Low‐latency low‐complexity heap‐based extended min‐sum algorithms for non‐binary low‐density parity‐check codes

Abstract

The extended min-sum (EMS) and improved EMS (I-EMS) algorithms for non-binary low-density parity-check codes over GF(q) significantly reduce the decoding complexity with an acceptable performance degradation, but they suffer from high latency because of many serial computations, including a sorting process. On the other hand, the trellis-based EMS algorithm can greatly reduce the latency, but it does not solve the complexity problem in high-order fields (q ≥ 64). To improve the latency problem with low-complexity advantages, the authors propose heap-based EMS (H-EMS) and heap-based I-EMS (HI-EMS) algorithms that are modifications of the EMS and I-EMS algorithms, respectively. The authors also propose double H-EMS and double HI-EMS algorithms trading off the latency against the performance by heaping messages twice. Numerical results show that the H-EMS algorithm has 2.74-9.52 times lower latency than the EMS algorithm with a negligible performance degradation over a wide range of code rates, whereas the HI-EMS algorithm has 1.20-1.62 times lower latency than the I-EMS algorithm. Furthermore, the proposed algorithms may be employed regardless of the decoding schedules.

Selection-based Low-cost Check Node Operation for Extended Min-Sum Algorithm

“…Notably, the complexity of a sorting algorithm is O(nlog(n)) in the best case, when n denotes the number of elements to be sorted. There are no other works that focus on the message sorting for MT except [13]. To reduce the complexity of message sorting, a heap-based message-vector truncation has been proposed, wherein the heap was a partially sorted tree-based data structure [13].…”

“…There are no other works that focus on the message sorting for MT except [13]. To reduce the complexity of message sorting, a heap-based message-vector truncation has been proposed, wherein the heap was a partially sorted tree-based data structure [13]. However, the heap-based truncation had low error-correction performance because less reliable symbols could be included in the truncated message vectors.…”

“…Heap sort combines the advantages of merge sort and insertion sort, and its average time complexity is also O(nlog(n)). It exactly sorts an unordered list unlike the partial sorting used in the heap-based data-structure method [13]. Table 2 lists the evaluation results of the HW implementation of a single MT unit for both sorting and selection algorithms, respectively.…”

“…Recently studied decoding algorithms, which revises T-EMS algorithm, even aims to reduce the amount of computation while minimizing the decrease in error-correction performance [9][10][11][12]. Meanwhile, Y. Hwang et al proposed a heap-based message-sorting method, wherein a complete binary tree was used to reduce the computation complexity of message sorting [13]. By employing heap data structure, the messages were stored as nearly sorted; however, the error-correction performance degraded because less reliable symbols could also be included in the truncated message vectors.…”

“…In the proposed CN operation, we decrease the computation complexity of MT using the quick selection algorithm, which can find the k th largest or smallest element in O(N), where N denotes the number of elements. Unlike the previously reported partially sorted heap data structure [13], the quick selection algorithm can select exactly nm reliable symbols. Experimental results show that the proposed LC CN operation simultaneously reduces the execution time and increases the decoding capability.…”