Application of RS Codes in Decoding QR Code

The QR Code is a 2 dimensional matrix code with high error correction capability. It employs RS codes to generate error correction codewords in encoding and recover errors and damages in decoding. This paper presents several QR Code’s virtues, analyzes RS decoding algorithm and gives a software flow chart of decoding the QR Code with RS decoding algorithm.

ERASED-CHASE DECODING FOR RS-CODED MPSK SIGNALING OVER A RAYLEIGH FADING CHANNEL

In this paper,a novel dual-metric,the maximum and minimum Squared Euclidean Distance Increment (SEDI) brought by changing the hard decision symbol,is introduced to measure the reli-ability of the received M-ary Phase Shift Keying (MPSK) symbols over a Rayleigh fading channel. Based on the dual-metric,a Chase-type soft decoding algorithm,which is called erased-Chase algorithm,is developed for Reed-Solomon (RS) coded MPSK schemes. The proposed algorithm treats the unre-liable symbols with small maximum SEDI as erasures,and tests the non-erased unreliable symbols with small minimum SEDI as the Chase-2 algorithm does. By introducing optimality test into the decoding procedure,much more reduction in the decoding complexity can be achieved. Simulation results of the RS(63,42,22)-coded 8-PSK scheme over a Rayleigh fading channel show that the proposed algorithm provides a very efficient tradeoff between the decoding complexity and the error performance. Finally,an adaptive scheme for the number of erasures is introduced into the decoding algorithm.

Channel Coding Based on Power Line Communication

This paper focuses on the forward error correction(FEC),the basic parameters determination of the RS convolution code,Turbo code and the LDPC code,and the corresponding encoding and decoding algorithm in power line communication(PLC)standard.Simulation experiment which is designed for narrow-band power line communication system based on OFDM is done.The coding using RS convolution code,Turbo code and LDPC code are compared,and further it is determined that which encoding method is more suitable for power line communication in China.

Improved Berlekamp-Massy Algorithm and Its Software Implementation on DSP

Based on the Berlekamp-Massy （BM） algorithm for Reed-Solomon（RS） decoding, an improved version is proposed, which focuses on how to find the error locator polynomial using least iterative operations. The conditions to end the iterative operations is derived. As a special case, criterion of only one error symbol in one received codeword is derived as well. Steps are listed concerning the implementation of the improved iterative decoding algorithm, which is carried out as software on the platform of TI＇s C6416 DSP. Decoding performance and decoding-delay of both improved and original algorithms under different （n,k） conditions are simulated. The results of simulations demonstrate that the improved algorithm has less computational complexity when the number of errors in a received codeword is relatively small. Therefore, in channels with low noise power spectrum density, the improved algorithm results in less decoding-delay than BM algorithm.

Error Detecting Dual Basis Bit Parallel Systolic Multiplication Architecture over GF（2^m）

An error tolerant hardware efficient verylarge scale integration （VLSI） architecture for bitparallel systolic multiplication over dual base, which canbe pipelined, is presented. Since this architecture has thefeatures of regularity, modularity and unidirectionaldata flow, this structure is well suited to VLSIimplementations. The length of the largest delay pathand area of this architecture are less compared to the bitparallel systolic multiplication architectures reportedearlier. The architecture is implemented using Austria Micro System＇s 0.35 μm CMOS （complementary metaloxide semiconductor） technology. This architecture canalso operate over both the dual-base and polynomialbase.