Soft List Decoding of Polar Codes

Abstract

Soft-output (SO) decoding is proposed for the Logarithmic Successive Cancellation List (Log-SCL) polar decoder for the first time, by exploiting the left-to-right propagation of the Belief Propagation (BP) decoder, which opens new avenues for its employment in powerful turbo-receivers. In the case of decoding a half-rate polar code having a block length of 1024 bits, the proposed soft list polar decoder achieves a 1.5 dB Block Error Ratio (BLER) performance gain, 50% latency improvement and 26% complexity reduction, compared to the state-of-the-art SO Soft Cancellation (SCAN) polar decoder in a polar-coded Multiple-Input Multiple-Output (MIMO) system. Furthermore, we conceive a Memory-Efficient (ME) soft list polar decoder, which requires only 16% of the soft list polar decoder's memory, at the cost of slightly increased latency and complexity. I. INTRODUCTION Polar codes [1] have been selected for protecting the 5G New Radio (NR) control channels, as a benefit of their superior Block Error Ratio (BLER) performance at short block lengths [2]. Therefore, both Hard-Output (HO) and Soft-Output (SO) polar decoders have been investigated in the literature [1, 3-8]. The soft-input HO (SIHO) polar decoders typically rely on the original Successive Cancellation (SC) decoder proposed in [1] or sphere decoder of [9], whereas SISO may be produced by the Belief Propagation (BP) algorithm [3, 10]. The SC decoder is capable of approaching the Binary-Input Discrete Memoryless Channel (B-DMC) capacity for infinite block lengths [1] where the channel is sufficiently polarized, but exhibits poor BLER performance for realistic finite block lengths due to the associated error propagation. Considering a list of candidate bit sequences and operating on the basis of Logarithmic Likelihood Ratios (LLRs), the Logarithmic Successive Cancellation List (Log-SCL) polar decoder, developed from the SCL decoder of [11], improves the error-correction performance of the SC decoder in the case of practical block lengths [4]. The software and hardware implementations of the Log-SCL decoder have been investigated in [12-15], which have a low memory requirement and a low decoding latency. However, the Log-SCL decoder is not a SISO scheme, and hence fails to exploit the iterative LLR updates gleaned from the detector of a turbo-receiver [5, 16].

Iterative Receiver Design for Polar-Coded SCMA Systems

“…The complexity of EC-IDD lies mainly in the GA-MP detection and the SLD. According to [31], the number of floating point operations (flops) required to perform the Z = 4 SLD to decode the E = 256 half-rate polar code in a single outer iteration is 1.2 × 10 4 . Hence, for decoding a polar-coded SCMA system supporting K users each using E = 256 half-rate polar code, the decoding complexity C SLD per outer iteration is expressed as C SLD = 1.2 × 10 4 K. Furthermore, the number of flops required for GA-MP detection within a single outer iteration is calculated as C GA-MP = IF {U N d c [15M + 18(d c + 1)] + K(16d x + 2)} [52].…”

“…By contrast, the family of soft-output polar decoders include SCAN list [29] and BP list [30] polar decoders, mitigating the performance loss of SCAN or BP decoding. Elaborating further on SISO decoder, we have previously proposed a novel soft list decoder (SLD) [31], which outperforms the hard-output SCL polar decoder, hence facilitating promising applications of the polarcoded SCMA.…”

“…Motivated by efficiently exploiting the output information of both the SCMA detector and of the polar decoder, we propose a joint receiver design relying on a low-complexity Gaussianapproximated message passing (GA-MP) detection [39], our previously proposed SISO SLD [31] and the edge cancellation (EC). Additionally, the proposed receiver design is intrinsically amalgamated with decision-directed (DD)-CE [40] under imperfect channel state information (CSI), which achieves a similar BER performance to that under perfect CSI.…”

Soft-Output Successive Cancellation Stack Polar Decoder

“…More sophisticated soft-output polar decoders have been investigated [16][17][18][19][20]. By designing permuted polar code factor graphs for generating a list of codewords and performing BP decoding, a belief propagation list (BPL) decoder is proposed in [16], which achieves comparable BER performance to that of the SCL decoder.…”

“…Similarly, by applying SCAN decoding independently to a list of permuted polar codewords, the SCAN list (SCANL) decoding scheme of [17] attains slightly better BER performance than the BPL decoder. Recently, soft-output of the SCL decoder has been achieved in [18,19]. Furthermore, Feng et al [20] proposed an iterative adjustable soft list (IASCL) polar decoder, which relied on the soft cancellation (SCAN) polar decoding principle for generating soft decisions for the entire candidate lists.…”