Achieving the Secrecy Capacity of Wiretap Channels Using Polar Codes

By Hessam Mahdavifar, Alexander Vardy. IEEE Transactions on Information Theory, 2010

541 citations recorded by the source corpus.

Suppose that Alice wishes to send messages to Bob through a communication channel C1, but her transmissions also reach an eavesdropper Eve through another channel C2. This is the wiretap channel model introduced by Wyner in 1975. The goal is to design a coding scheme that makes it possible for Alice to communicate both reliably and securely. Reliability is measured in terms of Bob's probability of error in recovering the message, while security is measured in terms of the mutual information between the message and Eve's observations. Wyner showed that the situation is characterized by a single constant Cs, called the secrecy capacity, which has the following meaning: for all ε >; 0, there exist coding schemes of rate R ≥ Cs-ε that asymptotically achieve the reliability and security objectives. However, his proof of this result is based upon a random-coding argument. To date, despite consider able research effort, the only case where we know how to construct coding schemes that achieve secrecy capacity is when Eve's channel C2 is an erasure channel, or a combinatorial variation thereof. Polar codes were recently invented by Arikan; they approach the capacity of symmetric binary-input discrete memoryless channels with low encoding and decoding complexity. In this paper, we use polar codes to construct a coding scheme that achieves the secrecy capacity for a wide range of wiretap channels. Our construction works for any instantiation of the wiretap channel model, as long as both C1 and C2 are symmetric and binary-input, and C2 is degraded with respect to C1. Moreover, we show how to modify our construction in order to provide strong security, in the sense defined by Maurer, while still operating at a rate that approaches the secrecy capacity. In this case, we cannot guarantee that the reliability condition will also be satisfied unless the main channel C1 is noiseless, although we believe it can be always satisfied in practice.

Subfields: Computer Networks and Communications, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/933ba7a063598c4448e50c99f28fc6554bebdea7

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Citations in the corpus

Secure Multiterminal Source Coding With Side Information at the Eavesdropper (2011, unknown): “, nested codes for (Gaussian and binary) type-II wiretap channels [36], LDPC [37] and lattice [38] codes for the Gauss ian wiretap channel, polar codes for binary symmetric channels [39], and construction of sec ur codes from ordinary channel codes [40].”
Principles of Physical Layer Security in Multiuser Wireless Networks: A Survey (2010, methodology): “The recently proposed polar coding scheme has been shown to achieve the secrecy capacity for binary symmetric and deterministic wiretap channels [217], [218].”
How to Construct Polar Codes (2011, background): “In terms of applications, polar coding has been used with great success in the context of multiple-access channels [2,23], wiretap channels [16], data compression [1,4], write-once channels [6], and channels with memory [21].”
A Semi-Parallel Successive-Cancellation Decoder for Polar Codes (2013, background): “Polar codes were also shown to be good at solving other information theoretic problems in an efficient manner [6]–[8].”
A Survey on Multiple-Antenna Techniques for Physical Layer Security (2017, background): “, Wyner codes [4], polar codes [7], and low-density paritycheck (LDPC) codes [8], to guarantee communication security and reliability simultaneously at physical layer based on the randomness of wireless channels.”
Physical Layer Security for Next Generation Wireless Networks: Theories, Technologies, and Challenges (2017, methodology): “coding [177], [178], and polar coding [179] were proposed to Fig.”
A Survey of Physical Layer Security Techniques for 5G Wireless Networks and Challenges Ahead (2018, methodology): “It is proved in [22] that this coding scheme can achieve the secrecy capacity.”
Classifications and Applications of Physical Layer Security Techniques for Confidentiality: A Comprehensive Survey (2019, background): “In [47], a new multi-block polar coding scheme is introduced on top of [45] to resolve the difficulty in providing both strong security and reliability using polar codes, which occurs due to the existence of a small number of bit-channels that are both unreliable and unsecure.”