Enhanced Quasi-Maximum Likelihood Decoding of Short LDPC Codes Based on Saturation

Abstract

In this paper, we propose an enhanced quasimaximum likelihood (EQML) decoder for LDPC codes with short block lengths. After the failure of the conventional belief propagation (BP) decoding, the proposed EQML decoder selects unreliable variable nodes (VNs) and saturates their associated channel output values to generate a list of decoder input sequences. Each decoder input sequence in the list is then decoded by the conventional BP decoder to obtain the most likely codeword. To improve the accuracy of selecting unreliable VNs, we propose an edge-wise selection method based on the sign fluctuation of VNs' extrinsic messages. A partial pruning stopping (PPS) rule is also presented to reduce the decoding latency. Simulation results show that the proposed EQML decoder outperforms the conventional BP decoder and the augmented BP decoder for short LDPC codes. It even approaches the performance of ML decoding within 0.3 dB in terms of frame error rate. In addition, the proposed PPS rule achieves a lower decoding latency compared to the list decoding stopping rule.

Generalized Mutual Information-Maximizing Quantized Decoding of LDPC Codes with Layered Scheduling

“…For irregular LDPC codes, the same conclusion can be drawn by substituting L × S dv−1 with L × S D v . This indicates that the RFs defined by (17) lead to an information optimum Q v with sufficiently large q v .…”

“…From (17), we observed that |φ ch | max + d v,max |φ v | max can be much smaller than 2 qv−1 − 1 especially for initial decoding iterations, where…”

“…The reason is that |φ v,ch | max is set to a fixed value for all iterations and |φ * v (s)| computed by ( 16) is much smaller than |φ * v,ch | max at the beginning of decoding. Thus, φ v (s) reconstructed by (17) has a small magnitude and results in…”

“…Low-density parity-check (LDPC) codes [1] and their variations [2]- [7] have been widely applied to wireless communication and data storage systems, for their capacity approaching performance under iterative message passing decoding [8]. Many researchers have put their efforts on the development of the LDPC decoders in terms of the decoding algorithms [9]- [12] and architectures [13]- [17], for achieving a good trade-off between the error performance and decoding complexity. Most of these LDPC decoders make use of the messages represented by log-likelihood ratios (LLRs).…”

Belief Propagation Bit-Flip Decoder for Polar Codes

“…Bit-flip means that the priori knowledge of the flipped information bit is set to infinity, i.e., if u i is flipped to 0, then the so-called R message of u i is set to plus infinity, and vice versa. Note that in LDPC codes, there exist bit saturation methods [18]- [20] that set the initial channel LLRs of variable nodes to infinity for better BLER performance. However, in this paper, we flip the priori knowledge of information bits, not that of variable nodes.…”