Majority-logic Algorithm Research Articles

Joint detection and decoding for physical‐layer network coding in power line channel

In this study, a joint detection and generalised sum-product decoding algorithm for a two-way relay physical-layer network coding (PLNC) system in power line communication is proposed. Distinct from the existing works which mainly focused on separate or iterative PLNC detection and decoding, the proposed algorithm is a belief propagation-based joint PLNC detection and decoding algorithm, which integrates the PLNC, symbol detector and channel decoder together. The proposed algorithm is described by a joint factor graph, in which the detection nodes are connected to the factor graph of a generalised sum-product decoder. The PLNC demodulation is redesigned to make sure that the degree of each detection node in the joint factor graph is more than one. A low computational complexity solution of the proposed joint decoding algorithm based on the majority-logic algorithm is also proposed. The simulation results reveal the validity of the proposed algorithms.

Matrix embedding in steganography with binary Reed–Muller codes

This study presents a modified majority-logic decoding algorithm of Reed-Muller (RM) codes for matrix embedding (ME) in steganography. An ME algorithm uses linear block code to improve the embedding efficiency in steganography. The optimal embedding algorithm in steganography is equivalent to the maximum likelihood decoding (MLD) algorithm in error-correcting codes. The main disadvantage of ME is that the equivalent MLD algorithm of lengthy embedding codes requires highly complex embedding. This study used RM codes to embed data in binary host images. The authors propose a novel low-complexity embedding algorithm that uses a modified majority-logic algorithm to decode RM codes, in which a message-passing algorithm (i.e. sum-product, min-sum, or bias propagation) is performed on the highest order of information bits in the RM codes. The experimental results indicate that integrating bias propagation into the proposed scheme achieves superior embedding efficiency (relative to when the sum-product or min-sum algorithm is used) and can even achieve the embedding bound of RM codes.

Dynamic Check Message Majority-Logic Decoding Algorithm for Non-binary LDPC Codes

Majority-logic algorithms are devised for decoding non-binary LDPC codes in order to reduce computational complexity. However, compared with conventional belief propagation algorithms, majority-logic algorithms suffer from severe bit error performance degradation. This paper presents a low-complexity reliability-based algorithm aiming at improving error correcting ability of majority-logic algorithms. Reliability measures for check nodes are novelly introduced to realize mutual update between variable message and check message, and hence more efficient reliability propagation can be achieved, similar to belief-propagation algorithm. Simulation results on NB-LDPC codes with different characteristics demonstrate that our algorithm can reduce the bit error ratio by more than one order of magnitude and the coding gain enhancement over ISRB-MLGD can reach 0.2-2.0dB, compared with both the ISRB-MLGD and IISRB-MLGD algorithms. Moreover, simulations on typical LDPC codes show that the computational complexity of the proposed algorithm is closely equivalent to ISRB-MLGD algorithm, and is less than 10% of Min-max algorithm. As a result, the proposed algorithm achieves a more efficient trade-off between decoding computational complexity and error performance.

Class of linear binary codes

A class of algebraic linear codes is introduced in which the parity-check matrix of the code is constructed by using a subset of the Abelian group of Walsh functions. These codes meet the Helgert and Stinaff upper bounds on minimum Hamming distance, and all the codes of this class are easily decodable by a one-step majority-logic algorithm.