Generation Method of Multiple Polar Codes Based on Multiplicative Repetition

Abstract

The invention discloses a multiplicative repetition-based construction method for a non-binary polar code generation matrix, and mainly aims at solving the problem that the decoding complexity of an existing non-binary polar code is too high. According to the scheme, the method comprises the steps that the non-binary field size q is determined according to a modulation order m of the non-binary polar code; a finite field GF(q) is constructed according to the non-binary field size q, and a primitive element alpha of the non-binary field is determined; the needed non-binary code length n is determined according to the information length k and the code rate R; r non-zero field elements on the GF(q) are generated randomly; the structure of the non-binary polar code is nested by means of the non-zero field elements and non-binary polar code nuclear matrixes to generate a generation matrix with the code length of n, and bit flipping column permutation is conducted to construct the final generation matrix. The recursive decoding structure of the non-binary polar code generated by the generation matrix is consistent with that of a binary polar code, and the non-binary polar code has the low decoding complexity and can decrease the layer number of a decoding tree, enhance parallelization, achieve good performances by a small list size and be applied to a satellite communication system and a cellular communication system.

Description

technical field [0001] The invention belongs to the technical field of wireless communication, and in particular relates to a construction method of a multi-polarization code, which can be used in a satellite communication system and a cellular communication system. Background technique [0002] In order to achieve low latency and highly reliable transmission, polar codes with a high degree of parallelism are required to perform high-quality communication with a small decoding list size. The error index reflects the downward trend of the decoding error probability of the polar code under the generator matrix and the continuous cancellation (SC) decoding algorithm. The larger the index is, the faster the decoding error probability decreases. Therefore, using a kernel matrix with a large polarization index to construct polar codes, such as q-ary polar codes, has become an effective method to improve the performance of polar codes with limited length. [0003] In 2010, Mori an...

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Problems solved by technology

[0003] In 2010, Mori and Tanaka proposed in "Non-Binary Polar Codes using Reed-Solomon Codes and Algebraic Geometry Codes" that q-element polar codes can use the generator matrix of RS code or Hermitian code as the kernel matrix construction, but due to the RS code and The generation matrix of the Hermitian code is more complex, resulting in a sharp increase in the decoding complexity of the multi-polar code

In 2016, in "Encoder and List Decoder of Reed-Solomon Kernel Based Polar Codes", Cheng et al. used the 4-dimensional RS code on GF(4) as the 4-element polar code polarization kernel matrix, but the structure does not It is suitable for any q-element polar code, and it is still constructed based on the RS code generation matrix, which still has the disadvantage of high decoding complexity

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