Effects of Single-Cycle Structure on Iterative Decoding of Low-Density Parity-Check Codes

利幸 田中, Toshiyuki Tanaka, 健太 笠井 +3 more

Olgica Milenković, Kiran Prakash, Bane V. Vasic

James A. McGowan

Ryuhei Mori, Toshiyuki Tanaka, Kenta Kasai +1 more

We consider communication over the binary erasure channel (BEC) using low-density parity-check (LDPC) codes and belief propagation (BP) decoding. For fixed numbers of BP iterations, the bit error probability approaches a limit as the blocklength tends to infinity, and the limit is obtained via density evolution. The finite-blocklength correction behaves like α(ε,t)/n+Θ(n-2) as the blocklengthntends to infinity where α(ε,t) denotes a specific constant determined by the code ensemble considered, the numbertof iterations, and the erasure probability ε of the BEC. In this paper, we derive a set of recursive formulas which allows the evaluation of the constant α(ε,t) for standard irregular ensembles. The dominant difference α(ε,t)/ncan be considered as effects of cycle-free and single-cycle structures of local graphs. Furthermore, it is confirmed via numerical simulations that estimation of the bit error probability using α(ε,t) is accurate even for small blocklengths.

Kamil Sh. Zigangirov, Michael Lentmaier

N. Miladinovic, M.P.C. Fossorier

A generalized low-density parity check code (GLDPC) is a low-density parity check code in which the constraint nodes of the code graph are block codes, rather than single parity checks. In this paper, we study GLDPC codes which have BCH or Reed-Solomon codes as subcodes under bounded distance decoding (BDD). The performance of the proposed scheme is investigated in the limit case of an infinite length (cycle free) code used over a binary erasure channel (BEC) and the corresponding thresholds for iterative decoding are derived. The performance of the proposed scheme for finite code lengths over a BEC is investigated as well. Structures responsible for decoding failures are defined and a theoretical analysis over the ensemble of GLDPC codes which yields exact bit and block error rates of the ensemble average is derived. Unfortunately this study shows that GLDPC codes do not compare favorably with their LDPC counterpart over the BEC. Fortunately, it is also shown that under certain conditions, objects identified in the analysis of GLDPC codes over a BEC and the corresponding theoretical results remain useful to derive tight lower bounds on the performance of GLDPC codes over a binary symmetric channel (BSC). Simulation results show that the proposed method yields competitive performance with a good decoding complexity trade-off for the BSC.