This study investigates the decoding algorithms of binary Reed–Muller (RM) codes. The main goal of the study is to modify majority‐logic decoding using sum‐product or min‐sum decoding algorithms at the highest‐order information bits in RM codes. Numerical results show that compared with the traditional majority‐logic decoding algorithm, the modified majority‐logic decoding method proposed in this study can reduce the bit error rate by a large margin. This is achieved without incurring a significant increase in decoding complexity because soft‐decision decoding is only used in the highest information bits in RM codes whereas majority‐logic decoding is still applied at the other orders of information bits in RM 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.

A novel steganographic algorithm for ternay data based on ZZW construction over F_3 is proposed to improve the embedding efficiency. Contrast to the conventional ZZW construction using binary Hamming codes in the second channel, the proposed method employs ternary Hamming codes to embed the message at the second channel. For the first channel, a low rate convolutional codes is presented to enhance the embedding efficiency of this modified ZZW construction. The ZZW construction over F_3 provides excellent embedding efficiency for ternary signal, and can be greatly extended to embedding algorithm for non-binary steganography.

A novel suboptimal hiding algorithm for binary data based on weight approximation embedding, WAE, is proposed. Given a specified embedding rate, this algorithm exhibits an advantage of efficient binary embedding with reduced embedding complexity. The suboptimal WAE algorithm performs an embedding procedure through a parity check matrix. The optimal embedding based on maximal likelihood algorithm aims to locate the coset leader to minimize the embedding distortion. On the contrary, the WAE algorithm looks for a target vector close to the coset leader in an efficiently iterative manner. Given an linear embedding code C(n, k), the embedding complexity using the optimal algorithm is O(2k), while the complexity in the suboptimal WAE is reduced to O(sk) where s is the average iterations.

This paper proposes a novel peak-to-average power ratio (PAPR) reduction method with low complexity by combining the RM-PTS scheme with the PCGA-PTS scheme, called RM-PCGA-PTS. The RM-PTS scheme not only the transmitted signal has error correction capability but also the transmitter has no need to transmit side information. However, one major drawback of the RM-PTS scheme is high computational loads which also occur in the PTS scheme for finding the transmitted signal with minimum PAPR out. Therefore, this paper investigates a suboptimal PAPR reduction method with low computational loads by using the improved genetic algorithm used the partheno-crossover operator (PCGA) as the selection mechanism of RM-PTS scheme. The GA-PTS scheme is an active PAPR reduction method, which has better PAPR performance than the GD-PTS scheme and has lower computational load than the PTS scheme and the GD-PTS scheme. Note that the GA-PTS scheme has no error correction capability and is a suboptimal PAPR reduction method. Based on the same computational loads, the RM-PCGA-PTS scheme with natural ordering has better PAPR performance than the GA-PTS scheme with adjacent partition in simulation results.

This paper proposes a joint JPEG-block coding system (JJBC) based on BCJR decoding with expurgating trellis that maintains an acceptable image quality over AWGN and wireless channels. The joint design of JPEG compression and block codes in the transmitter has the advantage of avoiding error propagation and of low decoding complexity over the conventional tandem system with separate optimization of source coding and channel coding. The PSNR performance of the JJBC system is much better than that of the tandem system when the signal to noise ratio is low. Experimental results show that the proposed JJBC system achieves 6 dB (3 dB) reduction at PSNR=20dB, compared to the conventional tandem system, over wireless IEEE 802.11b (AWGN) channels.

A modified PTS algorithm by partitioning an OFDM block into non-disjoint OFDM sub-blocks is presented in this paper for PAPR reduction of M-QAM OFDM signals. Since a 16-QAM constellation can be written as sum of two QPSK sets, a non-disjoint sub-block partition of the 16-QAM OFDM block is obtained by applying two different disjoint partitions on QPSK OFDM blocks. Compared to a disjoint sub-block partition in conventional PTS, numerical results show that the modified PTS with a non-disjoint partition achieves an improvement of PAPR reduction and BER performance for interleaved, adjacent, and random partitioning schemes.

This paper proposed a PAPR reduction method for BPSK OFDM systems and 16-QAM OFDM systems respectively. The strategy of the algorithms is to use a correction subcode for error control and a scrambling subcode for PAPR control. The transmitted OFDM sequence is selected with minimum PAPR from a number of candidates which form a coset of scrambling subcode for each codeword of correction subcode. In a BPSK OFDM system, the PAPR reduction is obtained by combining the SLM method with binary cyclic codes. In a 16-QAM OFDM system, the PAPR reduction is achieved by combining the SLM with block coded modulation. The received signal of the modified SLM can be decoded without the need of explicit side information and the proposed scheme achieves good PAPR reduction.

In this paper, we consider reduction of PAPR in OFDM systems with BPSK subcarriers by combining SLM and binary cyclic codes. This combining strategy can be used for both error correction and PAPR reduction. We decompose a binary cyclic code into direct sum of two cyclic subcodes: the correction subcode used for error correction and the scrambling subcode for PAPR reduction. The transmitted OFDM signal is selected that achieves minimum PAPR, from the set of binary cyclic codewords. The received signal can be easily decoded without the need of any side information. Simulations show that the proposed scheme with simplex code as scrambling subcode achieves good PAPR reduction.

In this paper, the reduction of the peak-to-average power ratio (PAPR) of M-quadrature amplitude modulation (QAM) signals in orthogonal frequency division multiplexing (OFDM) systems are studied. The block coded modulation (BCM) techniques and Golay sequences to trade off the PAPR, the code rate, and the squared Euclidean distance in M-QAM OFDM signals are combined. In particular, 16-QAM and 64-QAM OFDM sequences with low PAPR and good squared Euclidean distance are presented.

This paper examines the performance gains achievable by adding interblock memory to, and altering the mapping of coded bits to symbols in, block-coded modulation systems. The channel noise considered is additive Gaussian, and the twin design goals are to maximize the asymptotic coding gain and to minimize the number of apparent nearest neighbors. In the case of the additive white Gaussian noise channel, these goals translate into the design of block codes of a given weighted or 'normalized' distance whose rate is as high as possible, and whose number of codewords at minimum normalized distance is low. The effect of designing codes for normalized distance rather than Hamming distance is to ease the problem of determining the best codes for given parameters in the cases of greatest interest, and many such best codes are given.