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Soft-Input Soft-Output (SISO) polar decoding algorithms, such as Belief Propagation (BP) and Soft Cancellation (SCAN) polar decoding, offer iteration capability for facilitating turbo-style detection. However, at lower Signal-to-Noise Ratios (SNRs), the performance of the BP and SCAN decoders is about 1.5 dB and 0.5 dB worse than that of the state-of-the-art hard-decision Successive Cancellation List (SCL) decoding algorithm, respectively, despite iteratively exchanging information with a Multiple Input Multiple Output (MIMO) detector. Motivated by this gap, we conceive a novel G-SCAN polar decoder, which generates both soft-decision and hard-decision outputs. This is achieved by intrinsically amalgamating a list decoder with a novel SISO decoder. These soft-decision outputs may be used for turbo-detection, but they also support the hard-decision outputs of the SCL algorithm for achieving superior block error rate (BLER) performance. As a result of these benefits, the proposed G-SCAN algorithm using a list size of $L = 2$ offers around 1 dB BLER gain compared to the conventional hard-decision SCL decoder relying on $L = 32$. Furthermore, we have carried out its Extrinsic Information Transfer (EXIT) chart analysis, and characterized the performance vs. the complexity of the proposed G-SCAN algorithm, and compared it to various soft- and hard-decision output benchmarks for a wide variety of different rate-matching modes and block lengths. Furthermore, in order to reduce the complexity of the proposed algorithm, a novel Cyclic Redundancy Check (CRC)-aided G-SCAN algorithm is also proposed, which facilitates early termination and improves the BLER performance. [ABSTRACT FROM AUTHOR]

An interleaved concatenation scheme of polar codes with non-binary low-density parity check (NBLDPC) codes is proposed in this paper to improve the error-correcting performance of polar codes with finite code length. The information blocks of inner polar codes are split into several information sub-blocks, and several segment successive cancellation list (S-SCL) decoders are carried out in parallel for all inner polar codes. Moreover, for a better error-correcting performance, an improved SCL decoder with a selective extension is proposed for the concatenated polar codes, which will be referred to selective extended segment SCL (SES-SCL) decoder. The SES-SCL decoder uses soft information of some unreliable information sub-blocks for the decoding of subsequent sub-blocks so as to mitigate the error propagation of premature hard decision of S-SCL decoder. Simulation results show that NBLDPC-polar codes can outperform Reed Solomon -polar codes. The NBLDPC-polar codes with the proposed SES-SCL algorithm can also be comparable with pure polar codes with cyclic redundancy check aided successive cancellation list (CA-SCL) decoding with list size L = 4 in the high SNR, but require lower decoding storage. Therefore, the NBLDPC-polar codes may strike a better balance between memory space and performance compared with the state-of-the-art schemes in the finite length regime.

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. [ABSTRACT FROM AUTHOR]

As the first provably capacity-achieving codes, polar codes have been selected as the coding scheme for 5G enhanced mobile broadband (eMBB) control channels. Furthermore, if the bottleneck in decoding complexity is addressed, polar codes are still promising for long code length scenarios in the future with superior error-correcting performance. Considering the demand of cloud radio access network (C-RAN) in 5G system, the low-latency software polar decoder is studied in this paper. Two novel algorithms are proposed to reduce the latency of the successive cancellation list (SCL) decoding, including the segmented list-pruning (SLP) algorithm and the modified distributed sorting (MDS) algorithm. Moreover, the proposed SLP algorithm improves the decoding performance compared to existing segmentation schemes. In terms of the software implementation, our decoder is nearly $20\%$ faster than the state-of-the-art flexible software polar list decoder. [ABSTRACT FROM AUTHOR]

In this letter, we propose a low-complexity uplink non-orthogonal multiple access (NOMA) scheme based on polar codes. The proposed scheme, called polar coding-based NOMA (PC-NOMA), relies on the separation of user signals transmitted in the same physical resources using binary-valued patterns embedded in the frozen bit locations of polar codes. By means of frozen bit patterns unique to each user, the superimposed user signals are separated at the receiver by an interference-cancelation algorithm and a polar decoder. We demonstrate that the proposed scheme performs well even when the received powers of the multiplexed users are not significantly distinct. [ABSTRACT FROM AUTHOR]

Polar codes are of great interest, since they are the first provably capacity-achieving forward error correction codes. To improve throughput and to reduce decoding latency of polar decoders, maximum likelihood (ML) decoding units are used by successive cancellation list (SCL) decoders as well as SC decoders. This paper proposes an approximate ML (AML) decoding unit for SCL decoders first. In particular, we investigate the distribution of frozen bits of polar codes designed for both the binary erasure and additive white Gaussian noise channels, and take advantage of the distribution to reduce the complexity of the AML decoding unit, improving the throughput-area efficiency of the SCL decoders. Furthermore, a multimode (MM) SCL decoder with variable list sizes and parallelism is proposed. If high throughput or small latency is required, the decoder decodes multiple received words in parallel with a small list size. However, if error performance is of higher priority, the MM-SCL decoder switches to a serial mode with a bigger list size. Therefore, the MM-SCL decoder provides a flexible tradeoff between latency, throughput, and error performance at the expense of small overhead. Hardware implementation and synthesis results show that our polar decoders not only have a better throughput-area efficiency but also easily adapt to different communication channels and applications. [ABSTRACT FROM PUBLISHER]

This brief presents an efficient sorting architecture for successive-cancellation-list decoding of polar codes. In order to avoid performing redundant sorting operations on the metrics that are already sorted in the previous step of decoding, the proposed architecture separately processes the sorted metrics and unsorted ones. In addition, the odd–even sort network is adopted as a basic building block to further reduce the hardware complexity while sustaining low latencies for various list sizes. On average, the proposed architecture requires less than 50% of the compare-and-swap units demanded by the area-efficient sorting networks in the literature. [ABSTRACT FROM PUBLISHER]