• ETRI Journal
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• 제31권5호
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• pp.518-524
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• 2009

Single parity check (SPC) product codes are simple yet powerful codes that are used to correct errors and/or recover erasures. The focus of this paper is to evaluate the performance of such codes under erasure scenarios and to develop a closed-form tight upper bound for the post-decoding erasure rate. Closed-form exact expressions are derived for up to seven erasures. Previously published closed-form bounds assumed that all unrecoverable patterns should contain four erasures in a square. Additional non-square patterns are accounted for in the proposed expressions. The derived expressions are verified using exhaustive search. Eight or more erasures are accounted for by using a bound. The developed expressions improve the evaluation of the recoverability of SPC product codes without the need for simulation or search algorithms, whether exhaustive or novel.

• ETRI Journal
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• 제31권5호
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• pp.585-592
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• 2009

This paper presents a method for decoding high minimal distance ($d_{min}$) short codes, termed Cortex codes. These codes are systematic block codes of rate 1/2 and can have higher$d_{min}$ than turbo codes. Despite this characteristic, these codes have been impossible to decode with good performance because, to reach high $d_{min}$, several encoding stages are connected through interleavers. This generates a large number of hidden variables and increases the complexity of the scheduling and initialization. However, the structure of the encoder is well suited for analog decoding. A proof-of-concept Cortex decoder for the (8, 4, 4) Hamming code is implemented in subthreshold 0.25-${\mu}m$ CMOS. It outperforms an equivalent LDPC-like decoder by 1 dB at BER=$10^{-5}$ and is 44 percent smaller and consumes 28 percent less energy per decoded bit.

• 대한수학회보
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• 제52권3호
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• pp.915-923
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• 2015

Self-dual codes have been actively studied because of their connections with other mathematical areas including t-designs, invariant theory, group theory, lattices, and modular forms. We presented the building-up construction for self-dual codes over GF(q) with $q{\equiv}1$ (mod 4), and over other certain rings (see [19], [20]). Since then, the existence of the building-up construction for the open case over GF(q) with $q=p^r{\equiv}3$ (mod 4) with an odd prime p satisfying $p{\equiv}3$ (mod 4) with r odd has not been solved. In this paper, we answer it positively by presenting the building-up construction explicitly. As examples, we present new optimal self-dual [16, 8, 7] codes over GF(7) and new self-dual codes over GF(7) with the best known parameters [24, 12, 9].

• 디지털산업정보학회논문지
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• 제8권1호
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• pp.147-155
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• 2012

Fountain codes ensure reliability and robustness for time varying channels in wireless communication. In this paper, the concatenated fountain codes for AWGN and slow fading channels are investigated. Wireless system model, which includes the concatenated fountain code and modulation, is proposed. Maximum achievable rate is used for analyzing the performance of the system model for AWGN and fading channels. Belief Propagation (BP) algorithm is used for exploiting the soft information received at the decoder. Simulation results show that, concatenated fountain codes performs significantly better than that of a conventional Fountain codes with large packet lengths for higher Signal to Noise Ratio (SNR) in slow fading channels.

• 한국식품위생안전성학회지
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• 제20권2호
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• pp.103-113
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• 2005

Sanitary codes of retail ffod establishment of Korea, Japan, China, and America were reviewed in order to figure out the differences of the codes. The codes of Korea & Japan are similar in many aspects. The code of America regulates food safety procedures in detail and are easy to interpret. The code of China is broad and not specific in the procedures. Korean code deals with many administration affairs and Japanese code deals with food test and business. Chinese code also deals with administration and standards. American code defines 90 different terms while the codes of rest of the countries define only few terms. For sanitization American code specifies the procedures in specific terms in detail but others do not specify the procedures. For facilities, the American code specifies location, material and procedures but other codes also specify the material but the contents of the codes are not so much specific to compare with American code.

• Journal of applied mathematics & informatics
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• 제36권5_6호
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• pp.359-368
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• 2018

In this paper, we investigate quasi-cyclic codes over the ring $R={\mathbb{F}}_2+v{\mathbb{F}}_2$, where $v^2=v$. We investigate the structure of generators for one-generator quasi-cyclic codes over R and their minimal spanning sets. Moreover, we find the rank and a lower bound on minimum distances of free quasi-cyclic codes over R. Further, we find a relationship between cyclic codes over a different ring and quasi-cyclic codes of index 2 over R.

• Korean Journal of Mathematics
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• 제25권3호
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• pp.379-388
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• 2017

Self-dual codes of lengths less than 5 over ${\mathbb{Z}}_p$ are completely classified by the second author [The classification of self-dual modular codes, Finite Fields Appl. 17 (2011), 442-460]. The number of such self-dual codes are also determined. In this article we will extend the results to classify self-dual codes over ${\mathbb{Z}}_{p^2}$ of length less than 5 and give the number of codes in each class. Explicit and complete classifications for small p's are also given.

• Journal of Communications and Networks
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• 제17권4호
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• pp.346-350
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• 2015

It is known that the progressive edge-growth (PEG) algorithm can be used to construct low-density parity-check (LDPC) codes at finite code lengths with large girths through the establishment of edges between variable and check nodes in an edge-by-edge manner. In [1], the authors derived a class of LDPC codes for relay communication systems by extending the full-diversity root-LDPC code. However, the submatrices of the parity-check matrix H corresponding to this code were constructed separately; thus, the girth of H was not optimized. To solve this problem, this paper proposes a modified PEG algorithm for use in the design of large girth and full-diversity LDPC codes. Simulation results indicated that the LDPC codes constructed using the modified PEG algorithm exhibited a more favorable frame error rate performance than did codes proposed in [1] over block-fading channels.

• Journal of Communications and Networks
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• 제13권3호
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• pp.205-210
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• 2011

This paper presents an approach to the construction of multiple-rate quasi-cyclic low-density parity-check (LDPC) codes. Parity-check matrices of the proposed codes consist of $q{\times}q$ square submatrices. The block rows and block columns of the parity-check matrix correspond to the hyperplanes (${\mu}$-fiats) and points in Euclidean geometries, respectively. By decomposing the ${\mu}$-fiats, we obtain LDPC codes of different code rates and a constant code length. The code performance is investigated in term of the bit error rate and compared with those of LDPC codes given in IEEE standards. Simulation results show that our codes perform very well and have low error floors over the additive white Gaussian noise channel.

• Journal of Communications and Networks
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• 제17권3호
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• pp.221-230
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• 2015

Rateless codes have been shown to be able to provide greater flexibility and efficiency than fixed-rate codes for multicast applications. In the following, we optimize rateless codes for unequal error protection (UEP) for multimedia multicasting to a set of heterogeneous users. The proposed designs have the objectives of providing either guaranteed or best-effort quality of service (QoS). A randomly interleaved rateless encoder is proposed whereby users only need to decode symbols up to their own QoS level. The proposed coder is optimized based on measured transmission properties of standardized raptor codes over wireless channels. It is shown that a guaranteed QoS problem formulation can be transformed into a convex optimization problem, yielding a globally optimal solution. Numerical results demonstrate that the proposed optimized random interleaved UEP rateless coder's performance compares favorably with that of other recently proposed UEP rateless codes.