• Title, Summary, Keyword: codes

Search Result 4,706, Processing Time 0.044 seconds

Nonlinear Product Codes and Their Low Complexity Iterative Decoding

  • Kim, Hae-Sik;Markarian, Garik;Da Rocha, Valdemar C. Jr.
    • ETRI Journal
    • /
    • v.32 no.4
    • /
    • pp.588-595
    • /
    • 2010
  • This paper proposes encoding and decoding for nonlinear product codes and investigates the performance of nonlinear product codes. The proposed nonlinear product codes are constructed as N-dimensional product codes where the constituent codes are nonlinear binary codes derived from the linear codes over higher order alphabets, for example, Preparata or Kerdock codes. The performance and the complexity of the proposed construction are evaluated using the well-known nonlinear Nordstrom-Robinson code, which is presented in the generalized array code format with a low complexity trellis. The proposed construction shows the additional coding gain, reduced error floor, and lower implementation complexity. The (64, 24, 12) nonlinear binary product code has an effective gain of about 2.5 dB and 1 dB gain at a BER of $10^{-6}$ when compared to the (64, 15, 16) linear product code and the (64, 24, 10) linear product code, respectively. The (256, 64, 36) nonlinear binary product code composed of two Nordstrom-Robinson codes has an effective gain of about 0.7 dB at a BER of $10^{-5}$ when compared to the (256, 64, 25) linear product code composed of two (16, 8, 5) quasi-cyclic codes.

Construction of Optimal Concatenated Zigzag Codes Using Density Evolution with a Gaussian Approximation

  • Hong Song-Nam;Shin Dong-Joon
    • The Journal of Korean Institute of Communications and Information Sciences
    • /
    • v.31 no.9C
    • /
    • pp.825-830
    • /
    • 2006
  • Capacity-approaching codes using iterative decoding have been the main subject of research activities during past decade. Especially, LDPC codes show the best asymptotic performance and density evolution has been used as a powerful technique to analyze and design good LDPC codes. In this paper, we apply density evolution with a Gaussian approximation to the concatenated zigzag (CZZ) codes by considering both flooding and two-way schedulings. Based on this density evolution analysis, the threshold values are computed for various CZZ codes and the optimal structure of CZZ codes for various code rates are obtained. Also, simulation results are provided to conform the analytical results.

OPTIMAL LINEAR CODES OVER ℤm

  • Dougherty, Steven T.;Gulliver, T. Aaron;Park, Young-Ho;Wong, John N.C.
    • Journal of the Korean Mathematical Society
    • /
    • v.44 no.5
    • /
    • pp.1139-1162
    • /
    • 2007
  • We examine the main linear coding theory problem and study the structure of optimal linear codes over the ring ${\mathbb{Z}}_m$. We derive bounds on the maximum Hamming weight of these codes. We give bounds on the best linear codes over ${\mathbb{Z}}_8$ and ${\mathbb{Z}}_9$ of lengths up to 6. We determine the minimum distances of optimal linear codes over ${\mathbb{Z}}_4$ for lengths up to 7. Some examples of optimal codes are given.

ONE-HOMOGENEOUS WEIGHT CODES OVER FINITE CHAIN RINGS

  • SARI, MUSTAFA;SIAP, IRFAN;SIAP, VEDAT
    • Bulletin of the Korean Mathematical Society
    • /
    • v.52 no.6
    • /
    • pp.2011-2023
    • /
    • 2015
  • This paper determines the structures of one-homogeneous weight codes over finite chain rings and studies the algebraic properties of these codes. We present explicit constructions of one-homogeneous weight codes over finite chain rings. By taking advantage of the distance-preserving Gray map defined in [7] from the finite chain ring to its residue field, we obtain a family of optimal one-Hamming weight codes over the residue field. Further, we propose a generalized method that also includes the examples of optimal codes obtained by Shi et al. in [17].

Some Characteristics of Unit-Distance Duo-Decimal Codes (단위거리 12진부호의 몇가지 특성)

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

  • PDF

An Optimal Space Time Coding Algorithm with Zero Forcing Method in Underwater Channel (수중통신에서 Zero Forcing기법을 이용한 최적의 시공간 부호화 알고리즘)

  • Kwon, Hae-Chan;Park, Tae-Doo;Chun, Seung-Yong;Lee, Sang-Kook;Jung, Ji-Won
    • Journal of Navigation and Port Research
    • /
    • v.38 no.4
    • /
    • pp.349-356
    • /
    • 2014
  • In the underwater communication, the performance of system is reduced because of the inter-symbol interference occur by the multi-path. In the recent years, to deal with poor channel environment and improve the throughput, the efficient concatenated structure of equalization, channel codes and Space Time Codes has been studied as MIMO system in the underwater communication. Space Time Codes include Space Time Block Codes and Space Time Trellis Codes in underwater communication. Space Time Trellis Codes are optimum for equalization and channel codes among the Space Time Codes to apply in the MIMO environment. Therefore, in this paper, turbo pi codes are used for the outer code to efficiently transmit in the multi-path channel environment. The inner codes consist of Space Time Trellis Codes with transmission diversity and coding gain in the MIMO system. And Zero Forcing method is used to remove inter-symbol interference. Finally, the performance of this model is simulated in the underwater channel.

Finite Soft Decision Data Combining for Decoding of Product Codes With Convolutional Codes as Horizontal Codes (길쌈부호를 수평부호로 가지는 곱부호의 복호를 위한 유한 연판정 데이터 결합)

  • Yang, Pil-Woong;Park, Ho-Sung;Hong, Seok-Beom;Jun, Bo-Hwan;No, Jong-Seon;Shin, Dong-Joon
    • The Journal of Korean Institute of Communications and Information Sciences
    • /
    • v.37 no.7A
    • /
    • pp.512-521
    • /
    • 2012
  • In this paper, we propose feasible combining rules for a decoding scheme of product codes to apply finite soft decision. Since the decoding scheme of product codes are based on complex tanh calculation with infinite soft decision, it requires high decoding complexity and is hard to practically implement. Thus, simple methods to construct look-up tables for finite soft decision are derived by analyzing the operations of the scheme. Moreover, we focus on using convolutional codes, which is popular for easy application of finite soft decision, as the horizontal codes of product codes so that the proposed decoding scheme can be properly implemented. Numerical results show that the performance of the product codes with convolutional codes using 4-bit soft decision approaches to that of same codes using infinite soft decision.

THE CLASSIFICATION OF SELF-DUAL CODES OF LENGTH 6 OVER ℤm FOR SMALL m

  • Park, Young Ho
    • Journal of the Chungcheong Mathematical Society
    • /
    • v.23 no.4
    • /
    • pp.893-902
    • /
    • 2010
  • In this article we study self-dual codes of length 6 over ${\mathbb{Z}}_m$. A classification of such codes for $m{\leq}24$ is given. Main tool for the classification is the new double cosets decomposition method given in the recent article of the author.

QUADRATIC RESIDUE CODES OVER GALOIS RINGS

  • Park, Young Ho
    • Korean Journal of Mathematics
    • /
    • v.24 no.3
    • /
    • pp.567-572
    • /
    • 2016
  • Quadratic residue codes are cyclic codes of prime length n defined over a finite field ${\mathbb{F}}_{p^e}$, where $p^e$ is a quadratic residue mod n. They comprise a very important family of codes. In this article we introduce the generalization of quadratic residue codes defined over Galois rings using the Galois theory.