Analysis of decoding error probability for finite length LDPC codes

T. Nozaki, Takayuki Nozaki

R. Yazdani, Masoud Ardakani

An efficient method for finite-length low-density parity-check (LDPC) code analysis is proposed. This method is based on studying the channel variations when observed during a finite-length codeword. To this end, channel parameters are interpreted as random variables and their distributions are found. Assuming that a decoding failure is the result of an observed channel worse than the code's decoding threshold, the block error probability of finite-length LDPC codes is estimated. Using an extrinsic information transfer chart analysis, bit error probability is obtained from the block error probability. Our results suggest that by considering only the channel variations around its expected behavior and even ignoring the effects of cycles, one can closely predict the performance of LDPC codes of a few thousand bits or longer in the waterfall region.

Michael Lentmaier, Dmitri V. Truhachev, Daniel J. Costello +1 more

Yang Liu, Sha Sun, Yuzhi Zhang +1 more

Spatially coupled low density parity check (SC-LDPC) are prominent candidates for future communication standards due to their "threshold saturation" properties. To evaluate the finite-length performance of SC-LDPC codes, a general and efficient finite-length analysis from the perspective of the base matrix is proposed. We analyze the evolution of the residual graphs resulting at each iteration during the decoding process based on the base matrix and then derive the expression for the error probability. To verify the effectiveness of the proposed finite-length analysis, we consider the SC-LDPC code ensembles constructed by parallelly connecting multiple chains (PC-MSC-LDPC). The analysis results show that the predicted error probabilities obtained by using the derived expression for the error probability match the simulated error probabilities. The proposed finite-length analysis provides a useful engineering tool for practical SC-LDPC code design and for analyzing the effects of the code parameters on the performances.

David Burshtein, Gadi Miller

Shiva Kumar Planjery, Bane V. Vasic, David Declercq +1 more