A Performance Improvement and Error Floor Avoidance Technique for Belief Propagation Decoding of LDPC Codes

Abstract

In this work, we introduce a unique technique that improves the performance of the BP decoding in waterfall and error-floor regions by reversing the decoder failures. Based on the short cycles existing in the bipartite graph, an importance sampling simulation technique is used to identify the bit and check node combinations that are the dominant sources of error events, called trapping sets. Then, the identified trapping sets are used in the decoding process to avoid the pre-known failures and to converge to the transmitted codeword. With a minimal additional decoding complexity, the proposed technique is able to provide performance improvements for short-length LDPC codes and push or avoid error-floor behaviors of longer codes.

A New High Performance Decoder for LDPC Codes

“…In [13], the authors propose a post-processing technique to lower the error floor by using a look-up table of known trapping sets. After conventional BPA decoding, this table is used to process the residual error blocks much like a syndrome decoder.…”

LDPC decoder strategies for achieving low error floors

“…In [13], the authors propose a post-processing technique to lower the error floor by using a look-up table of known trapping sets. After conventional SPA decoding, this table is used to process the residual error blocks much like a syndrome decoder.…”

“…The look-up table post-processing decoder in [13] is based on the fact that there usually is a 1-1 correspondence between a set of unsatisfied CNs and a trapping set. It was also observed that in the error-floor region, after running extensive Monte Carlo simulations, most of the error patterns correspond to the so-called elementary trapping sets [27], whose induced subgraphs have only degree-one and degree-two CNs.…”

“…However, from the G-LDPC decoder's point of view, not all of the 1320 subgraphs are isomorphic. For example, a (13,5) subgraph in the original Tanner graph, which has the same structure as in Fig. 11, is a dominant trapping set for the G-LDPC I decoder if and only if its five unsatisfied CNs are not involved in any GCP and the VN with two unsatisfied CNs is attached to the rest of the subgraph through a GCP.…”

“…Further, we can target these new trapping sets and group appropriately selected SPCs into more GCPs. According to Table III, three trapping set classes amount to over 90% of the floor of G-LDPC I: (11,5), (13,5) and (15,5). We can thus combine the five non-overlapping unsatisfied SPCs of these trapping sets, arriving at a graph with 229 standard CNs and 258 GCPs, i.e., 82.6% of the SPCs in the original graph are combined.…”