Fast and Flexible Successive-Cancellation List Decoders for Polar Codes

Abstract

Abstract-Polar codes have gained significant amount of attention during the past few years and have been selected as a coding scheme for the next generation of mobile broadband standard. Among decoding schemes, successive-cancellation list (SCL) decoding provides a reasonable trade-off between the error-correction performance and hardware implementation complexity when used to decode polar codes, at the cost of limited throughput. The simplified SCL (SSCL) and its extension SSCL-SPC increase the speed of decoding by removing redundant calculations when encountering particular information and frozen bit patterns (rate one and single parity check codes), while keeping the error-correction performance unaltered. In this paper, we improve SSCL and SSCL-SPC by proving that the list size imposes a specific number of path splitting required to decode rate one and single parity check codes. Thus, the number of splitting can be limited while guaranteeing exactly the same error-correction performance as if the paths were forked at each bit estimation. We call the new decoding algorithms Fast-SSCL and Fast-SSCL-SPC. Moreover, we show that the number of path forks in a practical application can be tuned to achieve desirable speed, while keeping the error-correction performance almost unchanged. Hardware architectures implementing both algorithms are then described and implemented: it is shown that our design can achieve 1.86 Gb/s throughput, higher than the best state-of-the-art decoders.

An Asymmetric Adaptive SCL Decoder Hardware for Ultra-Low-Error-Rate Polar Codes

“…In addition, we provide a reference design through an efficient emulation platform in an FPGA, and evaluate the ultra-low FER performance of Polar codes to demonstrate its practical value. The proposed A2SCL decoder not only achieves FER ≈ 10 −12 , but also supports list sizes 1, 2, 4, 8 with maximum code length N max = 2 10 . The emulation platform has the following features:…”

Practical Product Code Construction of Polar Codes

“…Table I reports δ N required by standard SC and SCL decoders, and the relative ∆ N for the proposed two-step decoder SC-HD, SCL-HD, and SCL-SD, at different code lengths and rates. For SC decoding, δ SC N = 2N − 2, while for SCL δ SCL N = 2N + K − 2 [20], [21]. For the proposed decoding approach, ∆ N is evaluated for both hard decision (HD) and soft decision (SD) decoding, in the worst case (WC), that assumes t avg = t = 4 and γ = 1, and best case (BC), that assumes t avg = 1 and γ = 0.…”

A Two-Staged Adaptive Successive Cancellation List Decoding for Polar Codes

“…The overall throughput of TA-SCL is also higher than that of the SCL decoders with smaller list sizes as shown in Fig. 1 [12], [13].…”

“…This algorithm first uses a single SC to decode a codeword. If the decoded vector List size Throughput (Gbps) TSP18' [8] TSP17' [13] TVLSI16' [12] cannot pass CRC, the list size is doubled and the decoding repeats. This process is iterated until a valid vector is obtained or a pre-defined L max is reached.…”