Idempotents, Mattson-Solomon Polynomials and Binary LDPC codes
R.Horan, C.Tjhai, M.Tomlinson, M.Ambroze, M.Ahmed
TL;DR
This paper presents an algorithm in the Mattson-Solomon domain for constructing binary idempotents, enabling the design of binary LDPC codes with controllable properties such as sparsity, rate, and minimum distance.
Contribution
It introduces a novel algorithm for searching binary idempotents in the Mattson-Solomon domain to construct LDPC codes with customizable parameters.
Findings
New binary LDPC codes with desirable properties
Algorithm effectively controls code parameters
Demonstrated codes with improved performance
Abstract
We show how to construct an algorithm to search for binary idempotents which may be used to construct binary LDPC codes. The algorithm, which allows control of the key properties of sparseness, code rate and minimum distance, is constructed in the Mattson-Solomon domain. Some of the new codes, found by using this technique, are displayed.
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Taxonomy
TopicsError Correcting Code Techniques · Coding theory and cryptography · Advanced Wireless Communication Techniques