On the Construction of Polar Codes for Achieving the Capacity of Marginal Channels

Achieving security against adversaries with unlimited computational power is of great interest in a communication scenario. Since polar codes are capacity achieving codes with low encoding-decoding complexity and they can approach perfect secrecy rates for binary-input degraded wiretap channels in symmetric settings, they are investigated extensively in the literature recently. In this paper, a polar coding scheme to achieve secrecy capacity in non-symmetric binary input channels is proposed. The proposed scheme satisfies security and reliability conditions. The wiretap channel is assumed to be stochastically degraded with respect to the legitimate channel and message distribution is uniform. The information set is sent over channels that are good for Bob and bad for Eve. Random bits are sent over channels that are good for both Bob and Eve. A frozen vector is chosen randomly and is sent over channels bad for both. We prove that there exists a frozen vector for which the coding scheme satisfies reliability and security conditions and approaches the secrecy capacity. We further empirically show that in the proposed scheme for non-symmetric binary-input discrete memoryless channels, the equivocation rate achieves its upper bound in the whole capacity-equivocation region

Strong Secrecy on a Class of Degraded Broadcast Channels Using Polar Codes

Different polar coding schemes are proposed for the memoryless degraded broadcast channel under different reliability and secrecy requirements: layered decoding and/or layered secrecy. In this setting, the transmitter wishes to send multiple messages to a set of legitimate receivers keeping them masked from a set of eavesdroppers. The layered decoding structure requires receivers with better channel quality to reliably decode more messages, while the layered secrecy structure requires eavesdroppers with worse channel quality to be kept ignorant of more messages. The implementation of the proposed polar coding schemes is discussed and their performance is evaluated by simulations for the symmetric degraded broadcast channel.Comment: 35 pages. Published in "MDPI Entropy". A short version of this paper had been accepted to the 3rd Workshop on Physical-Layer Methods for Wireless Security, IEEE CNS 201

Polar Coding for the Large Hadron Collider: Challenges in Code Concatenation

In this work, we present a concatenated repetition-polar coding scheme that is aimed at applications requiring highly unbalanced unequal bit-error protection, such as the Beam Interlock System of the Large Hadron Collider at CERN. Even though this concatenation scheme is simple, it reveals significant challenges that may be encountered when designing a concatenated scheme that uses a polar code as an inner code, such as error correlation and unusual decision log-likelihood ratio distributions. We explain and analyze these challenges and we propose two ways to overcome them.Comment: Presented at the 51st Asilomar Conference on Signals, Systems, and Computers, November 201