Forward Error Correction (FEC) schemes have played an important role in intensity-modulation direct-detection (IM/DD) Visible Light Communication (VLC) systems. While hard-decision FEC schemes are inferior to soft-decision FEC codes in terms of decoding performance, they are widely used in these VLC systems because receivers are only capable of recognizing logical values 0 and 1. In this letter, we propose a method to calculate the log-likelihood ratios (LLR) values which are used as input of soft-decision FEC decoders. Simulation results show that Polar decoder using proposed method performs better than that of using the hard-decision technique.

This letter proposes extended single parity check product codes and presents their empirical performances on a Gaussian channel by belief propagation (BP) decoding algorithm. The simulation results show that the codes can achieve close-to-capacity performance in high coding rate. The code of length 9603 and of rate 0.96 is only 0.77 dB away from the Shannon limit for a BER of 10-5.

Soft-decision decoding techniques are applied to asynchronous frequency-hop/spread-spectrum multiple-access (FH/SSMA) networks, where M-ary frequency shift keying (MFSK) is employed to transmit one modulated symbol per hop. Coding schemes using soft-decision decoded binary convolutional codes or turbo codes are considered, both with or without bit-interleaving. Performances of several soft metrics are examined for each coding scheme. It is shown that when multiple access interference is the main source of errors, the product metric offers the best performance among the soft metrics considered for all coding schemes. Furthermore, the application of soft-decision decoded convolutional codes or turbo codes without bit-interleaving is shown to allow for a much larger number of simultaneously transmitting users than hard-decision decoded Reed-Solomon codes. Finally, it is observed that when soft-decision decoding techniques are employed, synchronous networks attain better performance than asynchronous networks.

Collusion-secure codes are used for digital fingerprinting and for traitor tracing. In both cases, the goal is to prevent unauthorized copying of copyrighted material, by tracing at least one guilty user when illegal copies appear. The most well-known collusion-secure code is due to Boneh and Shaw (1995/98). In this paper we improve the decoding algorithm by using soft output from the inner decoder, and we show that this permits using significantly shorter codewords.

We consider a soft-decision iterative bounded distance decoding algorithm for binary linear block codes. In the decoding algorithm, bounded distance decodings are carried out with respect to successive input words, called the search centers. A search center is the sum of the hard-decision sequence of a received sequence and a sequence in a set of test patterns which are generated beforehand. This set of test patterns has influence on the error performance of the decoding algorithms as simulation results show. In this paper, we propose a construction method of a set of candidate test patterns and a selection method of test patterns based on an introduced measure of effectiveness of test patterns. For several BCH codes of lengths 127, 255 and 511, we show the effectiveness of the proposed method by simulation.

New algorithms for the soft-decision and the hard-decision maximum likelihood decoding (MLD) for binary linear block codes are proposed. It has been widely known that both MLD can be regarded as an integer programming with binary arithmetic conditions. Recently, Conti and Traverso have proposed an efficient algorithm which uses Grobner bases to solve integer programming with ordinary integer arithmetic conditions. In this paper, the Conti-Traverso algorithm is extended to solve integer programming with modulo arithmetic conditions. We also show how to transform the soft-decision and the hard-decision MLD to integer programming for which the extended Conti-Traverso algorithm is applicable.

This letter presents the empirical error performance of combining method of a binary numerical code and a single error correcting code on Gaussian channel by belief propagation (BP) decoding algorithm. The numerical codes mentioned here are constructed with any symbol value and have the parity check matrices in reduced-echelon form whose elements are binary (0 and 1). The simulation results show that the method yields good decoding error performance for medium code lengths.

In this paper, soft decision decoding of linear block codes based on the reprocessing of several information sets is considered. These information sets are chosen according to the reliability measures of the received symbols and constructed from the most reliable information set, referred to as the most reliable basis. Each information set is then reprocessed by a multi-stage decoding algorithm until either the optimum error performance, or a desired level of error performance is achieved. General guidelines for the trade-offs between the number of information sets to be processed, the number of computations for reprocessing each information set, and the error performance to be achieved are provided. It is shown that with a proper selection of few information sets, low-complexity near-optimum soft decision decoding of relatively long block codes (64 N 128) can be achieved with significant reduction in computation complexity with respect to other known algorithms. This scheme, which generalizes the reprocessing of the most reliable basis with the ordered statistic algorithm proposed by Fossorier and Lin, is particularly efficient for codes with rate R 1/2.

A unified algorithm is presented for solving key equations for decoding alternant codes. The algorithm can be applied to various decoding techniques, including bounded distance decoding, generalized minimum distance decoding, Chase decoding, etc.

We proposed a soft-decision decoding algorithm for cyclic codes based on energy minimization principle. This letter presents the algorithm which improves decoding performance and decoding complexity of the previous method by giving more initial positions and introducing a new criterion for terminating the decoding procedure. Computer simulation results show that both the decoded block error rate and the decoding complexity decrease by this method more than by the previous method.

We propose a novel soft-decision decoding algorithm for cyclic codes based on energy minimization principle. The well-known soft-decision decoding algorithms for block codes perform algebraic (hard-decision) decoding several times in order to generate candidate codewords using the reliability of received symbols. In contrast, the proposed method defines energy as the Euclidean distance between the received signal and a codeword and alters the values of information symbols so as to decrease the energy in order to seek the codeword of minimum energy, which is the most likely codeword. We let initial positions be the information parts of signals obtained by cyclically shifting a received signal and look for the point, which represents a codeword, of minimum energy by moving each point from several initial positions. This paper presents and investigates reducing complexity of the soft-decision decoding algorithm. We rank initial positions in order of reliability and reduce the number of initial positions in decoding. Computer simulation results show that this method reduces decoding complexity.

The performance of APP (a posteriori probability) decoding algorithm which is well known as a soft decision decoding algorithm for majority logic decodable codes is further improved by iterating the algorithm one or more times. This letter shows that there exists the optimal non-zero threshold value of the decision function that minimizes the decoded error rate in two-pass APP decoding though the optimal threshold value in one-pass APP decoding is zero.

A soft-decision decoding algorithm for binary linear block codes is proposed. This algorithm seeks to minimize the block error probability. With careful examinations of the first hard-decision decoded results, the candidate codewords are efficiently searched for. Thus, we can reduce the decoding complexity (the number of hard-decision decodings) and lower the block error probability. Computer simulation results are presented for the (23, 12) Golay code. They show that the decoding complexity is considerably reduced and the block error probability is close to that of the maximum likelihood decoder.