Improving Iterative Soft Decision Decoding of Reed Solomon Codes Using Deep Learning

Abstract

Telecommunications in the current information age is increasingly dependent on efficient transmission of data through a noisy channel. Therefore, utilizing For- ward Error Correction (FEC) in the development of decoding algorithms is an active area of research. This dissertation work focuses on exploiting deep learn- ing techniques and error correction techniques to improve iterative soft decision decoding of Reed Solomon codes (RS). The parity check matrix of RS codes is characterized by a dense structure. This directly affects the exchange of soft information during the iterative decoding process. Therefore, to counter this issue, a bit-level implementation is utilized with the proposed decoding approach. Furthermore, additional techniques to add sparsity to the parity check matrix are presented in this research work. The proposed method for adding sparsity leverages the cyclical properties of RS codes to add low rate rows to the parity check matrix. This sparse implementation aids with the exchange of soft information during the message passing stage of the proposed iterative decoding process. The implementation of deep learning techniques to improve iterative soft decision decoders are also presented in this dissertation. The proposed approach makes adjustments to the Neural Belief Propagation (NBP) algorithm for RS codes. The proposed NBP utilizes the sparse implementation presented in this research to improve exchange of soft information. This in turn leads to gains in error correction performance without further adding complexity which is one of the main advantages of incorporating neural networks in the iterative decoding process. Additionally, this dissertation proposes a Graph Neural Network (GNN) imple- mentation for iterative soft decision decoding of RS codes. The approach employs the GNN architecture to construct a fully connected graph. This graph represents a message passing algorithm based on the Tanner graph, with trainable weights assigned to the graph nodes. This implementation improves the error correction performance of the proposed iterative soft decision decoder while reducing the number of iterations required to decode the received vector.