Iterative Decoding of Spatially-Coupled Product Codes using Guessing Random Additive Noise Decoding Algorithms

Abstract

Forward Error Correction Codes (FEC) in Coding Theory, Information Theory and Telecommunication is used to control the errors in information that was transmitted over a noisy channel. Low Density Parity Check (LDPC) codes are linear error correcting codes used to transmit messages over noisy channels. LDPC codes are capacity approaching, meaning that practical constructions exist in which noise threshold can be set very close to Shannon Limit. LDPC codes are defined by a sparse parity check matrix. It is transmitted through Additive White Gaussian Noise channel with Binary Phase Shift keying modulation. The noisy message data is decoded using Sum Product and Min Sum decoding algorithms. Short cycles in LDPC tanner graphs are called girths. They degrade the performance as they affect the independence of extrinsic information exchanged in iterative decoding. In this research, Simulated Annealing algorithm is used to construct QC-LDPC codes with Higher girth.

Product Codes are the combination of linear codes. It produces powerful error correcting codes through multiple low error correction capability codes. Since each code symbol appears once in the row element and once in the column element, the encoding of product codes is done in horizontal and vertical manner. Here Zipper Codes are used, a type of Product Codes.

This manuscript will be demonstrating through the research evidence gathered through various experimentation on Error Correction Codes, one of the efficient methods to achieving better Bit Error Rates. Zipper Codes, introduced in 2019, a framework for describing Spatially-Coupled Interleaved Codes with Sliding Window - Iterative Decoding Scheme. Here BCH Codes are used to demonstrate Zipper Codes.

Followed by that is GRAND - Decoder. A new form of decoding strategy where the error patterns are determined rather than determining entire code-words. Together this research intends to demonstrate that the system is able to efficiently decode at rates of 10^-7 by Sound-Noise-Ratios (SNR) 5dB in the Additive White Gaussian Noise Channel.