• Journal of Korea Society of Digital Industry and Information Management
• /
• v.11 no.3
• /
• pp.45-51
• /
• 2015

In this paper, we discuss the belief propagation decoding algorithm for polar codes. The performance of Polar codes for shorter lengths is not satisfactory. Motivated by this, we propose a novel technique to improve its performance at short lengths. We showed that the probability of messages passed along the factor graph of polar codes, can be increased by multiplying the current message of nodes with their previous message. This is like a feedback path in which the present signal is updated by multiplying with its previous signal. Thus the experimental results show that performance of belief propagation polar decoder can be improved using this proposed technique. Simulation results in binary-input additive white Gaussian noise channel (BI-AWGNC) show that the proposed belief propagation polar decoder can provide significant gain of 2 dB over the original belief propagation polar decoder with code rate 0.5 and code length 128 at the bit error rate (BER) of $10^{-4}$.

• Journal of the Korean Mathematical Society
• /
• v.43 no.6
• /
• pp.1357-1369
• /
• 2006

It is known that if C is an [24m + 2l, 12m + l, d] selfdual binary linear code with $0{\leq}l<11,\;then\;d{\leq}4m+4$. We present a sufficient condition for the nonexistence of extremal selfdual binary linear codes with d=4m+4,l=1,2,3,5. From the sufficient condition, we calculate m's which correspond to the nonexistence of some extremal self-dual binary linear codes. In particular, we prove that there are infinitely many such m's. We also give similar results for additive self-dual codes over GF(4) of length n=6m+1.

• Proceedings of the IEEK Conference
• /
• 2002.06a
• /
• pp.323-326
• /
• 2002

In this paper, we study the improved bounds on the performance of low-density parity-check (LDPC) codes over binary-input additive white Gaussian noise (AWGN) channels with belief propagation (BP) decoding in log domain. We define an extended Gallager ensemble based on a new method of constructing parity check matrix and make use of this way to improve upper bound of LDPC codes. At the same time, many simulation results are presented in this paper. These results indicate the extended Gallager ensembles based on Hamming codes have typical minimum distance ratio, which is very close to the asymptotic Gilbert Varshamov bound and the superior performance which is better than the original Gallager ensembles.

• Journal of Communications and Networks
• /
• v.5 no.3
• /
• pp.187-196
• /
• 2003

We consider the use of error control coding in direct sequence-code-division multiple access (OS-COMA) systems that employ multiuser detection (MUO) and space diversity. The relative performance gain between Reed-Solomon (RS) code and convolutional code (CC) is well known in [1] for the single user, additive white Gaussian noise (AWGN) channel. In this case, RS codes outperform CC's at high signal-to-noise ratios. We find that this is not the case for the multiuser interference channel mentioned above. For useful error rates, we find that soft-decision CC's to be uniformly better than RS codes when used with DS-COMA modulation in multiuser space-time channels. In our development, we use the Gaussian approximation on the interference to determine performance error bounds for systems with low number of users. Then, we check their accuracy in error rate estimation via system's simulation. These performance bounds will in turn allow us to consider a large number of users where we can estimate the gain in user-capacity due to channel coding. Lastly, the use of turbo codes is considered where it is shown that they offer a coding gain of 2.5 dB relative to soft-decision CC.

• Journal of Communications and Networks
• /
• v.16 no.5
• /
• pp.479-484
• /
• 2014

In this paper, we consider the construction of cyclic and quasi-cyclic structured q-ary low-density parity-check (LDPC) codes over a designated small field. The construction is performed with a pre-defined sliding-window, which actually executes the regular mapping from original field to the targeted field under certain parameters. Compared to the original codes, the new constructed codes can provide better flexibility in choice of code rate, code length and size of field. The constructed codes over small fields with code length from tenths to hundreds perform well with q-ary sum-product decoding algorithm (QSPA) over the additive white Gaussian noise channel and are comparable to the improved spherepacking bound. These codes may found applications in wireless sensor networks (WSN), where the delay and energy are extremely constrained.

• The Journal of the Korea institute of electronic communication sciences
• /
• v.13 no.1
• /
• pp.69-76
• /
• 2018

This paper studies the Turbo Codes, the concatenation of Turbo Codes and Reed-Solomon (RS) codes on Orthogonal frequency-division multiplexing (OFDM) in digital communication channel, and then analysis the performances of the new concatenated Forward Error Correct (FEC) scheme applied to an OFDM system based on the digital terrestrial video broadcasting (DVB-T) scheme. We compared the results with the standard DVB-T convolutional codes performances on Additive White Gaussian Noise (AWGN) channels. The simulation results shown that by employing turbo codes with only a few numbers of iterations, the performances of the overall system can be improved significantly. These results will be obtained by applying an appropriate interleaver technique in the concatenated FEC procedure.

• Journal of Broadcast Engineering
• /
• v.8 no.4
• /
• pp.437-451
• /
• 2003

With the rapid growth of internet technologies and wide availability of multimedia computing facilities, the enforcement of multimedia copyright protection becomes an important issue. Digital watermarking is viewed as an effective way to deter content users from illegal distributions. In recent years, digital watermarking has been intensively studied to achieve this goal. However, when the watermarked media is transmitted over the channels modeled as the additive white Gaussian noise (AWGN) channel, the watermark information is often interfered by the channel noise and produces a large number of errors. So many error-correcting codes have been applied in the digital watermarking system to protect the embedded message from the disturbance of the noise, such as BCH codes, Reef-Solomon (RS) codes and Turbo codes. Recently, low-density parity-check (LDPC) codes were demonstrated as good error correcting codes achieving near Shannon limit performance and outperforming turbo codes nth low decoding complexity. In this paper, in order to mitigate the channel conditions and improve the quality of watermark, we proposed the application of LDPC codes on implementing a fairly robust digital image watermarking system. The implemented watermarking system operates in the spectrum domain where a subset of the discrete wavelet transform (DWT) coefficients is modified by the watermark without using original image during watermark extraction. The quality of watermark is evaluated by taking Into account the trade-off between the chip-rate and the rate of LDPC codes. Many simulation results are presented in this paper, these results indicate that the quality of the watermark is improved greatly and the proposed system based on LDPC codes is very robust to attacks.

• Journal of Broadcast Engineering
• /
• v.16 no.6
• /
• pp.1026-1035
• /
• 2011

This paper presents generalization and application for the conventional SISO decoding algorithm of Block Turbo Codes. R. M. Pyndiah suggested an iterative SISO decoding algorithm for Product Codes, two-dimensionally combined linear block codes, on AWGN channel. It wascalled Block Turbo Codes. Based on decision of Chase algorithm which is SIHO decoding method, SISO decoder for BTC computes soft decision information and transfers the information to next decoder for iterative decoding. Block Turbo Codes show Shannon limit approaching performance with a little iteration at high code rate on AWGN channel. In this paper we generalize the conventional decoding algorithm of Block Turbo Codes, under BPSK modulation and AWGN channel transmission assumption, to the LLR value based algorithm and suggest an application example such as concatenated structure of LDPC codes and Block Turbo Codes.

• Journal of the Institute of Electronics Engineers of Korea TC
• /
• v.43 no.8 s.350
• /
• pp.59-68
• /
• 2006

The study on the uniform error property of codes has been restricted to additive white Gaussian noise (AWGN) channel, which is generally referred to as geometrical uniformity. In this paper, we extend the uniform error property to space-time codes in multiple-input multiple-output (MIMO) channel by directly treating the probability density functions fully describing the transmission channel and the receiver. Moreover, we provide the code construction procedure for the geometrically uniform space-time trellis codes in fast MIMO channels, which consider the distance spectrum. Due to the uniform error property, the complexity of code search is extensively reduced. Such reduction makes it possible to obtain the optimal space-time trellis codes with high order states. Simulation results show that new codes offer a better performance in fast MIMO channels than other known codes.

• 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.