Optimizing the error recovery capabilities of LDPC-staircase codes featuring a Gaussian elimination decoding scheme

Abstract

Abstract-This work focuses on the LDPC codes for the packet erasure channel, also called AL-FEC (Application-Level Forward Error Correction codes). Previous work has shown that the erasure recovery capabilities of LDPC-triangle and LDPCstaircase AL-FEC codes can be greatly improved by means of a Gaussian Elimination (GE) decoding scheme, possibly coupled to a preliminary Zyablov Iterative Decoding (ID) scheme. Thanks to the GE decoding, the LDPC-triangle codes were very close to an ideal code. If the LDPC-staircase performances were also improved, they were not as close to an ideal code as the LDPCtriangle codes were.The first goal of this work is to reduce the gap between the LDPC-staircase codes and the theoretical limit. We show that a simple modification of the parity check matrix can significantly improve their recovery capabilities when using a GE decoding. Unfortunately the performances of the same codes featuring an ID are negatively impacted, as well as the decoding complexity. The second goal of this work is therefore to find an appropriate balance between all these aspects.

Performance analysis of a high-performance real-time application with several AL-FEC schemes

“…In [19], four different FEC techniques, that utilize XOR (eXclusive-OR) and RSE erasure codes, are adopted according to the network conditions. In [11] the performances of the LDPC-staircase codes are studied when using a hybrid IT/ML decoding scheme, both from the erasure recovery capability and decoding complexity viewpoints. This work is one of the foundations of the current paper, with the difference that in our work we are considering real-time flows, with different goals.…”

“…If not, add one or two extra "1-s" randomly to these rows. In [10], [11], a hybrid ITerative/Maximum Likelihood (IT/ML) decoding was proposed to improve the erasure recovery capabilities (now close to that of MDS codes) while keeping a moderate decoding complexity. This algorithm combines the optimal correction capabilities of the ML decoding with the low complexity of the IT [9] decoding.…”

“…battery or CPU capabilities), independently from other receivers, which is a great asset. In order to have good erasure recovery performances under IT/ML decoding, even with small n values, we adjust the N 1 parameter as follows [11]…”

“…Based on experimental results [11], we set the threshold at k × (1.05), which corresponds to a very high decoding success probability and a low decoding complexity (IT decoding will significantly simplify the linear system to be solve during ML decoding). As soon as at least k × (1.05) symbols are received, FEC decoding is launched.…”

Optimizing the Decoding Complexity of PEG-Based Methods with an Improved Hybrid Iterative/Gaussian Elimination Decoding Algorithm

“…This suggests a hybrid (HB) decoding strategy which combines the above-mentioned IT with GE decoding algorithms in order to compromise between performance and complexity. References [8][9][10][11][12] proposed and implemented HB decoding algorithms in BECs with the basic idea of employing IT decoding first. If the IT decoding fails to recover all the erased symbols, the GE decoding is activated to complete the decoding process and resolve the simplified system.…”