• Proceedings of the Korean Institute of Communication Sciences Conference
• /
• 1984.10a
• /
• pp.15-18
• /
• 1984

The majority - logic decoding algorithm for Geometry code is more simply imlemented than the known decoding algorithm for BCH codes. Thus, the moderate code word, Geometry codes provide rather effective error control. The purpose of this paper is to investigate the Reed - Muller code and to design the encoder and decoder circuit and to find the performance for (15, 11) Reed - muller code. Experimental results show that the system has not only single error - correcting ability but also good performance.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.21 no.5
• /
• pp.1256-1265
• /
• 1996

Soft-decision detectors are used in many FEC and ARQ schemes to enhance the bit-error-probability and system throughput. Also, the hybrid-ARQ protocol is a very efficient schemeto achieve overall performance improvement. In this paper, we propose a new hybrid-ARQ protocol based on the first-order Reed-Muller codes employing soft-decision detectors. The Reed-Muller codes have the virtue of being able to use the fast Green machine decoder that is simple to implement. As the performance measures, the bit-error-probability and system throughput are evaluted for the proposed hybrid-ARQ procol, and compared with those of other hybrid-ARQ schemes. It is shown that the use of the proposed hybrid-ARQ protocol results in significant performance improvement without causing much loss in view of system complexity.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
• /
• 2010.10a
• /
• pp.162-164
• /
• 2010

Terrestrial trunked radio (TETRA) standard specifies shortened Reed-Muller (RM) codes as forward error correction means for control signals. In this paper, we compare decoding algorithms for RM codes in TETRA, in terms of performance and complexity trade-off. Belief propagation and majority logic decoding algorithms are selected for comparison.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.37 no.1A
• /
• pp.43-50
• /
• 2012

The use of an error-correcting code is essential in digital communication systems where the channel is noisy. Unless a receiver has accurate channel coding parameters, it becomes difficult to decode the digitized encoding bits correctly. In this paper, estimation algorithm for RM(Reed-Muller) codes using FHT (Fast Hadamard algorithm) is proposed. The proposed algorithm estimates the channel coding parameters of RM codes and then decodes the codes using the characteristic of FHT. And we also verify the algorithm by performing intensive computer simulation in additive white gaussian noise (AWGN) channel.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.38C no.1
• /
• pp.109-117
• /
• 2013

Polar codes are the first provable error correcting code achieving the symmetric channel capacity in a wide case of binary input discrete memoryless channel(BI-DMC). However, finite length polar codes have an error floor problem with successive-cancellation list(SCL) decoder. From previous works, we can solve this problem by concatenating CRC(Cyclic Redundancy Check) codes. In this paper we propose to make polar codes having extended-minimum distance from original polar codes without outer codes using correlation with generate matrix of polar codes and that of RM(Reed-Muller) codes. And we compare performance of proposed polar codes with that of polar codes concatenating CRC codes.

• Journal of the Korean Mathematical Society
• /
• v.47 no.6
• /
• pp.1167-1182
• /
• 2010

We study codes meeting a generalized version of the Singleton bound for higher weights. We show that some of the higher weight enumerators of these codes are uniquely determined. We give the higher weight enumerators for MDS codes, the Simplex codes, the Hamming codes, the first order Reed-Muller codes and their dual codes. For the putative [72, 36, 16] code we find the i-th higher weight enumerators for i = 12 to 36. Additionally, we give a version of the generalized Singleton bound for non-linear codes.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.10 no.5
• /
• pp.209-217
• /
• 1985

Using the Reed-Muller Codes, the encoder and decoder system has been designed and tested in this paper. The error correcting capability of this code is [J/2} or less and the error correcting procedure can be implemented easily by using simple logic circuitry. The encoding and decoding circuits are obtained by the cyclic property and for the O15, 11) Reed-Muller code majority-logic decoding is taken. The performance is measured in error probability and weight destribution. The encoder and decoder system has been designed, implemented and interfaced with the microcomputer by using the 8255 chip. Experimental results show that the system has single error-correcting capability and total execution time for a data is about 70usec. When the probability of channel error is $10^{-6}$~$10^{-4}$ the system using the (15, 11) Reed-Muller code works very good.