In this paper, a low complexity and memory-efficient concatenated codes called Parallel Interleaved Concatenated Gallager Codes are presented.
本文提出了一种具有低复杂度和低存储需求的并行级联码—并行交织级联Gallager码。
Low Density Parity-Check Codes were first discovered by Gallager in the early 1960s and recently have been rediscovered and generalized.
低密度奇偶校验码码是由Gallager在1962年首先提出的一种纠错码，在沉寂了多年之后，最近又重新成为通信技术研究的热点。
Parallel concatenated gallager codes are a new kind of concatenated codes based on component LDPC codes. They show the low complexity of encoding while maintaining a good performance compared to LDPC codes.
PCGC码是一种以LDPC码作为分量码的新型级联码，它在继承LDPC码优越的误比特率性能的同时，还拥有比LDPC码更低的编码复杂度。
Gallager put forward Low-Density Parity-Check Codes firstly, which were a kind of linear block codes that can be defined by the sparse parity-check matrix or the factor graph.
Gallager提出的，它是一类可以用稀疏校验矩阵或因子图进行描述的线性分组码，具有接近Shannon限的良好性能和因子图等有效的分析工具，因而近年来成为纠错码领域的研究热点。
LDPC codes were first introduced by Gallager in 1962 and were verified to possess superior properties in error-correcting field. Unfortunately, the past technology in 1960s wasn`t advanced enough to support their hardware implementation complexity.
低密奇偶校验编码最早是由Robert Gallager博士在1962於其博士文中发表，并且已被证实具有极为优越的性能。
Low-density Parity-check codes, introduced by Gallager in 1962, are linear block codes defined in terms of a sparse parity check matrix. Gallager came out two creative viewpoints:(1) to imitate the random codes by using the random permutation and the cascade of the simple sparse parity check matrix; (2) iterative decoding technique where a prior information and channel observation are both used to compute a posteriori and a priori information.
1962，Gallager提出了基于稀疏校验矩阵的线性分组码，即低密度分组校验(Low Density Parity-Check)码，他提出了两个创造性的观点：(1)用简单的稀疏校验矩阵的随机置换和级联来模拟随机码；(2)在信息的先验概率和信道特性已知情况下的迭代译码方法。
Low-density parity-check codes, Parallel Interleaved Concatenated Gallager Codes, low complexity, memory-efficient
低密度奇偶校验码，并行交织级联Gallager码，低复杂度，低存储量
In the scatter density evolution analysis, we get the evolution of the bit error probability in iterative decoding and the convergence of it under the control of a given original bit error probability.
在离散密度进化分析中，使用了Gallager最早提出的硬判决译码算法，获得了迭代译码中误码率的进化，得到在一定初始误码率的条件下，译码误码率的收敛情况。
It includes the methods of Gallager and Mackay. And some other construction methods based on finite geometry, graph theory and group theory are also depicted.
包括最早由Gallager提出的构造方法、Mackay对其改进的构造方法、基于有限几何、图论及群论上的构造方法等。
It is provided the detailed deduction and demonstration of the Gallager soft and hard decision decoding algorithm.
给出了Gallager软判决和硬判决译码算法的详细推导和证明，对置信传播译码算法在不同码长和迭代次数下进行了仿真和性能分析。
Simulation results demonstrated that the modified codes is better than Gallager codes when block length is small.
仿真结果表明，改进的编码在分组长度较短时甚至优于Gallager码的性能。
Low density parity-check (LDPC) code was proposed in 1962 by Gallager, which is a kind of linear block codes based on a sparse check matrix. its decoding performance can achieve Shannon Limit.
低密度奇偶校验（LDPC）码是由Gallager于1962年提出的一种基于稀疏校验矩阵的线性分组码，具有逼近香农限的良好译码性能。
To reduce the computation complexity of the decoder of parallel concatenated Gallager code, two kinds of low complexity stop criterion were proposed.
提出了两种低复杂度的终止准则，以用于降低PCGC（并行级联Gallager码，ParallelConcatenatedGallagerCode）的译码器运算量。
Low-Density Parity-Check (LDPC) code is a class of linear block code which has the sparse check matrix, was firstly introduced by Gallager in 1962.
低密度奇偶校验（LDPC）码是Gallager在1962年提出的一种基于稀疏校验矩阵的线性分组码。
LDPC (Low Density Parity Check Code) was initially proposed by Gallager in his doctoral dissertation in 1962, and it is also called Gallager code. It is a kind of linear block error-correcting code that is represented by very sparse matrix.
低密度奇偶校验（LowDensityParityCheckcode，LDPC）码是Gallager于1962年在他的博士论文中首次提出的一种可以用非常稀疏的校验矩阵表示的线性分组纠错码，亦称Gallager码。
Because the computing condition is limited and most people consider that concatenated coder is easy to implement, people ignore Gallager codes little by little.
由于当时计算机水平发展有限和人们普遍认为级联码更易于实现，导致人们逐渐忽视了Gallager码的存在。