Research On Repeat Accumulate Decoding Algorithms

The goal of communication field is to increase the reliability and validity of information transmission. With the development of channel coding technology, especially the advancement of the Tubro code and LDPC code, etc, the performance of channel coding algorithm is extremely close to the performance of Shannon capacity. Although Tubro coding is provided with good encoding complexity and performance, decoding algorithm is rather complicated because it adopts the maximum a posteriori probability (MAP) algorithm; LDPC coding is provided with good decoding complexity and performance, but the encoding algorithm of it is complicated, and coding complexity and code length is in square relationship. The target of channel coding research is to find a good code which has both the linear encoding and decoding complexity, and performance that closes to Shannon limit. The encoding algorithm of Repeat Accumulate (RA) code is simple, which is similar to that of Turbo code, and its check matrix is sparse matrix (the same characteristics with LDPC code), which can decode by adopting decoding algorithm of high-speed parallel Belief Propagation (BP) algorithm. With the advantages of both Turbo code and LDPC code, RA code can encode and decode within linear time. Besides, due to the fact that RA code has the performance which is close to Shannon limit, it has become the research topic in the field of channel coding.Based on the previous research, this thesis will make a deep study of RA code based on the Tanner graph of BP algorithm, analyze the performance of different decoding algorithm of RA code, and put forward an improved decoding algorithm base on BP algorithm which can obtain better effect. The contents of the research are mainly divided into the following aspects:1) Introduce the system model, integrated digital communication system model; introduce the Tanner graph, a widely applied and schematized mode of encoding and decoding; analyze the graphics based BP algorithm and the derivation process of Belief Propagation.2) Introduce RA and the irregular RA encoding and decoding algorithm and provide the corresponding Tanner graph and check matrix respectively; present the performance of the RA code and the irregular RA code based on BP algorithm and analyze the major factors that influence the performance.3) Introduce different decode algorithm of RA code systematically and present the detail algorithm process and the change of complexity and performance under the comparison with BP algorithm; BP algorithm calculates through complex functions which affects the application in the practical communication systems. Although minimum algorithm has the relative low complexity, it reduces the performance intensely. In response to this, researchers put forward a series of algorithms to improve the minimum and BP algorithm, but the reduction of complexity also brings with the reduction of performance. In order to solve this contradiction, this thesis puts forward an improved BP decoding algorithm. By using the piecewise linear function to approximate the primitive function, which transformed and simplified by BP algorithm, while obtaining an adjusted value by look-up table method, it can revise the error between the approximate function and transformed primitive function by this adjusted value. It can reduce the complexity of algorithm and at the same time keep the performance closed to BP algorithm.