Polar codes achieve outstanding error correction performance when using successive cancellation list (SCL) decoding with cyclic redundancy check. A larger list size brings better decoding performance and is essential for practical applications such as 5G communication networks. However, the decoding speed of SCL decreases with increased list size. Adaptive SCL (A-SCL) decoding can greatly enhance the decoding speed, but the decoding latency for each codeword is different so A-SCL is not a good choice for hardware-based applications. In this paper, a hardware-friendly two-staged adaptive SCL (TA-SCL) decoding algorithm is proposed such that a constant input data rate is supported even if the list size for each codeword is different. A mathematical model based on Markov chain is derived to explore the bounds of its decoding performance. Simulation results show that the throughput of TA-SCL is tripled for good channel conditions with negligible performance degradation and hardware overhead.

Polar code is a breakthrough in coding theory. Using list successive cancellation decoding with large list size L, polar codes can achieve excellent error correction performance. The L partial decoded vectors are stored in the path memory and updated according to the results of list management. In the state-of-the-art designs, the memories are implemented with registers and a large crossbar is used for copying the partial decoded vectors from one block of memory to another during the update. The architectures are quite area-costly when the code length and list size are large. To solve this problem, we propose two optimization schemes for the path memory in this work. First, a folded path memory architecture is presented to reduce the area cost. Second, we show a scheme that the path memory can be totally removed from the architecture. Experimental results show that these schemes effectively reduce the area of path memory.

Polar codes are the first class of forward error correction (FEC) codes with a provably capacity-achieving capability. Using list successive cancellation decoding (LSCD) with a large list size, the error correction performance of polar codes exceeds other well-known FEC codes. However, the hardware complexity of LSCD rapidly increases with the list size, which incurs high usage of the resources on the field programmable gate array (FPGA) and significantly impedes the practical deployment of polar codes. To alleviate the high complexity, in this paper, two low-complexity decoding schemes and the corresponding architectures for LSCD targeting FPGA implementation are proposed. The architecture is implemented in an Altera Stratix V FPGA. Measurement results show that, even with a list size of 32, the architecture is able to decode a codeword of 4096-bit polar code within 150 μs, achieving a throughput of 27Mbps.

Owing to their capacity-achieving performance and low encoding and decoding complexity, polar codes have drawn much research interests recently. Successive cancellation decoding (SCD) and belief propagation decoding (BPD) are two common approaches for decoding polar codes. SCD is sequential in nature while BPD can run in parallel. Thus BPD is more attractive for low latency applications. However BPD has some performance degradation at higher SNR when compared with SCD. Concatenating LDPC with Polar codes is one popular approach to enhance the performance of BPD, where a short LDPC code is used as an outer code and Polar code is used as an inner code. In this work we propose a new way to construct concatenated LDPC-Polar code, which not only outperforms conventional BPD and existing concatenated LDPC-Polar code but also shows a performance improvement of 0.5 dB at higher SNR regime when compared with SCD.

Owing to their capacity-achieving performance and low encoding and decoding complexity, polar codes have received significant attention recently. Successive cancellation decoding (SCD) and belief propagation decoding (BPD) are two popular approaches for decoding polar codes. SCD, despite having less computational complexity when compared with BPD, suffers from long latency due to the serial nature of the SC algorithm. BPD, on the other hand, is parallel in nature and is more attractive for low-latency applications. However, due to the iterative nature of BPD, the required latency and energy dissipation increase linearly with the number of iterations. In this paper, we propose a novel scheme based on subfactor-graph freezing to reduce the average number of computations as well as the average number of iterations required by BPD, which directly translates into lower latency and energy dissipation. Simulation results show that the proposed scheme has no performance degradation and achieves significant reduction in computation complexity over the existing methods. Moreover, the hardware architecture for the proposed scheme is developed and compared with the state-of-the-art BPD implementations for (1024, 512) polar codes. A decoding throughput of 13.9 Gb/s is achieved along with a 60%-73% improvement in energy reduction and two times increase in hardware efficiency when compared with the existing BPD implementations.

The performance of List Successive-Cancellation Decoding (LSCD) of Polar Codes with large list size have exceeded that of Turbo codes and Low-Density Parity-Check codes. However, large list size results in huge computation complexity and this limits the applicability of LSCD in high-throughput and power- sensitive applications. In this work, a low complexity design for LSCD with large list size based on list pruning is proposed. In particular, the property of the relative path metric (RPM) of each list candidate with respect to that of the most-likely candidate is investigated. It is found that the correct candidate has a low possibility of having a large value of RPM and based on this property, a list pruning method and the corresponding low-complexity LSCDs are proposed. From the simulation results, as compared to the conventional LSCD, the proposed LSCDs have negligible performance loss while the computation complexity is reduced by more than 80%. In addition, the proposed design is hardware-friendly and easily adaptable to the existing LSCDs hardware architectures.

Polar codes are an exciting new class of error correcting codes that achieve the symmetric capacity of memoryless channels. Many decoding algorithms were developed and implemented, addressing various application requirements: from error-correction performance rivaling that of LDPC codes to very high throughput or low-complexity decoders. In this work, we review the state of the art in polar decoders implementing the successive-cancellation, belief propagation, and list decoding algorithms, illustrating their advantages.

Due to their provably capacity-achieving performance, polar codes have attracted a lot of research interest recently. For a good error-correcting performance, list successive-cancellation decoding (LSCD) with large list size is used to decode polar codes. However, as the complexity and delay of the list management operation rapidly increase with the list size, the overall latency of LSCD becomes large and limits the applicability of polar codes in high-throughput and latency-sensitive applications. Therefore, in this work, the low-latency implementation for LSCD with large list size is studied. Specifically, at the system level, a selective expansion method is proposed such that some of the reliable bits are not expanded to reduce the computation and latency. At the algorithmic level, a double thresholding scheme is proposed as a fast approximate-sorting method for the list management operation to reduce the LSCD latency for large list size. A VLSI architecture of the LSCD implementing the selective expansion and double thresholding scheme is then developed, and implemented using a UMC 90 nm CMOS technology. Experimental results show that, even for a large list size of 16, the proposed LSCD achieves a decoding throughput of 460 Mbps at a clock frequency of 658 MHz.

For polar codes with short-to-medium code length, list successive cancellation decoding is used to achieve a good error-correcting performance. However, list pruning in the current list decoding is based on the sorting strategy and its timing complexity is high. This results in a long decoding latency for large list size. In this work, aiming at a low-latency list decoding implementation, a double thresholding algorithm is proposed for a fast list pruning. As a result, with a negligible performance degradation, the list pruning delay is greatly reduced. Based on the double thresholding, a low-latency list decoding architecture is proposed and implemented using a UMC 90nm CMOS technology. Synthesis results show that, even for a large list size of 16, the proposed low-latency architecture achieves a decoding throughput of 220 Mbps at a frequency of 641 MHz.

Bit-interleaved coded modulation with iterative decoding has been widely adopted in modern wireless communication systems because of its spectral efficiency and low detection complexity. Because of the iterative decoding structure, the overall decoding latency depends on the latency of both the demapper and the channel decoder. In this work, a parallel demapper architecture is proposed for a low latency implementation. Two look-ahead techniques are proposed to further reduce the latency of the parallel architecture. Techniques exploiting the symmetry property of the labeling and the common terms of the look-ahead pre-calculation are also presented to reduce the computation complexity overhead of the proposed architecture. Implementation results show that the latency is reduced by 40% when comparing with traditional sequential demapper architecture.

Gray mapping and signal space diversity (SSD) are adopted in DVB-T2 to achieve better performance and system robustness. However, the traditional maximum a posteriori demapping for Gray mapped SSD signal is complicated for higher order modulation and it is not practical to be used in the iterative receiver structure. In this work, simplified demappers are proposed by approximating the 2-dimensional detection with 1-dimensional detection and compensating the loss due to the correlation between the I and Q components. Simulation results show that the proposed simplified demappers can approach the optimal demapper performance with a much lower complexity.

Multi-level superposition coded modulation (SCM) is a scalable technique for wireless video broadcast/ multicast, in which iterative turbo structures provide receivers with multi-resolution demodulations subject to a high complexity. Forward error correction using low-density parity-check (LDPC) code is helpful for better received video quality but further increasing the receiver complexity. In this paper, a method is proposed to reduce the receiver complexity by using a sequential structure with a faster convergence for demodulation. In addition, the iterative demodulator and the LDPC decoder are jointly designed as a multi-loop iterative structure to reduce the decoding complexity. Experimental results show that up to 67% decoding complexity is reduced and better video quality is achieved at receivers under low signal-to-noise ratios.