Selective Video Coding based on Bezier Curves

In this paper the problem of reconstruction of video frames is addressed, when there are missing pixels in each video frame or is corrupted with noise and also the locations of corrupted pixels are not known. The modified data can be corrected using Forward Error Correcting Codes. Forward Error correcting codes detect and correct errors with the help of complex decoders. This work proposes a new approach called Selective encoding for reconstruction of Video Frames from Error. This algorithm combines the Bezier curves over Galois Field GF (p^m) and the Low Density Parity Check Codes for performing encoding and decoding. The proposed decoder is capable of detecting and correcting errors in each video frame, where only selected pixel values are encoded and decoded. This reduces the decoding time significantly. Further, when binary representation of the Galois Field is used, the speed of the decoder is enhanced as there is no carry generation and carry propagation when any modular arithmetic operation is carried out. Further time complexity is improvised by using parallel processing. The coding of the algorithm is carried out using MATLAB. Keyword: Selective Encoding, Error Recovery, LDPC codes, Bezier curve, Galois field. __________________________________________________*****_________________________________________________ I. Literature Survey The work of Daniel Costello J et al. in “Applications of Error-Control Coding” mainly discusses the various error control methods in mobile communication, like the different FEC codes like Hamming code, Reed Solomon Code, Golay code, Low Density Parity Check codes (LDPC) and Turbo coding for GSM and CDMA along with the different data rates[1]. M H Azmi in his PhD Thesis on “Design of low-density parity-check codes in relay channels “ , discusses about the capacity of LDPC which is the subject of intense interest in research[2]. Sheryl L. Howard in his work on “Error control coding in wireless sensor networks “ mainly discusses about the specific error control coding like Checksum, Reed Solomon, Cyclic Redundancy Check and Convolution codes in WSN‟s. The authors have implemented several decoders like Reed Solomon, Hard decision Viterbi, Soft Decision Viterbi, LDPC codes, for the data in different environments[3]. The works of sanjeev kumar et al. mainly discusses the methods of improving the total BER which is obtained through the combination of RS codes for correcting burst errors and convolution codes which are good for correcting random errors, that are caused due to a noisy channel. LDPC codes are known to perform well in the presence of Additive White Gaussian Noise (AWGN) but for very large block lengths[5]. The authors of “Performance study of non-binary LDPC codes over Galois field”, V S Ganepola et al. Have proposed to define the codes over higher order Galois fields to overcome the limitations of having a large block length[6]. The authors of” Review paper on the decoding of LDPC codes using Advanced Gallagers algorithm” Padmini U Wasule et al. mainly discusses on the decoding of Low Density Parity Check Codes using Advanced Gallagers algorithm, which has a fully parallel implementation to reduce the Bit Error Rate and lower the hardware complexity at the cost of increase in area to achieve maximum throughput[7]. Alin Sindhu has proposed “A Galois field based very fast and compact error correcting technique” which discusses on Euclidean Geometry based LDPC where serial one step majority logic decoder is used. The received vector is cyclically shifted and then fed to the shift register circuit to perform the error correction. However, as the number of bits increases, the decoding time increases. Also the hardware complexity enhances, if the information to be encoded increases, as the proposed method uses p-input XOR gates, depending on the size of the parity matrix[8]. M. P. C. Fossorier et al. In their work on “ Reduced complexity iterative decoding of low density parity check nodes based on belief propagation”, discusses on Fast decoding algorithms based on Fast Fourier Transform to reduce the computation complexity of the belief propagation algorithm using higher order Galois field but for moderate code lengths. The algorithm reduces the computational complexity by simplifying the check node computation. But the algorithm is unable to improve the decoding performance of the LDPC codes[9]. J.P chen et al. Have discussed on “Density evolution for two improved BP-based decoding algorithm for LDPC codes”, which have an improvement in the decoding performance, but decoding performance suffers from degradation when output is near to zero[10]. The work of Meng Xu et al. is on Modified Offset min-sum algorithm (MOMS), which has an improvement in the decoding performance and requires P + 2 more addition operations compared, to OMS algorithm[11]. International Journal on Recent and Innovation Trends in Computing and Communication ISSN: 2321-8169 Volume: 5 Issue: 2 133 – 143 _______________________________________________________________________________________________ 134 IJRITCC | February 2017, Available @ http://www.ijritcc.org _______________________________________________________________________________________ From the Literature Survey, it is observed that a better performance in decoding is required. The proposed algorithm is on Selective Encoding. Here the complexity of the hardware can be simplified and a better performance of the decoder can be achieved even when output is zero. Further the improvement achieved in the proposed work, is reduction in the area as the Hardware used is XOR gates. Further, there is No performance degradation seen when output is zero. Also, K-P modulo-additions are required for decoding, where K is the length of the information digits and P is the number of non zero digits of the Parity matrix. It has been observed that a better improvement in the decoder performance is achieved using Selective Encoding in Galois Field GF (2 m ).