Analysis of Error Floors of Non-binary LDPC Codes over BEC

Abstract

Takayuki NOZAKI†a) , Student Member, Kenta KASAI †b) , Member, and Kohichi SAKANIWA †c) , Fellow SUMMARYIn this paper, we investigate the error floors of the nonbinary low-density parity-check codes transmitted over the binary erasure channels under belief propagation decoding. We propose a method to improve the decoding erasure rates in the error floors by optimizing labels in zigzag cycles in the Tanner graphs of codes. Furthermore, we give lower bounds on the bit and the symbol erasure rates in the error floors. The simulation results show that the presented lower bounds are tight for the codes designed by the proposed method.

Message Passing Decoder with Decoding on Zigzag Cycles for Non-binary LDPC Codes

“…The red curves and the green curves give the symbol erasure rates by the BP algorithm and the proposed decoding algorithm, respectively. The dashed lines and the solid lines give the symbol erasure rates for the non-binary LDPC codes constructed in the cycle cancellation [5] and the improved cycle cancellation [11], respectively. From Figs.…”

“…Fig. 5 The symbol erasure rates for non-binary LDPC codes constructed in the cycle cancellation [5] and the improved cycle cancellation [11] under the BP algorithm and the proposed decoding algorithm through the BEC.…”

“…All the zigzag cycles cause decoding erasures under BP decoding for the BEC if all the bits in the zigzag cycles are received erasures, i.e., ∀i ∈ V zc ∀ j ∈ [1; m] y i, j =? [11,Appendix A.2]. However, most of the zigzag cycles are decodable under MAP decoding even if all the bits in the zigzag cycles are received erasures.…”