Soft-input soft-output polar decoding

Abstract

Arikan's polar codes offer near-capacity error correction performance across a wide range of block lengths, as well as coding rates. The standardization of polar codes by the Third Generation Part­nership Project (3GPP) 5th Generation (5G) New Radio (NR) in 2016, significantly increased the interest in polar codes. In particular, polar codes have been adopted by the 3GPP SG NR, since they provide near-capacity error correction for the short control messages transmitted in the control channels of the 3GPP SG NR, where other state-of-the-art channel decoders have struggled. The state-of-the-art Soft-Input Hard-Output (SIHO) Successive Cancellation List (SCL) and Cyclic Re­dundancy Check-Aided SCL (CA-SCL) polar decoders offer the best hard-decision performance among the polar decoders but they do not have a soft-output capability, which is necessary for achieving iterative gains in turbo-detection or in Joint Source Channel Coding (JSCC). Hence, there is a distinct knowledge-gap concerning Soft-Input Soft-Output (SISO) polar decoders capa­ble of outperforming the well-known SISO Belief Propagation (BP), the Soft Cancellation (SCAN) polar decoders, as well as that of the hard-decision SCL polar decoder. Against this background, a pair of novel SISO polar decoding algorithms are proposed, which outperform both the SISO BP and SCAN polar decoders, as well as the state-of-the-art SCL polar decoder across a wide range of block lengths and coding rates. Additionally, both the error correction and error detection perfor­mance of these novel polar codes are characterised. More specifically, a two-stage serially concatenated scheme of polar codes exchanging extrinsic information with an inner decoder is conceived. Explicitly, the first stage comprising a SG NR polar decoder, and a second stage comprising a turbo-detected 2x2 Multiple Input Multiple Output (MIMO)-aided scheme is designed, by proposing a novel SISO G-SCAN polar decoding scheme. The G-SCAN decoding scheme advocated offers the best of both worlds by generating soft out­puts for achieving iterative decoding gains, and hard outputs that improve the SCL decoding per­formance. Furthermore, the Two-Dimensional (2D) Extrinsic Information Transfer (EXIT) chart analysis of this two-stage serially concatenated scheme is carried out. Furthermore, a three-stage serially concatenated scheme is designed, which exchanges extrinsic soft information between the polar decoder as well as an inner and outer decoder. Explicitly, the first stage is a JSCC scheme, the second stage is a 5G NR polar decoder, and the third stage is a 2x2 MIMO scheme, which is investigated. Additionally, a novel hybrid polar decoder algorithm is proposed, which is capable of generating soft outputs for iterative extrinsic information exchange with an inner and outer decoder. Finally, a Three-Dimensional (3D) EXIT chart analysis of SISO polar codes is provided for the first time.

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Identifiers

ORCID for Zeynep Kaykac Egilmez: orcid.org/0000-0001-5547-6354

ORCID for Rob Maunder: orcid.org/0000-0002-7944-2615

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