Non-linear Cyclic Codes that Attain the Gilbert-Varshamov Bound

We prove that there exist non-linear binary cyclic codes that attain the Gilbert-Varshamov bound

On formulas for decoding binary cyclic codes

We adress the problem of the algebraic decoding of any cyclic code up to the true minimum distance. For this, we use the classical formulation of the problem, which is to find the error locator polynomial in terms of the syndroms of the received word. This is usually done with the Berlekamp-Massey algorithm in the case of BCH codes and related codes, but for the general case, there is no generic algorithm to decode cyclic codes. Even in the case of the quadratic residue codes, which are good codes with a very strong algebraic structure, there is no available general decoding algorithm. For this particular case of quadratic residue codes, several authors have worked out, by hand, formulas for the coefficients of the locator polynomial in terms of the syndroms, using the Newton identities. This work has to be done for each particular quadratic residue code, and is more and more difficult as the length is growing. Furthermore, it is error-prone. We propose to automate these computations, using elimination theory and Grbner bases. We prove that, by computing appropriate Grbner bases, one automatically recovers formulas for the coefficients of the locator polynomial, in terms of the syndroms

FPGA based Novel High Speed DAQ System Design with Error Correction

Present state of the art applications in the area of high energy physics experiments (HEP), radar communication, satellite communication and bio medical instrumentation require fault resilient data acquisition (DAQ) system with the data rate in the order of Gbps. In order to keep the high speed DAQ system functional in such radiation environment where direct intervention of human is not possible, a robust and error free communication system is necessary. In this work we present an efficient DAQ design and its implementation on field programmable gate array (FPGA). The proposed DAQ system supports high speed data communication (~4.8 Gbps) and achieves multi-bit error correction capabilities. BCH code (named after Raj Bose and D. K. RayChaudhuri) has been used for multi-bit error correction. The design has been implemented on Xilinx Kintex-7 board and is tested for board to board communication as well as for board to PC using PCIe (Peripheral Component Interconnect express) interface. To the best of our knowledge, the proposed FPGA based high speed DAQ system utilizing optical link and multi-bit error resiliency can be considered first of its kind. Performance estimation of the implemented DAQ system is done based on resource utilization, critical path delay, efficiency and bit error rate (BER).Comment: ISVLSI 2015. arXiv admin note: substantial text overlap with arXiv:1505.04569, arXiv:1503.0881

Low Cost Radiation Hardened Software and Hardware Implementation for CubeSats

CubeSats are small satellites used for scientific experiments because they cost less than full sized satellites. Each CubeSat uses an on-board computer. The on-board computer performs sensor measurements, data processing, and CubeSat control. The challenges of designing an on-board computer are costs, radiation, thermal stresses, and vibrations. An on-board computer was designed and implemented to solve these challenges. The on-board computer used special components to mitigate radiation effects. Software was also used to provide redundancies in cases of faults. This paper may aid future spacecraft design as it improves the reliability of spacecraft, while keeping costs low

Efficient decoding of some classes of binary cyclic codes beyond the Hartmann-Tzeng bound

International audienceA new bound on the distance of binary cyclic codes is proposed. The approach is based on the representation of a subset of the roots of the generator polynomial by a rational function. A new bound on the minimum distance is proven and several classes of binary cyclic codes are identified. For some classes of codes, this bound is better than the known bounds (e.g. BCH or Hartmann-Tzeng bound). Furthermore, a quadratic-time decoding algorithm up to this new bound is developed