Abstract
Noise can scramble a message that is sent. This is true for both voicemails and digital communications transmitted to and from computer systems. During transmission, mistakes tend to happen. Computer memory is the most commonplace to use Hamming code error correction. With extra parity/redundancy bits added to Hamming code, single-bit errors may be detected and corrected. Short-distance data transmissions often make use of Hamming coding. The redundancy bits are interspersed and evacuated subsequently when scaling it for longer data lengths. The new hamming code approach may be quickly and easily adapted to any situation. As a result, it's ideal for sending large data bitstreams since the overhead bits per data bit ratio is much lower. The investigation in this article is extended Hamming codes for product codes. The proposal particularly emphasises on how well it functions with low error rate, which is critical for multimedia wireless applications. It provides a foundation and a comprehensive set of methods for quantitatively evaluating this performance without the need of time-consuming simulations. It provides fresh theoretical findings on the well-known approximation, where the bit error rate roughly equal to the frame error rate times the minimal distance to the codeword length ratio. Moreover, the analytical method is applied to actual design considerations such as shorter and punctured codes along with the payload and redundancy bits calculation. Using the extended identity equation on the dual codes, decoding can be done at the first instance. The achievement of 43.48% redundancy bits is obtained during the testing process which is a huge proportion reduced in this research work.
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