Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE Transactions on Information Theory

Efficient decoding algorithms for linear codes on soft-quantized channels (Ph.D. Thesis abstr.)

C. Yu

Published Nov 1, 1978• 0 citations
Publisher
DOI
10.1109/tit.1978.1055977

Related papers

AN EFFICIENT ALGORITHM FOR SOFT-DECISION DECODING OF LINEAR BINARY BLOCK CODES

Yong Geol Shin, Choong Woong Lee

IEEE International Symposium on Circuits and Systems proceedings•Jan 1, 1989•0 citations

Majority Voting Procedure Allowing Soft Decision Decoding of Linear Block Codes on Binary Channels

Saïd Nouh, Achraf El Khatabi, Mostafa Belkasmi

In this paper we present an efficient algorithm to decode linear block codes on binary channels. The main idea consists in using a vote procedure in order to elaborate artificial reliabilities of the binary received word and to present the obtained real vector r as inputs of a SIHO decoder (Soft In/Hard Out). The goal of the latter is to try to find the closest codeword to r in terms of the Euclidean distance. A comparison of the proposed algorithm over the AWGN channel with the Majority logic decoder, Berlekamp-Massey, Bit Flipping, Hartman-Rudolf algorithms and others show that it is more efficient in terms of performance. The complexity of the proposed decoder depends on the weight of the error to decode, on the code structure and also on the used SIHO decoder.

International Journal of Communications Network and System Sciences•Jan 1, 2012•11 citations

Efficient Maximum Likelihood Decoding Algorithms for Linear Codes over Z-Channel (Special Section on Information Theory and Its Applications)

Tomohiko Uyematsu

IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences•Sep 25, 1993•0 citations

Compound codes based on irregular graphs and their iterative decoding.

Telex Magloire Ngatched. Nkouatchah

Low-density parity-check (LDPC) codes form a Shannon limit approaching class of linear block codes. With iterative decoding based on their Tanner graphs, they can achieve outstanding performance. Since their rediscovery in late 1990's, the design, construction, and decoding of LDPC codes as well as their generalization have become one of the focal research points. This thesis takes a few more steps in these directions. The first significant contribution of this thesis is the introduction of a new class of codes called Generalized Irregular Low-Density (GILD) parity-check codes, which are adapted from the previously known class of Generalized Low-Density (GLD) codes. GILD codes are generalization of irregular LDPC codes, and are shown to outperform GLD codes. In addition, GILD codes have a significant advantage over GLD codes in terms of encoding and decoding complexity. They are also able to match and even beat LDPC codes for small block lengths. The second significant contribution of this thesis is the proposition of several decoding algorithms. Two new decoding algolithms for LDPC codes are introduced. In principle and complexity these algorithms can be grouped with bit flipping algorithms. Two soft-input soft-output (SISO) decoding algorithms for linear block codes are also proposed. The first algorithm is based on Maximum a Posteriori Probability (MAP) decoding of low-weight subtrellis centered around a generated candidate codeword. The second algorithm modifies and utilizes the improved Kaneko's decoding algorithm for soft-input hard-output decoding. These hard outputs are converted to soft-decisions using reliability calculations. Simulation results indicate that the proposed algorithms provide a significant improvement in error performance over Chase-based algorithm and achieve practically optimal performance with a significant reduction in decoding complexity. An analytical expression for the union bound on the bit error probability of linear codes on the Gilbert-Elliott (GE) channel model is also derived. This analytical result is shown to be accurate in establishing the decoder performance in the range where obtaining sufficient data from simulation is impractical.

•Jan 1, 2004•0 citations

Non-uniform Quantization of Soft Information for 5G LDPC Codes

Xiaohua Chang, Yu Zhang

Abstract This paper proposes a non-uniform quantization algorithm of soft information based on density evolution for the decoding of low-density parity check (LDPC) codes, which applies a non-linear transform function to soft information, and provides good block error rate performance. The transform function is obtained by minimizing weighted mean square quantization error for every combination of modulation type and LDPC codes and has an analytical expression of distribution of soft information. It can be realized as look-up table via quantization of transform function and has low complexity of implementation. Simulation results show that the error performance of proposed algorithm is close to no quantization condition and has a gain of around 0.3 dB compared to uniform quantization algorithm for 5G’s rate 2/3 LDPC codes with APSK modulation over additive white Gaussian noise (AWGN) channel.

Journal of Physics Conference Series•Aug 1, 2020•0 citations

Soft-Decision Decoding Algorithms for Binary Linear Block Codes

Hitoshi Tokushige

•Dec 19, 2000•0 citations
In this paper we present an efficient algorithm to decode linear block codes on binary channels. The main idea consists in using a vote procedure in order to elaborate artificial reliabilities of the binary received word and to present the obtained real vector r as inputs of a SIHO decoder (Soft In/Hard Out). The goal of the latter is to try to find the closest codeword to r in terms of the Euclidean distance. A comparison of the proposed algorithm over the AWGN channel with the Majority logic decoder, Berlekamp-Massey, Bit Flipping, Hartman-Rudolf algorithms and others show that it is more efficient in terms of performance. The complexity of the proposed decoder depends on the weight of the error to decode, on the code structure and also on the used SIHO decoder.
Low-density parity-check (LDPC) codes form a Shannon limit approaching class of linear block codes. With iterative decoding based on their Tanner graphs, they can achieve outstanding performance. Since their rediscovery in late 1990's, the design, construction, and decoding of LDPC codes as well as their generalization have become one of the focal research points. This thesis takes a few more steps in these directions. The first significant contribution of this thesis is the introduction of a new class of codes called Generalized Irregular Low-Density (GILD) parity-check codes, which are adapted from the previously known class of Generalized Low-Density (GLD) codes. GILD codes are generalization of irregular LDPC codes, and are shown to outperform GLD codes. In addition, GILD codes have a significant advantage over GLD codes in terms of encoding and decoding complexity. They are also able to match and even beat LDPC codes for small block lengths. The second significant contribution of this thesis is the proposition of several decoding algorithms. Two new decoding algolithms for LDPC codes are introduced. In principle and complexity these algorithms can be grouped with bit flipping algorithms. Two soft-input soft-output (SISO) decoding algorithms for linear block codes are also proposed. The first algorithm is based on Maximum a Posteriori Probability (MAP) decoding of low-weight subtrellis centered around a generated candidate codeword. The second algorithm modifies and utilizes the improved Kaneko's decoding algorithm for soft-input hard-output decoding. These hard outputs are converted to soft-decisions using reliability calculations. Simulation results indicate that the proposed algorithms provide a significant improvement in error performance over Chase-based algorithm and achieve practically optimal performance with a significant reduction in decoding complexity. An analytical expression for the union bound on the bit error probability of linear codes on the Gilbert-Elliott (GE) channel model is also derived. This analytical result is shown to be accurate in establishing the decoder performance in the range where obtaining sufficient data from simulation is impractical.
Abstract This paper proposes a non-uniform quantization algorithm of soft information based on density evolution for the decoding of low-density parity check (LDPC) codes, which applies a non-linear transform function to soft information, and provides good block error rate performance. The transform function is obtained by minimizing weighted mean square quantization error for every combination of modulation type and LDPC codes and has an analytical expression of distribution of soft information. It can be realized as look-up table via quantization of transform function and has low complexity of implementation. Simulation results show that the error performance of proposed algorithm is close to no quantization condition and has a gain of around 0.3 dB compared to uniform quantization algorithm for 5G’s rate 2/3 LDPC codes with APSK modulation over additive white Gaussian noise (AWGN) channel.