Performances analysis of polar codes decoding algorithms over variant binary-input channels

A cooperative partial message relaying (CPMR) scheme based on distributed polar codes (DPC) is proposed to achieve the maximal decode-and-forward (DF) rate of the stochastically degraded symmetric binary-input two-relay network with orthogonal receiver components (TRN-ORCs). In the proposed scheme, the code design problem of the degraded TRN-ORCs is transformed into a problem of polar codes with CPMR protocol. According to the nested structure of polar codes, the messages transmitted by the source and the first relay are recovered successfully at the two relays, respectively, and then the two relays yield correct partial messages for transmission to solve the uncertainty of the source message at the destination. With the help of the CPMR protocol, the destination should be able to reconstruct the source message correctly. In addition to the practical consideration of the construction of the CPMR protocol based on DPC, we also derived that the block error probability of the proposed scheme can be upper bounded by O(2-Nβ) for any constant β (0 < β < ½), and sufficiently large block length N.

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Novel Low Complexity BP Decoding Algorithms for Polar Codes: Simplifying on Non-Linear Operations

Electronics ◽

10.3390/electronics11010093 ◽

2021 ◽

Vol 11 (1) ◽

pp. 93

Author(s):

Yuhuan Wang ◽

Jianguo Li ◽

Neng Ye ◽

Xiangyuan Bu

Keyword(s):

Computational Complexity ◽

Hardware Implementation ◽

Low Complexity ◽

Bp Algorithm ◽

Polar Codes ◽

Decoding Algorithm ◽

Hyperbolic Tangent ◽

Decoding Algorithms ◽

Tangent Function ◽

Non Linear

The parallel nature of the belief propagation (BP) decoding algorithm for polar codes opens up a real possibility of high throughput and low decoding latency during hardware implementation. To address the problem that the BP decoding algorithm introduces high-complexity non-linear operations in the iterative messages update process, this paper proposes to simplify these operations and develops two novel low complexity BP decoding algorithms, namely, exponential BP (Exp-BP) decoding algorithm and quantization function BP (QF-BP) decoding algorithm. The proposed algorithms simplify the compound hyperbolic tangent function by using probability distribution fitting techniques. Specifically, the Exp-BP algorithm simplifies two types of non-linear operations into single non-linear operation using the piece-wise exponential model function, which can approximate the hyperbolic tangent function in the updating formula. The QF-BP algorithm eliminates non-linear operations using the non-uniform quantization in the updating formula, which is effective in reducing computational complexity. According to the simulation results, the proposed algorithms can reduce the computational complexity up to 50% in each iteration with a loss of less than 0.1 dB compared with the BP decoding algorithm, which can facilitate the hardware implementation.

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A Parallel Decoding Algorithm for Short Polar Codes Based on Error Checking and Correcting

The Scientific World JOURNAL ◽

10.1155/2014/895782 ◽

2014 ◽

Vol 2014 ◽

pp. 1-14

Author(s):

Yingxian Zhang ◽

Xiaofei Pan ◽

Kegang Pan ◽

Zhan Ye ◽

Chao Gong

Keyword(s):

Optimization Problem ◽

Optimal Solution ◽

Polar Codes ◽

Code Length ◽

Decoding Algorithm ◽

Parallel Method ◽

Decoding Algorithms ◽

Parallel Decoding ◽

Error Checking ◽

Maximization Principle

We propose a parallel decoding algorithm based on error checking and correcting to improve the performance of the short polar codes. In order to enhance the error-correcting capacity of the decoding algorithm, we first derive theerror-checking equationsgenerated on the basis of the frozen nodes, and then we introduce the method to check the errors in the input nodes of the decoder by the solutions of these equations. In order to further correct those checked errors, we adopt the method of modifying the probability messages of the error nodes with constant values according to the maximization principle. Due to the existence of multiple solutions of theerror-checking equations, we formulate a CRC-aided optimization problem of finding the optimal solution with three different target functions, so as to improve the accuracy of error checking. Besides, in order to increase the throughput of decoding, we use a parallel method based on the decoding tree to calculate probability messages of all the nodes in the decoder. Numerical results show that the proposed decoding algorithm achieves better performance than that of some existing decoding algorithms with the same code length.

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