Efficient T-EMS Based Decoding Algorithms for High-Order LDPC Codes

Abstract

Non-binary low-density parity-check (NB-LDPC) codes show larger coding gain and lower error floor than their binary counterparts in many cases. However, the existing soft decoding algorithms of NB-LDPC codes generally suffer from high computational complexity. Recently, the trellis-based extended min-sum (T-EMS) decoding algorithm has attracted much attention since it can achieve good decoding performance with high parallelism and low computational complexity. In this paper, we propose two new methods to further reduce the computational complexity and enhance the decoding performance. Firstly, we introduce, with theoretical justification, a universal scheme called threshold-based shrinking (TS) scheme, which facilitates significant reduction of computational complexity for decoding of NB-LDPC codes. Secondly, we present a modified two-extra-column (TEC) scheme and apply it to the T-EMS. Furthermore, a high-performance low-complexity decoding algorithm, named TEC-TEMS algorithm, is obtained. Combining the TS scheme with the TEC-TEMS, the new algorithm, named TS-TEC-TEMS algorithm, achieves much lower computational complexity and has negligible performance loss compared to the TEC-TEMS. For a 256-ary (256, 203) example code, compared to the T-EMS, the computational complexities of the TEC-TEMS and TS-TEC-TEMS algorithms are reduced by more than 50% and nearly 90%, respectively. Moreover, the TEC-TEMS and TS-TEC-TEMS both outperform the T-EMS by about 0.3dB when the frame error rate (FER) is around 10 −5 . INDEX TERMS Error correction codes, nonbinary low-density parity-check (NB-LDPC) codes, min-sum decoding algorithm, low computational complexity, forward error correction (FEC).

The Best, The Requested, and The Default Non-Binary LDPC Decoding Algorithm

“…The simulated decoder is based on the layered scheduling and a maximum of 10 decoding iterations. As shown in Fig.4, the proposed scheme has a performance similar to that of the EMS (n m = 20, n op = 25) and TEC-TEMS[9]. The performance is simulated down to a FER of 10 −5 and no significant performance degradation is experienced.…”

“…The BRD algorithm is a generic decoding algorithm used with any check node processing algorithm such as [3], [8], [9], [13] and for any variable/check node degree of connectivity d v and d c respectively (see Fig. 1(b)).…”

“…For the BRD algorithm, the message length is characterized by n cv = n B + n R . The CN process is based on the TEC-TEMS algorithm [9], with specific parameters given in the following section. The TEC-TEMS is also simulated where only n m = 20 candidates are analyzed from the full-set vector q = 64.…”

“…Recently, contributions were implemented to reduce the memory require-ments and the size of the messages exchanged. In [9], TS-TEC-TEMS is a threshold-based truncation decoding scheme where two thresholds are used to truncate the incoming messages of the CN M V 2C and the outgoing messages from the CN to the VN M C2V . In [10], the implemented decoder truncates the M V 2C vector to q/2 before proceeding with the TEMS decoding scheme.…”

“…The CN processing (line 9) is presented by the Φ function that processes the d c incoming M Vj 2C , j ∈ N (i) messages to generate d c M C2Vj , j ∈ N (i) messages. The function Φ could be any of the different algorithms used for CN processing, such as the Min-Max [13], Extended Min-Sum [3] or Trellis-EMS [9]. After the CN processing, all VNs connected to the CN are updated (line 13-17).…”