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IEICE Technical Report; IEICE Tech. Rep.

On Computing the Weight Spectrum of LDPC Convolutional Codes Constructed from Quasi-Cyclic Codes

Masanori Hirotomo, Masakatu Morii

Published Sep 20, 2012• 0 citations
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Improvement of the Method for Computing the Weight Spectrum of LDPC Convolutional Codes

Masanori Hirotomo, Masakatu Morii

IEICE Technical Report; IEICE Tech. Rep.•Sep 22, 2011•1 citation

An efficient method for computing the weight spectrum of LDPC convolutional codes constructed from quasi-cyclic codes

Masanori Hirotomo, Masakatu Morii

In this paper, we propose an efficient method for computing the weight spectrum of LDPC convolutional codes constructed from quasi-cyclic block codes. In the proposed method, we reduce the memory size of their parity-check matrices with the same distance profile as original codes, and apply a forward and backward tree search algorithm to the parity-check matrices of reduced memory. We show numerical results of computing the minimum free distance and the low-part weight spectrum of LDPC convolutional codes of memory about 130.

International Symposium on Information Theory and its Applications•Oct 1, 2012•1 citation

A Method for Computing the Weight Spectrum of LDPC Convolutional Codes Based on Circulant Matrices

Masanori Hirotomo, Masakatu Morii

In this paper, we propose an efficient method for computing the weight spectrum of LDPC convolutional codes based on circulant matrices of quasi-cyclic codes. In the proposed method, we reduce the memory size of their parity-check matrices with the same distance profile as the original codes, and apply a forward and backward tree search algorithm to the parity-check matrices of reduced memory. We show numerical results of computing the free distance and the low-part weight spectrum of LDPC convolutional codes of memory about 130.

IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences•Jan 1, 2014•0 citations

On Computing the Weight Distribution of LDPC Convolutional Codes

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Pseudo-Codewords in LDPC Convolutional Codes

Roxana Smarandache, Alí Emre Pusane, Pascal O. Vontobel +1 more

Iterative message-passing decoders for low-density parity-check (LDPC) block codes are known to be subject to decoding failures due to so-called pseudo-codewords. These failures can cause the large signal-to-noise ratio performance of message-passing decoding to be worse than that predicted by the maximum-likelihood decoding union bound. In this paper we study the pseudo-codeword problem for the class of LDPC convolutional codes decoded continuously using an iterative, sliding window, message-passing decoder. In particular, for an LDPC convolutional code derived by unwrapping a quasi-cyclic LDPC block code, we show that the free pseudo-weight of the convolutional code is at least as large as the minimum pseudo-weight of the underlying quasi-cyclic code. This result parallels the well-known relationship between the free Hamming distance of convolutional codes and the minimum Hamming distance of their quasi-cyclic counterparts. Finally, simulation results are included that show improved performance for unwrapped LDPC convolutional codes compared to their underlying quasi-cyclic codes

IEEE International Symposium on Information Theory (ISIT)•Jul 1, 2006•16 citations

Construction of LDPC convolutional codes via difference triangle sets

Gianira N. Alfarano, Julia Lieb, Joachim Rosenthal

•Jul 22, 2021•7 citations
In this paper, we propose an efficient method for computing the weight spectrum of LDPC convolutional codes constructed from quasi-cyclic block codes. In the proposed method, we reduce the memory size of their parity-check matrices with the same distance profile as original codes, and apply a forward and backward tree search algorithm to the parity-check matrices of reduced memory. We show numerical results of computing the minimum free distance and the low-part weight spectrum of LDPC convolutional codes of memory about 130.
In this paper, we propose an efficient method for computing the weight spectrum of LDPC convolutional codes based on circulant matrices of quasi-cyclic codes. In the proposed method, we reduce the memory size of their parity-check matrices with the same distance profile as the original codes, and apply a forward and backward tree search algorithm to the parity-check matrices of reduced memory. We show numerical results of computing the free distance and the low-part weight spectrum of LDPC convolutional codes of memory about 130.
Iterative message-passing decoders for low-density parity-check (LDPC) block codes are known to be subject to decoding failures due to so-called pseudo-codewords. These failures can cause the large signal-to-noise ratio performance of message-passing decoding to be worse than that predicted by the maximum-likelihood decoding union bound. In this paper we study the pseudo-codeword problem for the class of LDPC convolutional codes decoded continuously using an iterative, sliding window, message-passing decoder. In particular, for an LDPC convolutional code derived by unwrapping a quasi-cyclic LDPC block code, we show that the free pseudo-weight of the convolutional code is at least as large as the minimum pseudo-weight of the underlying quasi-cyclic code. This result parallels the well-known relationship between the free Hamming distance of convolutional codes and the minimum Hamming distance of their quasi-cyclic counterparts. Finally, simulation results are included that show improved performance for unwrapped LDPC convolutional codes compared to their underlying quasi-cyclic codes