Belief-Propagation-Approximated Decoding of Low-Density Parity-Check Codes

In this paper, we propose a new reduced-complexity decoding algorithm of Low-Density Parity-Check (LDPC) codes, called Belief-Propagation-Approximated (BPA) algorithm, which utilizes the idea of normalization and translates approximately the intricate nonlinear operation in the check nodes of the original BP algorithm to only one operation of looking up the table. The normalization factors can be obtained by simulation, or theoretically. Simulation results demonstrate that BPA algorithm exhibits fairly satisfactory bit error performance on the Additive White Gaussian Noise (AWGN) channel.     

低差错平底特性的非规则LDPC码的设计

介绍了非规则LDPC码的发展并给出了其优势及缺点，重点论述用ACE算法来构造非规则LDPC码从而降低其差错平底特性。对降低非规则LDPC码的差错平底特性的其它方法提出了展望。     

一类小缺陷码的链条件

利用射影几何方法在小缺陷码中,NMDS码是链条件码;给出k维NμMDS(0μk-2)码满足链条件的一个充要条件与一些易判断的充分条件.     

Aggregate error locator and error value computation in AG codes

The aggregate error locator is defined and a computation method is given. The aggregate error locator is then used in a type of Forney algorithm to compute the error values in the received words of a Ca,b algebraic geometry code.     

Some new results on superimposed codes

A (w,r) cover‐free family is a family of subsets of a finite set such that no intersection of w members of the family is covered by a union of r others. A (w,r) superimposed code is the incidence matrix of such a family. Such a family also arises in cryptography as the concept of key distribution pattern. In the present paper, we give some new results on superimposed codes. First we construct superimposed codes from super‐simple designs which give us results better than superimposed codes constructed by other known methods. Next we prove the uniqueness of the (1,2) superimposed code of size 9 × 12, the (2,2) superimposed code of size 14 × 8, and the (2,3) superimposed code of size 30 × 10. Finally, we improve numerical values of upper bounds for the asymptotic rate of some (w,r) superimposed codes. © 2004 Wiley Periodicals, Inc.     

The Minimum PAPR Code for OFDM Systems

In this letter, a block code that minimizes the peak‐to‐average power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) signals is proposed. It is shown that peak envelope power is invariant to cyclic shift and codeword inversion. The systematic encoding rule for the proposed code is composed of searching for a seed codeword, shifting the register elements, and determining codeword inversion. This eliminates the look‐up table for one‐to‐one correspondence between the source and the coded data. Computer simulation confirms that OFDM systems with the proposed code always have the minimum PAPR.     

一种改善Turbo乘积编码OFDM系统性能的新方法

本文提出一种利用对译码器软信息限幅来改善多径衰落信道中Turbo乘积编码OFDM(TPC-OFDM)系统性能的新方法。通过对不同多径衰落信道中QPSK映射和16QAM映射的TPC-OFDM系统性能的数值仿真，结果表明在10^-5误比特率下，这种新方法比传统的迭代译码大约有6～10dB的改进，对严重多径环境下TPC-OFDM系统的错误平底也有明显的改进。     

Gray code for derangements

We give a Gray code and constant average time generating algorithm for derangements, i.e., permutations with no fixed points. In our Gray code, each derangement is transformed into its successor either via one or two transpositions or a rotation of three elements. We generalize these results to permutations with number of fixed points bounded between two constants.     

The Covering Radius of Ternary Cyclic Codes with Length up to 25

The covering radius of all ternary cyclic codes of length up to 25 is given. Some of the results were obtained by computer and for others mathematical reasonings were applied. The minimal distances of all codes were recalculated.     

A New Simple Ultrahigh Speed Decoding Algorithm for BCH Code

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