The definition of polar codes given by Arikan is explicit, but the construction complexity is an issue. This is due to the exponential growth in the size of the output alphabet of the bit-channels as the codeword length increases. Tal and Vardy recently presented a method for constructing polar codes which controls this growth. They approximated each bit-channel with a “better” channel and a “w...

Two constructive linear coding methods, previously proposed for the Wyner-Ziv problem, are developed to achieve all points of the key-leakage-storage regions of the generatedand chosen-secret models of biometric secrecy systems. The models also apply to physical unclonable functions that are realized by fine hardware variations. The linear coding is implemented by using nested polar codes and t...

In this paper, a polar-coded space-time transmit diversity (STTD) scheme is proposed in order to improve the performance of multiple-input multiple-output (MIMO) system. In Rician fading MIMO channels, the corresponding polar-coded STTD system can be equivalent to a single transmission channel for each polar code bit. Density evolutions for the polar-coded STTD systems are proposed based on the...

The asymptotic performance of a polar code under successive cancellation decoding is determined by the exponent of its polarizing matrix. We first prove that the partial distances of a polarizing matrix constructed from the Kronecker product are simply expressed as a product of those of its component matrices. We then show that the exponent of the polarizing matrix is shown to be a weighted sum...

In this paper, density evolution-based construction methods to design good polar codes on impulsive noise channels for single-carrier and multi-carrier systems are proposed and evaluated. For a single-carrier system, the tight bound of the block error probability (BLEP) is derived by applying density evolution and the performance of the proposed construction methods are compared. For the multi-...

This paper proposes a polar code construction scheme that reduces constituent-code supplemented decoding latency. Constituent codes are the sub-codewords with specific patterns. They are used to accelerate the successive cancellation decoding process of polar code without any performance degradation. We modify the traditional construction approach to yield increased number of desirable constitu...

—In this paper, we propose a decision-aided scheme for parallel SC-List decoding of polar codes. At the parallel SC-List decoder, each survival path is extended based on multiple information bits, therefore the number of split paths becomes very large and the sorting to find the top L paths becomes very complex. We propose a decision-aided scheme to reduce the number of split paths and thus red...

We show that the performance of iterative belief propagation (BP) decoding of polar codes can be enhanced by decoding over different carefully chosen factor graph realizations. With a genie-aided stopping condition, it can achieve the successive cancellation list (SCL) decoding performance which has already been shown to achieve the maximum likelihood (ML) bound provided that the list size is s...

We consider the problem of using polar codes over slow fading wireless channels. For design, we focus on a parallel slow fading channel with 2 blocks, and polar codes with rate ≤ 1 2 . Motivated by Arikan’s systematic polar code construction, we propose an interleaver design for a general polar code. The interleaver comprises of using the bit reversal of the order of polarized bit channels. Thi...