Secrecy Coding for the Binary Symmetric Wiretap Channel via Linear Programming

In this paper, we use a linear programming (LP) optimization approach to evaluate the equivocation for a wiretap channel where the main channel is noiseless, and the wiretap channel is a binary symmetric channel (BSC). Using this technique, we present an analytical limit for the achievable secrecy rate in the finite blocklength regime that is tighter than traditional fundamental limits. We also propose a secrecy coding technique that outperforms random binning codes. When there is one overhead bit, this coding technique is optimum and achieves the analytical limit. For cases with additional bits of overhead, our coding scheme can achieve equivocation rates close to the new limit. Furthermore, we evaluate the patterns of the generator matrix and the parity-check matrix for linear codes and we present binning techniques for both linear and non-linear codes using two different approaches: recursive and non-recursive. To our knowledge, this is the first optimization solution for secrecy coding obtained through linear programming.Comment: Submitted for possible Journal publicatio

Double-Staged Syndrome Coding Scheme for Improving Information Transmission Security over the Wiretap Channel

This paper presents a study of a syndrome coding scheme for different binary linear error correcting codes that refer to the code families such as BCH, BKLC, Golay, and Hamming. The study is implemented on Wyner’s wiretap channel model when the main channel is error-free and the eavesdropper channel is a binary symmetric channel with crossover error probability (0 < Pe ≤ 0.5) to show the security performance of error correcting codes while used in the single-staged syndrome coding scheme in terms of equivocation rate. Generally, these codes are not designed for secure information transmission, and they have low equivocation rates when they are used in the syndrome coding scheme. Therefore, to improve the transmission security when using these codes, a modified encoder which consists of a double-staged syndrome coding scheme, is proposed. Two models are implemented in this paper: the first model utilizes one encoding stage of the conventional syndrome coding scheme. In contrast, the second model utilizes two encoding stages of the syndrome coding scheme to improve the results obtained from the first model. The C++ programming language, in conjunction with the NTL library, is used for obtaining simulation results for the implemented models. The equivocation rate results from the second model were compared to both the results of the first model and of the unsecured transmission (transmission of data without encryption). The comparison revealed that the security performance of the second model is better than the first model and the insecure system, as the equivocation for all the simulated codes over the proposed model reaches at least %97 at the Pe = 0.1.

Subspace Decomposition of Coset Codes

A new method is explored for analyzing the performance of coset codes over the binary erasure wiretap channel (BEWC) by decomposing the code over subspaces of the code space. This technique leads to an improved algorithm for calculating equivocation loss. It also provides a continuous-valued function for equivocation loss, permitting proofs of local optimality for certain finite-blocklength code constructions, including a code formed by excluding from the generator matrix all columns which lie within a particular subspace. Subspace decomposition is also used to explore the properties of an alternative secrecy code metric, the chi squared divergence. The chi squared divergence is shown to be far simpler to calculate than equivocation loss. Additionally, the codes which are shown to be locally optimal in terms of equivocation are also proved to be globally optimal in terms of chi squared divergence.Comment: 36 pages, 2 figures, submitted to Transactions on Information Theor