GLDPC-Staircase AL-FEC codes: a fundamental study and new results

Ferdaouss Mattoussi,Vincent Roca,Bessem Sayadi

doi:10.1186/s13638-016-0660-y

Ferdaouss Mattoussi, Vincent Roca + Show 1 more

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https://doi.org/10.1186/s13638-016-0660-y

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Abstract

This paper provides fundamentals in the design and analysis of Generalized Low-Density Parity Check (GLDPC)-Staircase codes over the erasure channel. These codes are constructed by extending an LDPC-Staircase code (base code) using Reed-Solomon (RS) codes (outer codes) in order to benefit from more powerful decoders. The GLDPC-Staircase coding scheme adds, in addition to the LDPC-Staircase repair symbols, extra-repair symbols that can be produced on demand and in large quantities, which provides small rate capabilities. Therefore, these codes are extremely flexible as they can be tuned to behave either like predefined rate LDPC-Staircase codes at one extreme, or like a single RS code at another extreme, or like small rate codes. Concerning the code design, we show that RS codes with “quasi” Hankel matrix-based construction fulfill the desired structure properties, and that a hybrid (IT/RS/ML) decoding is feasible that achieves maximum likelihood (ML) correction capabilities at a lower complexity. Concerning performance analysis, we detail an asymptotic analysis method based on density evolution (DE), extrinsic information transfer (EXIT), and the area theorem. Based on several asymptotic and finite length results, after selecting the optimal internal parameters, we demonstrate that GLDPC-Staircase codes feature excellent erasure recovery capabilities, close to that of ideal codes, both with large and very small objects. From this point of view, they outperform LDPC-Staircase and Raptor codes and achieve correction capabilities close to those of RaptorQ codes. Therefore, all these results make GLDPC-Staircase codes a universal Application-Layer FEC (AL-FEC) solution for many situations that require erasure protection such as media streaming or file multicast transmission.

Highlights

extrinsic information transfer (EXIT) technique is a tool for predicting the convergence behavior of iterative processors for a variety of communication problems [21]
We focused in our work on EXIT based on entropy to evaluate the performance of Generalized Low-Density Parity Check (GLDPC)-Staircase codes under (IT+RS) and maximum likelihood (ML) decoding
4.2 Experimental conditions For the finite length analysis, we have developed a GLDPC-Staircase codec based on RS codes under (IT+RS) and ML decoding methods, in C language, using the OpenFEC.org project

Summary

Introduction

EXIT technique is a tool for predicting the convergence behavior of iterative processors for a variety of communication problems [21]. To visualize the convergence of iterative systems, rather than mutual information, the entropy information can be used (i.e., one minus mutual information). We focused in our work on EXIT based on entropy to evaluate the performance of GLDPC-Staircase codes under (IT+RS) and ML decoding. We extended the method presented in [22]. The EXIT technique defined relates to the asymptotic performance of the ensemble E(λ, ρ, fe) under the decoding

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