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We obtain a necessary and sufficient condition for the security of multi-source linear network codes by studying the algebraic structure of such codes. This condition is useful for analyzing the security of such linear network codes, and it applies in cases when the random keys do not necessarily have uniform distributions. This condition also shows that the security of a linear network code does not depend on the source distribution.

We determine the secrecy capacity of the compound channel with quantum wiretapper and channel state information at the transmitter. Moreover, we derive a lower bound on the secrecy capacity of this channel without channel state information and determine the secrecy capacity of the compound classical-quantum wiretap channel with channel state information at the transmitter. We use this result to derive a proof for a lower bound on the entanglement generating capacity of the compound quantum channel. We also derive a proof for the formula for entanglement generating capacity of the compound quantum channel with channel state information at the encoder which was given in additional information [Bjelaković, Boche, and Nötzel, in Proceedings of International Symposium on Information Theory ISIT, Korea, 2009 (IEEE, New York, 2009), pp. 1889–1893].

For a multiple input channel, one may define different capacity regions, according to the criterions of error, types of codes, and presence of feedback. In this paper, we aim to draw a complete picture of relations among these different capacity regions. To this end, we first prove that the average-error-probability capacity region of a multiple input channel can be achieved by a random code under the criterion of maximum error probability. Moreover, we show that for a non-deterministic multiple input channel with feedback, the capacity regions are the same under two different error criterions. In addition, we discuss two special classes of channels to shed light on the relation of different capacity regions. In particular, to illustrate the roles of feedback, we provide a class of MAC, for which feedback may enlarge maximum-error-probability capacity regions, but not average-error-capacity regions. Besides, we present a class of MAC, as an example for which the maximum-error-probability capacity regions are strictly smaller than the average-error-probability capacity regions (first example showing this was due to G. Dueck). Differently from G. Dueck’s enlightening example in which a deterministic MAC was considered, our example includes and further generalizes G. Dueck’s example by taking both deterministic and non-deterministic MACs into account. Finally, we extend our results for a discrete memoryless two-input channel, to compound, arbitrarily varying MAC, and MAC with more than two inputs.

The continuous-time asynchronous channel as a model for time jitter in a communication system with no common clock between the transmitter and the receiver was introduced in N. Cai and R.W. Yeung (2002). The paper unveiled that it is not necessary for the receiver clock to re-synchronize with the transmitter clock within a fixed maximum time in order to achieve reliable communication. In this paper, the runlength limited code is shown not to be optimal for this channel model. An upper bound on the rate loss is given for the constraint that the transmitter and receiver clocks cannot be out of synchronization for a fixed maximum time. The probabilistic capacity of the asynchronous channel is determined and the result is used to design an optimal code. The relation between coding in constrained channels and random number generation is also discussed.

We study the asymptotically-achievable rate region of subspace codes for wireless network coding, where receivers have different link capacities due to the access ways or the faults of the intermediate links in the network. Firstly, an outer bound of the achievable rate region in a two-receiver network is derived from a combinatorial method. Subsequently, the achievability of the outer bound is proven by code construction, which is based on superposition coding. We show that the outer bound can be achieved asymptotically by using the code presented by Koetter and Kschischang, and the outer bound can be exactly attained in some points by using a q-analog Steiner structure. Finally, the asymptotically-achievable rate region is extended to the general case when the network has m receivers with different levels.