Polar Coding for the Broadcast Channel With Confidential Messages: A Random Binning Analogy

Abstract

Abstract-We develop a low-complexity polar coding scheme for the discrete memoryless broadcast channel with confidential messages under strong secrecy and randomness constraints. Our scheme extends previous work by using an optimal rate of uniform randomness in the stochastic encoder, and avoiding assumptions regarding the symmetry or degraded nature of the channels. The price paid for these extensions is that the encoder and decoders are required to share a secret seed of negligible size and to increase the block length through chaining. We also highlight a close conceptual connection between the proposed polar coding scheme and a random binning proof of the secrecy capacity region.

Polar codes for covert communications over asynchronous Discrete Memoryless Channels

“…Note that this falls short of 1 √ n , which would be required for the square-root-law of communication. Nevertheless, we are now able to extend Lemma 3 and Lemma 4 of [11] to the finite length regime, which forms the basis of our construction for covert communications.…”

“…Our code construction exploits recent results on polar codes that suggest how information-theoretic proofs exploiting source coding with side information and privacy amplification as primitives [16,17] may be converted into polar coding schemes by a suitable identification of polarization sets [11,18]. Specifically, the approach consists in recognizing that both primitives have counterparts based on polar codes, see Lemma 3 and Lemma 4 of [11], as well as [19,20].…”

“…In that regard, calling our codes "polar codes" is a slight abuse of terminology but follows standard practice [11,18,20]. Strictly speaking, our codes are only "polarization-based".…”

Strong secrecy on a class of Degraded Broadcast Channels using polar codes

“…Polar codes for the binary symmetric degraded wiretap channel were introduced in [9] and [10], and provide secrecy-capacity achieving polar codes under the weak and the strong secrecy condition, respectively. Recently, polar coding has been extended to the general wiretap channel in [11]- [14]. Furthermore, [13] and [14] generalize their results providing polar coding schemes for the broadcast channel with confidential messages and [12] also proposes polar coding strategies to achieve the best-known inner bounds on the secrecy-capacity region of some multi-user settings.…”

“…Recently, polar coding has been extended to the general wiretap channel in [11]- [14]. Furthermore, [13] and [14] generalize their results providing polar coding schemes for the broadcast channel with confidential messages and [12] also proposes polar coding strategies to achieve the best-known inner bounds on the secrecy-capacity region of some multi-user settings.…”