Abstract: As a component code of irregular Repeat Accumulate（RA） codes，the accumulate code has no explicit EXIT function on general channels except the binary erasure channel.Usually，the EXIT curves of the accumulate code is obtained via simulation，which not only causes the major complexity in convergence analysis of irregular RA codes with the EXIT chart technique but also leads to a situation that the whole degree profile design procedure can be realized online.In this paper，first proves the equivalence of serial sum product decoding and the BCJR decoding of the accumulate code；then proves a stationary property for the internal decoding variables in the serial sum product decoding of the accumulate code；using these properties，this paper derives an implicit expression for the EXIT function of the accumulate code，which can be numerically solved efficiently.Simulation results agree with the numerical results and thus validate the proposed method.

Key words: accumulate code, Extrinsic Information Transfer（EXIT） chart, factor graph, sum product algorithm, BCJR algorithm

摘要： 累积码作为非规则RA码的分量码之一，除了在纠删信道上具有显式的EXIT函数之外，在一般信道上其EXIT曲线均由仿真获得。由仿真获得累积码EXIT曲线不但增加了非规则RA码的设计复杂度，而且使得整个设计过程无法实时完成。首先证明对于累积码而言，串行和积算法与BCJR算法是等价的；在此基础上，证明了累积码在串行和积译码时，与译码中间变量相关的互信息具有平稳特性；利用该平稳特性，推导了累积码EXIT函数的隐式表达式，从而给出一种求解累积码EXIT曲线的高效数值算法。采用该方法获得的EXIT曲线与仿真结果一致，能够显著降低非规则RA码的设计复杂度，并使非规则RA码的设计实时化。

关键词: 累积码, 外信息转移曲线, 因子图, 和积算法, BCJR算法