• Proceedings of the IEEK Conference
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• 2003.07a
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• pp.89-92
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• 2003

A geometrically uniform code in AWGN channel has strong symmetry properties such as a) the distance profiles form codewords On C to all other codewords are all the same, and b) all Voronoi regions of codewords in C have the same shape. Such properties make the word error probability of geometrically uniform codes be transparent to the transmitted codeword. In this paper, we extend the geometrically uniform codes in AWGN channel to the geometrical uniform codes in fading channel with multiple transmit antennas.

• Proceedings of the IEEK Conference
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• 2001.06a
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• pp.273-276
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• 2001

In this thesis we propose symbol-based decoding for turbo codes which is used SOVA as a decoding algorithm. The proposed turbo codes that is interleaved on symbol-by-symbol basis and inputted as n-bit symbols to the decoder. This method makes that the stages of the original trellis are merged together and the trellis depth is reduced by 1/n. We research turbo codes with symbol size n=2 in this paper and its performance.

• Journal of Communications and Networks
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• v.15 no.1
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• pp.71-76
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• 2013

A new class of quantum low-density parity-check (LDPC) codes whose parity-check matrices are dual-containing matrices constructed based on lines of Euclidean geometries (EGs) is presented. The parity-check matrices of our quantum codes contain one and only one 4-cycle in every two rows and have better distance properties. However, the classical parity-check matrix constructed from EGs does not satisfy the condition of dual-containing. In some parameter conditions, parts of the rows in the matrix maybe have not any nonzero element in common. Notably, we propose four families of fascinating structure according to changes in all the parameters, and the parity-check matrices are adopted to satisfy the requirement of dual-containing. Series of matrix properties are proved. Construction methods of the parity-check matrices with dual-containing property are given. The simulation results show that the quantum LDPC codes constructed by this method perform very well over the depolarizing channel when decoded with iterative decoding based on the sum-product algorithm. Also, the quantum codes constructed in this paper outperform other quantum codes based on EGs.

• Journal of Communications and Networks
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• v.10 no.1
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• pp.5-9
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• 2008

Researchers have investigated many upper bound techniques applicable to error probabilities on the maximum likelihood (ML) decoding performance of turbo-like codes and low density parity check (LDPC) codes in recent years for a long codeword block size. This is because it is trivial for a short codeword block size. Previous research efforts, such as the simple bound technique [20] recently proposed, developed upper bounds for LDPC codes and turbo-like codes using ensemble codes or the uniformly interleaved assumption. This assumption bounds the performance averaged over all ensemble codes or all interleavers. Another previous research effort [21] obtained the upper bound of turbo-like code with a particular interleaver using a truncated union bound which requires information of the minimum Hamming distance and the number of codewords with the minimum Hamming distance. However, it gives the reliable bound only in the region of the error floor where the minimum Hamming distance is dominant, i.e., in the region of high signal-to-noise ratios. Therefore, currently an upper bound on ML decoding performance for turbo-like code with a particular interleaver and LDPC code with a particular parity check matrix cannot be calculated because of heavy complexity so that only average bounds for ensemble codes can be obtained using a uniform interleaver assumption. In this paper, we propose a new bound technique on ML decoding performance for turbo-like code with a particular interleaver and LDPC code with a particular parity check matrix using ML estimated weight distributions and we also show that the practical iterative decoding performance is approximately suboptimal in ML sense because the simulation performance of iterative decoding is worse than the proposed upper bound and no wonder, even worse than ML decoding performance. In order to show this point, we compare the simulation results with the proposed upper bound and previous bounds. The proposed bound technique is based on the simple bound with an approximate weight distribution including several exact smallest distance terms, not with the ensemble distribution or the uniform interleaver assumption. This technique also shows a tighter upper bound than any other previous bound techniques for turbo-like code with a particular interleaver and LDPC code with a particular parity check matrix.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.36 no.6A
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• pp.577-586
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• 2011

Modem digital communication systems are required to use forward error correction (FEC) codes to combat inevitable channel impairment. Turbo codes or low density parity check (LDPC) codes, using iterative decoding with soft decision detection (SDD) information, are the most common examples. The excellent performance of these codes should be conditioned on accurate estimation of soft decision detection information. In order to use FEC codes with iterative decoding for Multi-Input Multi-Output (MIMO) system, reliable soft decision channel gain should be provided. In this paper, we investigate efficient SDD methods for turbo-coded MIMO system, and derive the corresponding formulas of SDD for various MIMO detection schemes. We present simulation results of the derived SDD schemes for turbo-coded MIMO systems, and show that the presented results almost approximate to maximum likelihood detection performance with much less computational load.

• Journal of the Korean Institute of Telematics and Electronics
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• v.12 no.1
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• pp.7-11
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• 1975

Investigations on sole characteristics of unit-distance duo-decimal codes are carried out, and 31kinds of Prime Digit Sequence (PDS) are proposed in order to express various digit sequences. From these PDS, by means of the rotational conversion, 348 digit sequences which express the practical GC are obtained, and, ism these digit sequences, it is found that there are 120576 unit distance codes by the permutation of the coordinate number and the initial condition of the codes. Some special codes such as reflected or symmetrical codes and Lippel codes, and their application to the practical GC counter are also studied.

• Journal of information and communication convergence engineering
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• v.4 no.4
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• pp.136-140
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• 2006

In this paper, we consider the detection of orthogonal space-time block codes (OSTBCs) without channel state information (CSI) at the receiver. Based on the conventional blind cyclic decoder, we propose an enhanced blind cyclic decoder which has higher system performance than the conventional one. Furthermore, the proposed decoder offers low complexity since it does not require the computation of singular value decomposition.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1627-1638
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• 2018

In this paper, we study an special type of cyclic codes called skew cyclic codes over the ring ${\mathbb{F}}_p+v{\mathbb{F}}_p+v^2{\mathbb{F}}_p$, where p is a prime number. This set of codes are the result of module (or ring) structure of the skew polynomial ring (${\mathbb{F}}_p+v{\mathbb{F}}_p+v^2{\mathbb{F}}_p$)[$x;{\theta}$] where $v^3=1$ and ${\theta}$ is an ${\mathbb{F}}_p$-automorphism such that ${\theta}(v)=v^2$. We show that when n is even, these codes are either principal or generated by two elements. The generator and parity check matrix are proposed. Some examples of linear codes with optimum Hamming distance are also provided.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.31B no.4
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• pp.106-114
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• 1994

A new merging technique is adopted for combining rectangular parallelepipes produced by 2-D rectangular code into more intuitive 30D volume elements. Rectangular parallelepiped codes (RP codes) can be used in volume-based representation of a three-dimensional object. We proposed more regularity-conserving 2-D rectangular coding scheme to merge rectangular cells represented by RP codes in three-dimensional space. After being constructed from modified 2-D rectangular code, 3-D RP codes are merged in the two orthogonal directions using new merging algorithm. The shape of merged 3-D object reconstructed by proposed algorithm is shown to be much closer to the original object shape than that of conventional RP codes. The storage requirement of merged object can be also reduced.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.40 no.3
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• pp.491-496
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• 2015

In this paper, we introduce two classes of optimal codes, [$2^k-1$, k, $2^{k-1}$] simplex codes and [$2^k-1+k$, k, $2^{k-1}+1$] codes, attaining Griesmer bound with equality. We further present and compare the locality of them. The [$2^k-1+k$, k, $2^{k-1}+1$] codes have good locality property as well as optimal code length with given code dimension and minimum distance. Therefore, we expect that [$2^k-1+k$, k, $2^{k-1}+1$] codes can be applied to various distributed storage systems.