In this correspondence, we extend the Gaussian wiretap channel model introduced by Leung-Yan-Cheong and Hellman to the Gaussian wiretap channel with side information by introducing additive white Gaussian interference in the main channel, which is available to the encoder in advance. This model is also an extension of the dirty-paper channel introduced by Costa since its main channel is the dirty-paper channel. A perfect-secrecy-achieving coding strategy for the model is proposed. It is used to derive achievable rates with asymptotic perfect secrecy and an achievable rate-equivocation region. The achievable rates with asymptotic perfect-secrecy are then compared to upper and lower bounds. The comparison indicates that the proposed coding strategy is optimal in some cases.

The noiseless wire-tap channel of type II with coset coding scheme was provided by Ozarow and Wyner. In this correspondence, the user is split into multiple parties who are coordinated in coding their data symbols by using the same encoder. The adversary can tap not only partial transmitted symbols but also partial data symbols. We are interested in the equivocation of the data symbols to this adversary who has more power than that of Ozarow and Wyner. The generalized Hamming weight of Wei and the dimension/length profile (DLP) of Forney are extended to two-code formats: relative generalized Hamming weight and relative dimension/length profile (RDLP). Upper and lower bounds of the new concepts are investigated. They are useful to design a perfect secrecy coding scheme for the coordinated multiparty model. Under a general secrecy standard, the coordinated model can provide a higher transmission rate than an uncoordinated (time-sharing) model.

An inverse relative dimension/length profile (IRDLP) of a pair of codes was introduced to describe the equivocation. In this paper, the maximum distance separable (MDS) code is extended to a two-code format: relative MDS pair. For a code and a subcode, the pair is called a relative MDS pair if its inverse relative dimension-length profile (IRDLP) reaches the generalized singleton bound. We consider properties and constructions of relative MDS pairs.

This paper extends the Gaussian wiretap channel (GWC) model introduced by Leung-Yan-Cheong and Hellman (1978) to the Gaussian wiretap channel with side information (GWCSI) by adding an additive white Gaussian interference in the main channel, which is available to the encoder in advance. It can also be looked at as an extension of the dirty-paper channel (DPC) introduced by Costa (1983). We propose a coding strategy achieving perfect secrecy for the extended channel, called Gaussian wiretap channel with side information. The corresponding achievable rates with asymptotic perfect secrecy are obtained and compared to known upper and lower bounds.