Multi-scale error-correcting codes and their decoding using belief propagation

Matthias Hummert, Dirk Wübben, Armin Dekorsy

The problem of finding good error correcting codes for short block lenghts and its corresponding decoders is an open research topic. A frequently applied soft decoder is the Belief Propagation (BP) decoder, however with degraded performance in case of short loops in the Tanner graph. This is especially problematic for short length codes as loops of small length are more likely to occur. In this paper, we propose the Machine Learning Scaled Belief Propagation (MLS-BP) to mitigate the performance loss of BP decoding for short length codes by introducing a learned scaling factor for the receive signals. The key point of this approach is the fact that the implementation of the BP decoder is not changed and the simple scaling leads to performance results comparable to other proposed BP improvements.

François Leduc-Primeau, Saied Hemati, Vincent Gaudet +1 more

Hironori Uchikawa

Etienne Ackermann, Trienko Grobler, Gusti van Zyl +1 more

Special cases of the belief propagation algorithm are commonly used to decode various linear error correcting codes. We show that the belief propagation algorithm can also be applied to the decoding problem for nonlinear error correcting codes by considering a modified set of update rules. We demonstrate the modified belief propagation algorithm by applying it to the well-known Nordstrom-Robinson (15, 256, 5) nonlinear code. The Nordstrom-Robinson code contains many cycles, which means that belief propagation is suboptimal. Nevertheless, we observe a coding gain of about 1.2 dB with this method.

S. A. Madkour

Zahraa Abbas Hamza, Shereen Abdalkadum Shandal

Polar Codes are a new class of capacity-reaching codes that have low decoding complexity and excessive reliability. They are primarily based on the concept of channel polarization, which makes a few bits inside the codeword more reliable and a few much less reliable because the code duration increases. This examination comprehensively evaluates how effective Belief Propagation (BP) and Belief Propagation with List (BPL) Decoding algorithms are in the Binary Erasure Channel (BEC) setup. The fundamental purpose is to recognize how nicely these algorithms deal with errors and enhance the reliability of verbal exchange structures. Different code lengths and list sizes are examined to see how they affect the Block Error Rate (BLER). This paper considers 4 codes studied and carried out in the usage of MATLAB lengths: N=256, 512, 1024, and 2048, and varies the Energy per bit to Noise power (Eb/No) from 1 dB to a 3.5 dB with list sizes eight and sixteen. The experiments show how the BP and BPL algorithms perform in coping with erasure errors and ensuring reliable deciphering. The BLER figures provide an in-depth description and comparison of the BP and BPL interpreting algorithms. The analysis highlights the promising blunder-correction talents of each BP and BPL algorithm in the BEC context. As the code length increases, the capability to correct errors also improves, showing that these algorithms can scale effectively. The addition of list decoding in BPL similarly enhances blunder correction by offering multiple possible answers. These examine the effect of Eb/No stages on the performance of BP and BPL deciphering, displaying that better Eb/No stages enhance accuracy but also increase the erasure chance. This paper discusses the trade-offs between accuracy and complexity for BP and BPL deciphering, presenting insights into their performance traits and optimization.