LDPC code quadratic programming decoding method based on degree decomposition and alternating multiplier method

Abstract

The invention discloses an LDPC code quadratic programming decoding method based on degree decomposition and an alternating multiplier method. The LDPC code quadratic programming decoding method mainly solves the problems of slow decoding speed in the existing LDPC code mathematical programming decoding and error floors existing in information transmission decoding. The implementation scheme of the LDPC code quadratic programming decoding method comprises steps of: firstly, performing equivalent transformation on maximum likelihood decoding of an LDPC code into a linear integer programming model based on a decomposition verification equation; secondly, adding a penalty term to an objective function of linear integer programming, and slacking the equivalent linear integer programming modelinto a secondary programming model; and establishing an augmented Lagrange function according to the secondary programming model, and carrying out iterative solution on the augmented Lagrange functionby adopting an alternating direction multiplier method to obtain decoded codes. Compared with the existing decoding method based on mathematical programming, the LDPC code quadratic programming decoding method improves the decoding efficiency. Compared with the traditional BP decoding, the LDPC code quadratic programming decoding method reduces the error floors, and can be applied to magnetic storage, optical fiber communication and satellite digital video.

Description

technical field [0001] The invention belongs to the technical field of communication, in particular to a decoding method for low-density parity-check LDPC codes, which can be used in magnetic storage, optical fiber communication and satellite digital video. Background technique [0002] Low-density parity-check code LDPC is one of the best coding schemes that can approach the Shannon channel capacity limit. It has attracted the attention of domestic and foreign scholars and has been widely used in various communication fields. LDPC codes are usually decoded using the belief propagation BP algorithm. Since the BP algorithm is affected by many harmful characteristics in the codeword structure graph, including pseudo codewords, instantons, trap sets, etc., it is often affected by the error floor in the area of ​​high SNR, and the bit error rate varies with As the signal-to-noise ratio increases, it almost no longer decreases. Due to this, in systems that require high bit erro...

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Problems solved by technology

In addition, XiaoopengJiao et al. proposed a method of reducing projections to reduce the number of projections in the Alternate Direction Multiplier Algorithm ADMM, but this method requires a large number of odd-even polyhedron projection operations, which consumes a lot of decoding time

[0005] In all the above methods, the projection operation is still required for each iteration of the alternate direction multiplier algorithm ADMM, which prolongs the decoding time, and this operation is not easy to implement in practical applications

Although the decoding time of traditional BP decoding is shorter than that of the above-mentioned method using Alternating Direction Multiplier Algorithm ADMM, when the signal-to-noise ratio is high, BP decoding has better bit error performance than the above-mentioned method using Alternating Direction Multiplier Algorithm ADMM. Poor, there will be an error platform

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