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In this paper we assess, through theoretical arguments and numerical simulations, the performance and complexity of a novel family of quasi-cyclic low-density generator matrix (QC-LDGM) codes. The design of such codes, denoted as ψ-unitary codes, is based on a class of binary circulant matrices recently introduced by the authors. Such matrices can have sparse inverse though being neither identity...
We propose a novel family of bi-dimensional product codes that can be interpreted as Low-Density Parity-Check (LDPC) codes. They are based on the adoption, as components, of the so-called Multiple Serially Concatenated Multiple Parity-Check (M-SC-MPC) codes, we have recently introduced. The distinctive feature of these codes is encoding and decoding simplicity that make them a valid alternative to...
Binary cyclic codes achieve good error correction performance and allow the implementation of very simple encoder and decoder circuits. Among them, BCH codes represent a very important class of t-error correcting codes, with known structural properties and error correction capability. Decoding of binary cyclic codes is often accomplished through hard-decision decoders, although it is recognized that...
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