In this paper, a method for the asymptotic analysis of generalized low-density parity-check (GLDPC) codes on the binary erasure channel (BEC) is proposed. The considered GLDPC codes have block linear codes as check nodes. Instead of considering specific check component codes, like Hamming or BCH codes, random codes are considered, and a technique is developed for obtaining the expected check EX...

This work is dedicated to the design, analysis and optimization of Application-Level Forward Erasure Correction (AL-FEC) codes. In particular, we explore a class of Generalized LDPC (GLDPC) codes, named GLDPC-Staircase codes, involving the LDPCStaircase code (base code) as well as Reed-Solomon (RS) codes (outer codes). In the first part of this thesis, we start by showing that RS codes having “...

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1. Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.1. Block Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.1.1. Linear Block Codes . . . . . . . . . . . . . . . . . . 22 1.2. Commun...

Forward error correction (FEC) is as one of the key technologies enabling the next-generation high-speed fiber optical communications. In this paper, we propose a rate-adaptive scheme using a class of generalized low-density parity-check (GLDPC) codes with a Hamming code as local code. We show that with the proposed unified GLDPC decoder architecture, a variable net coding gains (NCGs) can be a...

Introduction: Multilevel coding (MLC) was proposed by Imai and Hirawaki [1] as a bandwidth-efficient coded modulation scheme designed for protecting each bit of a non-binary symbol with the aid of binary codes, while maintaining different target bit error rates (BERs). Parallel independent decoding (PID) [2] is employed as an efficient decoding strategy with reduced decoding delay, where there ...

A method for the asymptotic analysis of doublygeneralized low-density parity-check (D-GLDPC) codes on the binary erasure channel (BEC) is described. The proposed method is based on extrinsic information transfer (EXIT) charts. It permits to overcome the impossibility to evaluate the EXIT function for the check or variable component codes, in situations where the information functions or split i...

In this paper, we analyze the tradeoff between coding rate and asymptotic performance of a class of generalized low-density parity-check (GLDPC) codes constructed by including a certain fraction of generalized constraint (GC) nodes in the graph. The rate of the GLDPC ensemble is bounded using classical results on linear block codes, namely Hamming bound and Varshamov bound. We also study the im...

Generalized low-density parity-check (GLDPC) codes are a class of LDPC in which the standard single parity check (SPC) constraints replaced by defined linear block code. These stronger typically result improved error floor performance, due to better minimum distance and trapping set properties, at cost some increased decoding complexity. In this paper, we study spatially coupled generalized (SC...

A generalized low-density parity-check (GLDPC) code is a class of codes, where single parity check nodes in conventional (LDPC) are replaced by linear codes with higher constraints. In this paper, we introduce new method constructing GLDPC inserting the for partial doping. While protograph dopes replacing them nodes, constructed adding and partially doping selected variable to possess degrees f...