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IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences

Iterative Decoding of High Dimensionality Parity Code

Toshio Fukuta

Published Oct 1, 2003• 2 citations
OpenAlex

Abstract

Given the importance of the traffic on modern communication networks, advanced error correction methods are needed to overcome the changes expected in channel quality.Conventional countermeasures that use high dimensionality parity codes often fail to provide sufficient error correction capability.We propose a parity code with high dimensionality that is iteratively decoded.It provides better error correcting capability than conventional decoding methods.The proposal uses the steepest descent method to increase code bit reliability and the coherency between parities and code bits gradually.Furthermore, the quantization of the decoding algorithm is discussed.It is found that decoding with quantization can keep the error correcting capability high.

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Given the importance of the traffic on modern communication networks, advanced error correction methods are needed to overcome the changes expected in channel quality.Conventional countermeasures that use high dimensionality parity codes often fail to provide sufficient error correction capability.We propose a parity code with high dimensionality that is iteratively decoded.It provides better error correcting capability than conventional decoding methods.The proposal uses the steepest descent method to increase code bit reliability and the coherency between parities and code bits gradually.Furthermore, the quantization of the decoding algorithm is discussed.It is found that decoding with quantization can keep the error correcting capability high.
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Low-density parity-check (LDPC) codes have been one of the most popular error correction candidates in modern communication and data storage systems for the past three decades due to their capacity-approaching error correction capability under the Belief Propagation (BP) decoding algorithms. In this dissertation, we investigate three topics related to efficient and effective decoding algorithms and the code design of LDPC codes. In the first part of this dissertation, we propose a methodology with the help of artificial intelligence to design Finite Alphabet Iterative Decoders (FAID) for LDPC codes, which are not only of great theoretical but also practical importance. This model-driven neural network (NN) framework unfolds the decoding iterations, introduces quantized neural networks (QNN) to model the FAIDs, and proposes a new cost function, namely, bit error rate (BER), to address the inefficiency in discrete-output channel scenarios. The low precision activations in the QNN and quantization in the cost functions cause a critical issue that their gradients vanish almost everywhere, making it difficult to use classical backward propagation. We design and leverage straight-through estimators as surrogate gradients to tackle this issue and provide a joint training scheme. These QNN-aided FAIDs, are capable of surpassing the floating-point BP algorithms, with much lower complexity and faster convergence. The QNN-aided approach is general, as it can be applied to both continuous and discrete-output channels. In the second part of this dissertation, we propose a new code construction of LDPC codes based on the conventional parity-check matrices of Reed-Solomon (RS) codes. We investigate the girth and cycle structure and introduce an efficient searching algorithm to reduce short cycles in their Tanner graphs and to construct LDPC codes with a girth of at least eight. We use masking to further reduce the number of short cycles and to adjust the column and row weights of the parity-check matrices of the constructed codes for performance improvement. Our designs are systematic and flexible, which balance the requirements of good waterfall performance and low error-floor while maintaining a structure that facilitates implementation. In the third part of this dissertation, we investigate binary quasi-cyclic (QC) LDPC codes and their capability to correct phased bursts of erasures. We prove that the peeling algorithm when applied to such parity-check matrices of column weight two can correct all erasures that can be corrected by a maximum likelihood (ML) decoder. We show that by modifying the parity-check matrices of column weight two and globally coupling them, the erasure correcting capability can be further enhanced. For the Additive White Gaussian Noise (AWGN) channel, we design QC LDPC codes with parity-check matrices of column weight three or more that can correct phased bursts of erasures and perform well over the AWGN channel. Our analysis of QC-LDPC codes with parity-check matrices of column weight two is rather comprehensive as we determine, for all such codes, their dimensions, minimum Hamming distances, and their capabilities to correct phased bursts.
The decoding of Low-Density Parity-Check (LDPC) codes is operated over a redundant structure known as the bipartite graph, meaning that the full set of bit nodes is not absolutely necessary for decoder convergence. In 2008, Soyjaudah and Catherine designed a recovery algorithm for LDPC codes based on this assumption and showed that the error-correcting performance of their codes outperformed conventional LDPC Codes. In this work, the use of the recovery algorithm is further explored to test the performance of LDPC codes while the number of iterations is progressively increased. For experiments conducted with small blocklengths of up to 800 bits and number of iterations of up to 2000, the results interestingly demonstrate that contrary to conventional wisdom, the error-correcting performance keeps increasing with increasing number of iterations.
In modern data communication system Error Detection and Correction has great practical importance to maintain the data integrity across the noisy channel. To deal with this challenge, the theory of Error detection and correction need to get one's precise attention. To retrieve the original data, an efficient process is required. A class of error correcting codes which performs iterative decoding inside a graph is considered which can provide a good approximation. In this context Low Density Parity Check (LDPC) code comes with an excellent error correction performance. In this paper architecture and algorithms for Error Detection and Correction method based on LDPC code is proposed. Also, a simulator for the proposed algorithms is designed and tested successfully.
Abstract — Low-density parity-check codes have recently received extensive attention as a forward error correction scheme in a wide area of applications. The decoding algorithm is inherently parallelizable, allowing communication at high speeds. One of the main disadvantages, however, is large memory requirements for interim storing of decoding data. In this paper, we investigate a modification to the decoding algorithm, using early decisions for bits with high reliabilities. Currently, there are two early decision schemes proposed. We compare their theoretical performances and their suitability for hardware implementation. We also propose a new decision method, which we call weak decisions, that offers an increase in performance by a factor of two. 1