Properties Of Polar Codes Research Articles

Id-PC: An Identification Scheme based on Polar Codes

ABSTRACT In this paper, two polar code-based identification schemes are proposed in which the polar codes are used instead of random codes. The security of the proposed identification schemes is based on the hardness of coding problems such as general decoding problem (GDP) and syndrome decoding problem (SDP). By exploiting the properties of polar codes in the proposed identification schemes, it does not need to save the parity check or generator matrix of polar codes completely as a public data. Therefore, the public data size of the proposed identification schemes is reduced up to 90% in comparison with the Stern and Veron identification schemes. Also, by using the efficient techniques of seed generation and compression, it is shown that the communication costs of the proposed identification schemes are reduced up to 53% compared to the Stern and Veron identification schemes. Moreover, security analyses show that the proposed identification schemes have low cheating probability and also have proper resistance against information set decoding attack.

Polar Codes for Informed Receivers

The problem of sending independent messages to a receiver which already has been informed a subset of messages as side information is studied. Which messages are available at the receiver is assumed to be oblivious to the transmitter. A simple yet powerful construction of codes for informed receivers based on polar codes is proposed to efficiently and fairly convert side information into reduction in probability of errors for any message side information. Compared with existing designs based on codes on graph or algebraic codes, the proposed construction is both conceptually and practically simple. Moreover, the codes inherit many good properties of polar codes, including explicit construction and low-complexity encoding and decoding scaling such as $\mathcal {O}(N\log N)$ where $N$ is the blocklength. Extensions to high-order modulation and block fading channels are also proposed. Simulation results indicate that for every side information configuration, the proposed codes can convert side information into reduction in signal-to-noise ratio of roughly 6 dB/bit at bit error rate of 10−5 under additive white Gaussian noise channel or block fading channel.

Efficient Polar Code-Based Physical Layer Encryption Scheme

This letter presents an efficient polar code-based physical layer encryption (PLE) scheme with a short key length in comparison to the conventional symmetric key cryptosystems. By using the properties of polar codes, we consider several efficient techniques to reduce the key length and the computational overhead of the presented PLE scheme. Moreover, the results of the security analyses show that the proposed scheme has a high level of security against conventional attacks on the PLE schemes. In fact, reducing the key length and the computational overhead of the presented PLE scheme has no effect on its security level, which makes it suitable for secure mobile communication devices with limited resources.

A Simple Proof of Fast Polarization

Fast polarization is a key property of polar codes. It was proved for the binary polarizing $2 \times 2$ kernel by Arikan and Telatar. The proof was later adapted to the general case by Sasoglu. We give a simplified proof.

Improved Successive-Cancellation Decoding of Polar Codes Based on Recursive Syndrome Decomposition

In this letter an improved method for the successive-cancellation decoding of polar codes is proposed. To avoid computations associated with redundant tree-traversals and syndrome calculations, recursive properties of polar codes are newly exploited in the proposed algorithm. Instead of computing a syndrome vector at every node, some syndrome vectors are directly obtained by recursively decomposing the syndrome vector computed previously. Furthermore, a modified syndrome check rule is proposed to prune unnecessary sub-trees efficiently. Compared with the latest pruning method, the proposed method reduces the latency by 23% for a (2048, 1024) polar code without sacrificing the error-correcting performance.

An Efficient Partial-Sum Network Architecture for Semi-Parallel Polar Codes Decoder Implementation

Polar codes have recently received a lot of attention because of their capacity-achieving performance and low encoding and decoding complexity. The performance of the successive cancellation decoder (SCD) of the polar codes highly depends on that of the partial-sum network (PSN) implementation. Hence, in this work, an efficient PSN architecture is proposed, based on the properties of polar codes. First, a new partial-sum updating algorithm and the corresponding PSN architecture are introduced which achieve a delay performance independent of the code length. Moreover, the area complexity is also reduced. Second, for a high-performance and area-efficient semi-parallel SCD implementation, a folded PSN architecture is presented to integrate seamlessly with the folded processing element architecture. This is achieved by using a novel folded decoding schedule. As a result, both the critical path delay and the area (excluding the memory for folding) of the semi-parallel SCD are approximately constant for a large range of code lengths. The proposed designs are implemented in both FPGA and ASIC and compared with the existing designs. Experimental result shows that for polar codes with large code length, the decoding throughput is improved by more than 1.05 times and the area is reduced by as much as 50.4%, compared with the state-of-the-art designs.

Polynomial Representations of Polar Codes and Decoding under Overcomplete Representations

This letter proposes an alternative expression of polar codes using polynomial representations. Polynomial representations may help to explore further algebraic properties of polar codes, same as those for convolutional codes. The relationship between message and codeword polynomials of polar codes indicates that polar codes are highly related to convolutional codes with generator polynomials 1+D and 1/(1+D). By using polynomial representations, we show the input and output bit shift properties of polar codes. This property is then employed to construct redundant trellises for overcomplete representations. Simulation results show that belief propagation (BP) decoding over the proposed overcomplete representation can achieve a significant performance gain as compared with BP decoding over the overcomplete representation using trellis permutations.