Low Complexity Design of Non-binary LDPC Decoder Using Extended Min-sum Algorithm

Adrian Voicila, David Declercq, François S. Verdier +2 more

C.S.Elamaran

Low Density Parity Check (LDPC) codes, is a linear block code having the decoding performance closer to Shannon's limit.Nonbinary LDPC is the class of binary LDPC, which works on the higher order Galois field.The decoding performance of non-binary (NB) LDPC is better than binary LDPC for moderate code lengths.The increased computation with the increased order of field is the major challenge in hardware realization of NB-LDPC.The extension of conventional sum-product algorithm, known as extended Min-Sum (EMS) algorithm, with reduced computational complexity is used in this paper.However, a tradeoff exists between computational complexity and decoding performance. This paper aims at reducing the computational complexity by focusing on the Parity Check Matrix (PCM) modifications. The bottleneck of the design is large memory requirement and more computation intensive. The modification in the EMS algorithm can be incorporated to design low complexity hardware architecture of NB-LDPC decoder.

nbspAnjitha, nbspProf Sadanandan G K

Minho Kim, Kyeong-Bin Park, Ki‐Seok Chung

The extended min-sum algorithm (EMS) for decoding non-binary low density parity check (NB-LDPC) codes reduces the decoding complexity by truncating the message vector by retaining only the most reliable symbols. However, the EMS algorithm does not consider that the noise of the received codeword is gradually reduced as the iteration count goes up. In this paper, we propose a low-complexity adaptive EMS algorithm, called threshold-based EMS (TB-EMS). The TB-EMS algorithm has a simple adaptive rule to calculate the new message vector length compared to the A-EMS. The proposed algorithm selects one of two message vector lengths. Experimental results show that the proposed algorithm reduces the decoding complexity with minimal performance degradation compared with the EMS algorithm. Further, the decoding performance of the TB-EMS is better than A-EMS.

Fulong Wang, Ming Zhan, Qian Zhang +4 more

The extended min-sum (EMS) algorithm is adopted for non-binary low density parity check (NB-LDPC) codes. The high complexity of EMS algorithm is a hot topic in recent years. Aiming at the problem, a low-complexity EMS algorithm based on NB-LDPC codes is proposed. Dynamic bubble-check (DBC) algorithm in elementary check node (ECN) steps is adopted to reduce the complexity of check node. Furthermore, the proposed algorithm dynamically truncates the length of the message vector by the number of decoding iterations. Taking the length of message vector truncated again as half of the original one as an example, the simulation results and complexity are analyzed. Analysis shows that, compared to the EMS algorithm, computational complexity of comparisons and real additions of check node of the proposed algorithm have reduced by about 70% and 25% respectively. Meantime, the decoding performance of the proposed algorithm approach that of EMS algorithm and the loss is only near 0.08 dB when the bit error rate (BER) is 10−3and the Galois field$GF(q)(q=16)$.

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