Dynamic-SCFlip Decoding of Polar Codes

Abstract

This paper proposes a generalization of the recently introduced Successive Cancellation Flip (SCFlip) decoding of polar codes, characterized by a number of extra decoding attempts, where one or several positions are flipped from the standard Successive Cancellation (SC) decoding. To make such an approach effective, we first introduce the concept of higher-order bit-flips, and propose a new metric to determine the bit-flips that are more likely to correct the trajectory of the SC decoding. We then propose a generalized SCFlip decoding algorithm, referred to as Dynamic-SCFlip (D-SCFlip), which dynamically builds a list of candidate bit-flips, while guaranteeing that extra decoding attempts are performed by decreasing probability of success. Simulation results show that D-SCFlip is an effective alternative to SC-List decoding of polar codes, by providing very good error correcting performance, with an average computation complexity close to the one of the SC decoder.

Deep-Learning-Aided Successive-Cancellation Decoding of Polar Codes

“…2 compares the FER performance of various decoders for P(128, 64). In this figure, DL-SCLM denotes the proposed DL-SCL decoding algorithm with list size M = {1, 2, 4, 8}, and the bit-flipping SCL decoder with the bit-flipping metric proposed in [8] is denoted as SCLFM . In addition, the original SCL decoding in [14] is also considered for the comparison.…”

“…Fig. 1a shows an example of a factor graph for P (8,5). To obtain the estimated message word, the LLR values and the hard bit estimations are propagated through all the processing elements (PEs) in the factor graph that are depicted in Fig.…”

“…To enable numerically stable computations for a hardware implementation, the bit-flipping metric is defined as [8]…”

“…To overcome this problem, dynamic SCF (DSCF) decoding [8] defines a more accurate bit-flipping metric, which utilizes the LLR values of all the previously decoded information bits. It was shown in [8] that at practical signal-to-noise ratio (SNR) values, DSCF decoding can achieve an error-correction performance comparable to SCL decoding, while maintaining an average decoding complexity close to that of SC decoding. But the bit-flipping metric in DSCF decoding requires costly exponential and logarithmic computations, which hinders the algorithm to be efficiently implemented in hardware.…”

Neural Dynamic Successive Cancellation Flip Decoding of Polar Codes

“…It should be noted that α ∈ R + is a scaling factor for the magnitude of the LLR values and is determined by a Monte-Carlo simulation. To enable a trade-off between decoding latency and error-correction performance, instead of only flipping the most probable bit-flipping position, DSCF decoding attempts to improve SC decoding with a list of most probable bitflipping indices i * ω at each error order ω [8]. In order to have numerically stable computations in the hardware implementation of the DSCF decoder, the bitflipping metric in (6) can be written in the log-likelihood (LL) domain as…”