Publication Details
Abstract
Methods for synthesizing error-correcting codes are examined in the context of communication channels subjected to additive noise through permutation-based methods. This research is motivated by the increase in interference on modern communication systems and the need for enhanced data transmission efficiency as a result of that interference. New algorithms are created for the construction of error-correcting codes based on the structural properties and combinatorial properties of permutations, with an objective to reduce the incidence of decoding errors. The efficacy of these newly developed methods has been assessed against the traditional methods of error-correcting codes, namely Reed-Solomon codes, and Convolutional codes, through a comparison of simulated data. According to results from simulations, increasing the amount of noise immunity can be accomplished by reducing the amount of relative errors by in Bit Error Rate (BER) with (e.g. a reduction of with a Viterbi decoder to using a Structural Decoder and finally to with an ML decoder). With this we were also able to keep our transmission rate. All of the performance references were made in relation to the Shannon Limit.
The methods discussed above have been validated for code block lengths of up to by using subgroup construction of the normal group S n and Galois Field mapping. However, we only tested the experimental simulations for and because of the real-time decoding requirements established in the 5G URLLC and IoT applications running on an ARM Cortex M4 processor. Our algebraic framework can be extended for use with code block lengths of , and as a result of hardware acceleration. In the future, researchers will use various algebraic techniques to optimize the order of permutations. This research provides insight that can aid in developing coding theories that may be applied in both 5G and IoT systems.