  We consider polar subcodes (PSCs), which are polar codes (PCs) with
dynamically-frozen symbols, to increase the minimum distance as compared to
corresponding PCs. A randomized nested PSC construction with a low-rate PSC and
a high-rate PC, is proposed for list and sequential successive cancellation
decoders. This code construction aims to perform lossy compression with side
information. Nested PSCs are used in the key agreement problem with physical
identifiers. Gains in terms of the secret-key vs. storage rate ratio as
compared to nested PCs with the same list size are illustrated to show that
nested PSCs significantly improve on nested PCs. The performance of the nested
PSCs is shown to improve with larger list sizes, which is not the case for
nested PCs considered.
