Area-Efficient Early-Termination Technique for Belief-Propagation Polar Decoders

Choi Choi,Yoo Yoo

doi:10.3390/electronics8091001

Abstract

Early-termination techniques for a belief-propagation (BP) decoder of polar codes can improve the decoding throughput by finishing a decoding iteration when an early-termination condition is satisfied. In the BP decoders, the early-termination condition plays an important role, as it affects decoding iteration savings. In this letter, an area-efficient early-termination criterion is proposed, which simplifies the previous threshold-based termination condition by completely eliminating redundant computations. According to the experimental results, the proposed structure for (1024, 512) polar codes can reduce 72.7%, 66.5%, and 59.7% of hardware resources without any degradation in the error-correction performance and decoding throughput compared to the previous threshold-based, information-BER (bit error rate)-based, and frozen-BER-based early-termination techniques, respectively.

Highlights

Polar codes are the first error-correction codes proved to achieve a channel capacity with affordable encoding and decoding complexities [1,2,3]
The polar codes employ channel polarization, which implies that bit channels are polarized into completely error-free and noisy channels as the code length increases
likelihood ratio (LLR) values, the more reliable are the estimations expected. Using this LLR property, the previous threshold-based method presents a termination criterion to check whether all the magnitudes of t + R t at the left-most nodes are larger than the predetermined threshold [15]

Summary

Introduction

Polar codes are the first error-correction codes proved to achieve a channel capacity with affordable encoding and decoding complexities [1,2,3]. BP algorithm is one of thegraph most efficient algorithms decode polar codes, iteratively propagates over a factor [8]. Figure the factor graph of (8, 4) polar codes with three decoding stages. Given received messages yi (1 ≤ i ≤1 N), the factor graph ofestimated (8, 4) polarmessages codes withûthree decoding stages. As the BP algorithm iteratively such LLR values, the initialization in a BP decoder is important to decode polar codes successfully [8]. Propagates such LLR values, the initialization in a BP decoder is important to decode polar codes (Pr( y x = 0)/Pr( yi xi = 1))asand. The left-most nodes at s = 1 are initialized depending on the type of bit channels. A are initialized as the left-most nodes in set A are initialized as information bit channels, Li,. Left-LLRs and right-LLRsare areupdated updateduntil untilthe the maximum maximum number asas follows: left-LLRs and right-LLRs numberof ofiterations iterationsisisreached reached follows: Algorithm[15]

1: Threshold-based early-termination technique

Proposed Method

Experimental Results

Conclusions