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We consider polar subcodes (PSCs), which are polar codes (PCs) withdynamically-frozen symbols, to increase the minimum distance as compared tocorresponding PCs. A randomized nested PSC construction with a low-rate PSC anda high-rate PC, is proposed for list and sequential successive cancellationdecoders. This code construction aims to perform lossy compression with sideinformation. Nested PSCs are used in the key agreement problem with physicalidentifiers. Gains in terms of the secret-key vs. storage rate ratio ascompared to nested PCs with the same list size are illustrated to show thatnested PSCs significantly improve on nested PCs. The performance of the nestedPSCs is shown to improve with larger list sizes, which is not the case fornested PCs considered.

Randomized Nested Polar Subcode Constructions for Privacy, Secrecy, and Storage