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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Este artigo apresenta um novo algoritmo de decodificação baseado em otimização para códigos LDPC. O algoritmo de decodificação proposto é baseado em um método de gradiente proximal para resolver um problema de decodificação máximo aproximado a posteriori (MAP). A ideia chave do algoritmo proposto é o uso de um polinômio de restrição de código para penalizar um vetor distante de uma palavra-código como regularizador na função objetivo aproximada do MAP. Um operador proximal de código é naturalmente derivado de um polinômio de restrição de código. O algoritmo proposto, denominado decodificação proximal, pode ser descrito por uma fórmula recursiva simples que consiste no passo de descida do gradiente para uma função log-verossimilhança negativa correspondente à função de densidade de probabilidade condicional do canal e a operação proximal do código em relação ao polinômio de restrição de código. A decodificação proximal é experimentalmente demonstrada como aplicável a vários modelos de canais não triviais, como canais MIMO massivos codificados por LDPC, canais de ruído gaussianos correlacionados e canais vetoriais não lineares. Em particular, em canais MIMO, a decodificação proximal supera os algoritmos de detecção MIMO massivos conhecidos, como um detector MMSE com decodificação de propagação de crenças. A formulação simples de decodificação proximal baseada em otimização permite um caminho para o desenvolvimento de novos algoritmos de processamento de sinal envolvendo códigos LDPC.
Tadashi WADAYAMA
Nagoya Institute of Technology
Satoshi TAKABE
Tokyo Institute of Technology
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Tadashi WADAYAMA, Satoshi TAKABE, "Proximal Decoding for LDPC Codes" in IEICE TRANSACTIONS on Fundamentals,
vol. E106-A, no. 3, pp. 359-367, March 2023, doi: 10.1587/transfun.2022TAP0002.
Abstract: This paper presents a novel optimization-based decoding algorithm for LDPC codes. The proposed decoding algorithm is based on a proximal gradient method for solving an approximate maximum a posteriori (MAP) decoding problem. The key idea of the proposed algorithm is the use of a code-constraint polynomial to penalize a vector far from a codeword as a regularizer in the approximate MAP objective function. A code proximal operator is naturally derived from a code-constraint polynomial. The proposed algorithm, called proximal decoding, can be described by a simple recursive formula consisting of the gradient descent step for a negative log-likelihood function corresponding to the channel conditional probability density function and the code proximal operation regarding the code-constraint polynomial. Proximal decoding is experimentally shown to be applicable to several non-trivial channel models such as LDPC-coded massive MIMO channels, correlated Gaussian noise channels, and nonlinear vector channels. In particular, in MIMO channels, proximal decoding outperforms known massive MIMO detection algorithms, such as an MMSE detector with belief propagation decoding. The simple optimization-based formulation of proximal decoding allows a way for developing novel signal processing algorithms involving LDPC codes.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2022TAP0002/_p
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@ARTICLE{e106-a_3_359,
author={Tadashi WADAYAMA, Satoshi TAKABE, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Proximal Decoding for LDPC Codes},
year={2023},
volume={E106-A},
number={3},
pages={359-367},
abstract={This paper presents a novel optimization-based decoding algorithm for LDPC codes. The proposed decoding algorithm is based on a proximal gradient method for solving an approximate maximum a posteriori (MAP) decoding problem. The key idea of the proposed algorithm is the use of a code-constraint polynomial to penalize a vector far from a codeword as a regularizer in the approximate MAP objective function. A code proximal operator is naturally derived from a code-constraint polynomial. The proposed algorithm, called proximal decoding, can be described by a simple recursive formula consisting of the gradient descent step for a negative log-likelihood function corresponding to the channel conditional probability density function and the code proximal operation regarding the code-constraint polynomial. Proximal decoding is experimentally shown to be applicable to several non-trivial channel models such as LDPC-coded massive MIMO channels, correlated Gaussian noise channels, and nonlinear vector channels. In particular, in MIMO channels, proximal decoding outperforms known massive MIMO detection algorithms, such as an MMSE detector with belief propagation decoding. The simple optimization-based formulation of proximal decoding allows a way for developing novel signal processing algorithms involving LDPC codes.},
keywords={},
doi={10.1587/transfun.2022TAP0002},
ISSN={1745-1337},
month={March},}
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TY - JOUR
TI - Proximal Decoding for LDPC Codes
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 359
EP - 367
AU - Tadashi WADAYAMA
AU - Satoshi TAKABE
PY - 2023
DO - 10.1587/transfun.2022TAP0002
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E106-A
IS - 3
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - March 2023
AB - This paper presents a novel optimization-based decoding algorithm for LDPC codes. The proposed decoding algorithm is based on a proximal gradient method for solving an approximate maximum a posteriori (MAP) decoding problem. The key idea of the proposed algorithm is the use of a code-constraint polynomial to penalize a vector far from a codeword as a regularizer in the approximate MAP objective function. A code proximal operator is naturally derived from a code-constraint polynomial. The proposed algorithm, called proximal decoding, can be described by a simple recursive formula consisting of the gradient descent step for a negative log-likelihood function corresponding to the channel conditional probability density function and the code proximal operation regarding the code-constraint polynomial. Proximal decoding is experimentally shown to be applicable to several non-trivial channel models such as LDPC-coded massive MIMO channels, correlated Gaussian noise channels, and nonlinear vector channels. In particular, in MIMO channels, proximal decoding outperforms known massive MIMO detection algorithms, such as an MMSE detector with belief propagation decoding. The simple optimization-based formulation of proximal decoding allows a way for developing novel signal processing algorithms involving LDPC codes.
ER -