Survey of Beyond-BP Decoding Algorithms: Theory and Applications

低密度奇偶校验码因其具有逼近香农限的优异性能,现已在多种标准和系统中得到广泛的应用。但为了使其能够满足不同应用场景下通信系统对纠错性能、计算复杂; 性、译码时延、硬件资源损耗以及功耗等方面的要求,需要对用于LDPC码译码的置信传播算法进行进一步的研究与改进。该文从译码算法的改进动机、方法论、; 计算复杂度以及性能表现等角度入手,对近些年出现的一些Beyond-BP译码算法进行了综述。并在最后对用于迭代接收系统的译码算法改进工作进行了讨论; ,为未来算法的改进工作提供一点思路。Low Density Parity Check (LDPC) codes are employed in several standards; and systems, due to their Shannon limit approaching ability. However, in; order to satisfy the communication systems' requirements at the aspects; of error correction ability, computing complexity, decoding latency,; hardware source consumption and power consumption under different; application circumstances, the Belief Propagation (BP) algorithm used; for decoding LDPC codes needs to be further investigated and improved.; In this survey, authors summarize several different Beyond-BP algorithms; from the aspects of motivation, methodology, complexity and performance.; Moreover, this survey also discusses the optimization of decoding; algorithms for iterative receive system, which can provide a reference; for further investigation on this topic.国家自然科学基

On The Analysis of Spatially-Coupled GLDPC Codes and The Weighted Min-Sum Algorithm

This dissertation studies methods to achieve reliable communication over unreliable channels. Iterative decoding algorithms for low-density parity-check (LDPC) codes and generalized LDPC (GLDPC) codes are analyzed. A new class of error-correcting codes to enhance the reliability of the communication for high-speed systems, such as optical communication systems, is proposed. The class of spatially-coupled GLDPC codes is studied, and a new iterative hard- decision decoding (HDD) algorithm for GLDPC codes is introduced. The main result is that the minimal redundancy allowed by Shannon’s Channel Coding Theorem can be achieved by using the new iterative HDD algorithm with spatially-coupled GLDPC codes. A variety of low-density parity-check (LDPC) ensembles have now been observed to approach capacity with iterative decoding. However, all of them use soft (i.e., non-binary) messages and a posteriori probability (APP) decoding of their component codes. To the best of our knowledge, this is the first system that can approach the channel capacity using iterative HDD. The optimality of a codeword returned by the weighted min-sum (WMS) algorithm, an iterative decoding algorithm which is widely used in practice, is studied as well. The attenuated max-product (AttMP) decoding and weighted min-sum (WMS) decoding for LDPC codes are analyzed. Applying the max-product (and belief- propagation) algorithms to loopy graphs are now quite popular for best assignment problems. This is largely due to their low computational complexity and impressive performance in practice. Still, there is no general understanding of the conditions required for convergence and/or the optimality of converged solutions. This work presents an analysis of both AttMP decoding and WMS decoding for LDPC codes which guarantees convergence to a fixed point when a weight factor, β, is sufficiently small. It also shows that, if the fixed point satisfies some consistency conditions, then it must be both a linear-programming (LP) and maximum-likelihood (ML) decoding solution