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This paper investigates properties of polar-polar concatenated codes and their potential applications. We start by reviewing previous work on stopping set analysis for conventional polar codes, which we extend in this paper to concatenated architectures. Specifically, we present a stopping set analysis for the factor graph of concatenated polar codes, deriving an upper bound on the size of the minimum stopping set. To achieve this bound, we propose new bounds on the size of the minimum stopping set for conventional polar code factor graphs. The tightness of these proposed bounds is investigated empirically and analytically. We show that, in some special cases, the exact size of the minimum stopping set can be determined with a time complexity of O(N), where N is the codeword length. The stopping set analysis motivates a novel construction method for concatenated polar codes. This method is used to design outer polar codes for two previously proposed concatenated polar code architectures: augmented polar codes and local-global polar codes. Simulation results with BP decoding demonstrate the advantage of the proposed codes over previously proposed constructions based on density evolution (DE). 

Error correction coding schemes with local-global decoding are motivated by practical data storage applications where a balance must be achieved between low latency read access and high data reliability. As an example, consider a 4KB codeword, consisting of four 1KB subblocks, that supports a local-global decoding architecture. Local decoding can provide reliable, low-latency access to individual 1KB subblocks under good channel conditions, while global decoding can provide a “safety-net” for recovery of the entire 4KB block when local decoding fails under bad channel conditions. Recently, Ram and Cassuto have proposed such local-global decoding architectures for LDPC codes and spatially coupled LDPC codes. In this paper, we investigate a coupled polar code architecture that supports both local and global decoding. The coupling scheme incorporates a systematic outer polar code and a partitioned mapping of the outer codeword to semipolarized bit-channels of the inner polar codes. Error rate simulation results are presented for 2 and 4 subblocks.