Analysis and Design of Binary Message-Passing Decoders

Binary message-passing decoders for low-density parity-check (LDPC) codes are studied by using extrinsic information transfer (EXIT) charts. The channel delivers hard or soft decisions and the variable node decoder performs all computations in the L-value domain. A hard decision channel results in the well-know Gallager B algorithm, and increasing the output alphabet from hard decisions to two bits yields a gain of more than 1.0 dB in the required signal to noise ratio when using optimized codes. The code optimization requires adapting the mixing property of EXIT functions to the case of binary message-passing decoders. Finally, it is shown that errors on cycles consisting only of degree two and three variable nodes cannot be corrected and a necessary and sufficient condition for the existence of a cycle-free subgraph is derived.Comment: 8 pages, 6 figures, submitted to the IEEE Transactions on Communication

Mutual Information-Maximizing Quantized Belief Propagation Decoding of Regular LDPC Codes

In mutual information-maximizing lookup table (MIM-LUT) decoding of low-density parity-check (LDPC) codes, table lookup operations are used to replace arithmetic operations. In practice, large tables need to be decomposed into small tables to save the memory consumption, at the cost of degraded error performance. In this paper, we propose a method, called mutual information-maximizing quantized belief propagation (MIM-QBP) decoding, to remove the lookup tables used for MIM-LUT decoding. Our method leads to a very efficient decoder, namely the MIM-QBP decoder, which can be implemented based only on simple mappings and fixed-point additions. Simulation results show that the MIM-QBP decoder can always considerably outperform the state-of-the-art MIM-LUT decoder, mainly because it can avoid the performance loss due to table decomposition. Furthermore, the MIM-QBP decoder with only 3 bits per message can outperform the floating-point belief propagation (BP) decoder at high signal-to-noise ratio (SNR) regions when testing on high-rate codes with a maximum of 10-30 iterations

Finite Length Analysis of LDPC Codes

In this paper, we study the performance of finite-length LDPC codes in the waterfall region. We propose an algorithm to predict the error performance of finite-length LDPC codes over various binary memoryless channels. Through numerical results, we find that our technique gives better performance prediction compared to existing techniques.Comment: Submitted to WCNC 201

Decoding of Non-Binary LDPC Codes Using the Information Bottleneck Method

Recently, a novel lookup table based decoding method for binary low-density parity-check codes has attracted considerable attention. In this approach, mutual-information maximizing lookup tables replace the conventional operations of the variable nodes and the check nodes in message passing decoding. Moreover, the exchanged messages are represented by integers with very small bit width. A machine learning framework termed the information bottleneck method is used to design the corresponding lookup tables. In this paper, we extend this decoding principle from binary to non-binary codes. This is not a straightforward extension, but requires a more sophisticated lookup table design to cope with the arithmetic in higher order Galois fields. Provided bit error rate simulations show that our proposed scheme outperforms the log-max decoding algorithm and operates close to sum-product decoding.Comment: This paper has been presented at IEEE International Conference on Communications (ICC'19) in Shangha

The Effect of Saturation on Belief Propagation Decoding of LDPC Codes

We consider the effect of LLR saturation on belief propagation decoding of low-density parity-check codes. Saturation occurs universally in practice and is known to have a significant effect on error floor performance. Our focus is on threshold analysis and stability of density evolution. We analyze the decoder for certain low-density parity-check code ensembles and show that belief propagation decoding generally degrades gracefully with saturation. Stability of density evolution is, on the other hand, rather strongly affected by saturation and the asymptotic qualitative effect of saturation is similar to reduction of variable node degree by one.Comment: Submitted to ISIT. Longer version to be submitted to IT Transactions in preparatio