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Doctorate thesis defense of Hayfa BEN THAMEUR

Doctorate thesis defense on March 15th 2019 at 09H00 ,in Sup’Com Amphitheater Ibn Khaldoun.

Entitled :ADMM-LP decoding of LDPC convolutional codes : from algorithm to implementation

Presented by :



Chairman of the Jury


Professor at SUP’COM, Tunisia






Professor at ENIT, Tunisia


Olivier BERDER

Professor at IUT, France






Professor at SUP’COM, Tunisia




Thesis Director :


Professor at SUP’COM, Tunisia






Associate Professor at ISETCOM, Tunisia


Christophe JEGO

Professor at IPB/ENSEIRB-MATMECA, France


Bertrand LEGAL

Associate Professor at IPB/ENSEIRB-MATMECA, France





LDPC convolutional codes (LDPC-CC) have been the focus of intensive research works since their discovery in 1999, thanks to their near Shannon limit performance, their capability to outperform LDPC block codes (LDPC-BC) and to compete turbo codes for reliable decoding in many evolved communication systems; and their flexibility to meet packet-based as well as streaming-based applications’ requirements. As an alternative to message passing (MP) decoding, linear programming (LP) decoding is an approximation to maximum-likelihood decoding by relaxing the optimal decoding problem into a linear optimization problem. Recently, an efficient LP decoder has been proposed based on a popular distributed optimization method called alternating direction method of multipliers (ADMM).

The main objective of this thesis is to bring this innovative decoding technique to the sphere of LDPC-CC decoding (ADMM-CC). First, a proof of concept of its applicability to packed-based and streaming-based scenarios was provided. We demonstrated that the ADMM algorithm outperforms the BP decoding in high-reliability channels. Then, several algorithmic optimizations were applied and evaluated from a hardware standpoint. In fact, three check node centric schedules were proposed. We proved that the proposed approaches improve the convergence speed of the ADMM-CC decoder and reduce its computational complexity while preserving its error rate performances. Finally, we implemented the ADMM-CC decoder on an FPGA target using an optimized fixed-point representation, a pipeline architecture and the horizontal layered schedule. In addition, we proposed two improved techniques for designing the internal computations. The on chip implementation results demonstrated the applicability of the ADMM-CC algorithm on hardware targets though its hardware cost was found to be higher than the BP based decoder. To conclude, the work done in this thesis extends the use of the ADMM algorithm to LDPC-CC decoding. It demonstrates that the ADMM-CC can be a viable candidate for emergent communication systems.

Keywords :

LDPC convolutional codes, linear programming, alternate direction method of multipliers, iterative decoding, convergence, flooding/layered/informed dynamic schedules, throughput, pipeline architecture, HLS, FPGA.