a general multicast network, where a malicious error occurs on each edge with a fixed probability p at each transmission. A pair of upper and lower bounds on the capacity are given, which are proved to coincide for a unicast network with |ε| parallel channels connected directly from source to sink node, where ε is the edge set of the network. A scheme with non-linear coding at the source and linear coding at the intermediate nodes is proposed, which achieves a strictly higher transmission rate than linear network coding.

This paper considers a special class of wiretap networks with a single source node and K sink nodes. The source message is encoded into a binary digital sequence of length N, divided into K subsequences, and sent to the K sink nodes respectively through noiseless channels. The legitimate receivers are able to obtain subsequences from arbitrary ${\mu }_1=K{\alpha }_1$ sink nodes. Meanwhile, there exist eavesdroppers who are able to observe subsequences from arbitrary ${\mu }_2=K{\alpha }_2$ sink nodes, where $0\le {\alpha }_2<{\alpha }_1\le 1$ . The goal is to let the receivers be able to recover the source message with a vanishing decoding error probability, and keep the eavesdroppers ignorant about the source message. It is clear that the communication model is an extension of wiretap channel II. Secrecy capacity with respect to the strong secrecy criterion is established. In the proof of the direct part, a codebook is generated by a randomized scheme and partitioned by Csiszár’s almost independent coloring scheme. Unlike the linear network coding schemes, our coding scheme is working on the binary field and hence independent of the scale of the network.

In this paper, we consider an end-to-end loss network with a limited delay and investigate the maximum network coding rate achievable under a given block length and error probability. We first formulate block network coding for reliable data transmission as an optimization problem and then analyze the throughput, success probability and delay in terms of block length and packet loss probability for block network coding. Results show that the coding rate gradually approaches the capacity 1 – ε as the delay increases, where ε is the packet loss probability. When feedback is allowed in the limited delay, the rate increases in a faster way compared with no retransmission.

Existing solutions against wiretapping attacks for network coding either bring significant bandwidth overhead or incur a high computational complexity. In order to reduce the security overhead of the existing solutions for securing network coding, a novel securing network coding paradigm is presented relying on two coding models: intra-generation coding and inter-generation coding. The basic idea to secure network coding using intra-generation coding is to limit the encryption operations for each generation, and then subject the scrambled and the remaining original source vectors to a linear transformation. This method is then generalized seamlessly using inter-generation coding by further exploiting the algebraic structure of network coding. We show that the proposed schemes have properties of low-complexity security, little bandwidth consumption, and high efficiency in integrating with the existing security techniques effectively.

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; 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.