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In this paper we consider the problem of encoding data into repeat-free sequences in which sequences are imposed to contain any k-tuple at most once (for predefined k). First, the capacity of the repeat-free constraint are calculated. Then, an efficient algorithm, which uses two bits of redundancy, is presented to encode length-n sequences for k = 2 + 2 log (n). This algorithm is then improved to support any value of k of the form k = a log (n), for 1 < a, while its redundancy is o(n). We also calculate the capacity of repeat-free sequences when combined with local constraints which are given by a constrained system, and the capacity of multi-dimensional repeat-free codes. [ABSTRACT FROM AUTHOR]

Additional check bits, which are commonly attached to the message’s input data, are normally used to minimize the error during data transmission. The receiver system implements a checking algorithm to determine if an error was occurred in the received data. This algorithm will correct a corrupted bit and recover the original message. An enhanced error detection correction code was presented to better detect and correct the corrupted conveyed bits. It improves the existing limitations of utilizing cyclic redundancy checking (CRC), Hamming code, and other checksum techniques. Also, it reduced the length of the redundancy bits which exists in CRC, the overhead of interspersing of the redundancy bits in a typical Hamming code, and the system resources such as processor time and bandwidth in checksum techniques. This paper was synthesized and simulated using the Xilinx Spartan 6 (XC7Z020-2CLG4841) FPGA. Results show that the resource utilization of the designed memory architecture using EEDC is lower compared to CRC, Hamming, and Checksum algorithms. [ABSTRACT FROM AUTHOR]