Successive Cancellation Ordered Search Decoding of Modified GN\boldsymbol{G}_N-Coset Codes

A tree search algorithm called successive cancellation ordered search (SCOS) is proposed for $\boldsymbol{G}_N$-coset codes that implements maximum-likelihood (ML) decoding with an adaptive complexity for transmission over binary-input AWGN channels. Unlike bit-flip decoders, no outer code is needed to terminate decoding; therefore, SCOS also applies to $\boldsymbol{G}_N$-coset codes modified with dynamic frozen bits. The average complexity is close to that of successive cancellation (SC) decoding at practical frame error rates (FERs) for codes with wide ranges of rate and lengths up to $512$ bits, which perform within $0.25$ dB or less from the random coding union bound and outperform Reed--Muller codes under ML decoding by up to $0.5$ dB. Simulations illustrate simultaneous gains for SCOS over SC-Fano, SC stack (SCS) and SC list (SCL) decoding in FER and the average complexity at various SNR regimes. SCOS is further extended by forcing it to look for candidates satisfying a threshold on the likelihood, thereby outperforming basic SCOS under complexity constraints. The modified SCOS enables strong error-detection capability without the need for an outer code. In particular, the $(128, 64)$ PAC code under modified SCOS provides gains in overall and undetected FER compared to CRC-aided polar codes under SCL/dynamic SC flip decoding at high SNR.Comment: 14 pages, 9 figures, 3 tables. Submitted to IEEE journal. The revised version of the first submission. Major changes: 1) No dedicated section for numerical results. Instead, simulations are provided right after the relevant section. 2) More simulation results are added to compare all the state of art polar decoders in terms of the number of arithmetic operations. arXiv admin note: text overlap with arXiv:2105.0404

Evaluation of Channel Coding Methods for Next Generation Mobile Communication Standards

La codificación de canales es crucial para los sistemas de comunicación móvil, y los sistemas de comunicación inalámbrica 5G han decidido utilizar los códigos LDPC como esquema de codificación para sus canales de datos y los códigos Polares como esquema de codificación para sus canales de control. Este estudio se centra en los fundamentos de los códigos LDPC y los códigos Polares, especialmente los nuevos códigos polares, explicando en detalle sus características de polarización y las técnicas de decodificación recursiva. También se estudia las especificaciones de diseño relacionadas con estos dos esquemas de codificación de canales en 5G. Mediante simulaciones, se compara el rendimiento del nuevo esquema de codificación de canales inalámbricos 5G con el de los códigos Turbo a diferentes longitudes de bloque y tasas de código, y se extraen conclusiones relevantes para demostrar la aplicabilidad del esquema de codificación de canales 5G NR.Channel coding is essential for mobile communication systems, and the 5G wireless standardization committees decided to use LDPC codes as the coding scheme of its data channel and Polar codes as the coding scheme of its control channel. This study focuses on the fundamentals of LDPC codes and Polar codes, especially the emerging Polar codes, with detailed explanations of their polarization characteristics and recursive decoding techniques. It is also focused on the design specification related to these two channel coding schemes in 5G. The performance of the 5G New Radio channel coding scheme is compared with that of LTE Turbo codes at different block lengths and code rates through simulations, and relevant conclusions are drawn to demonstrate the suitability of the 5G NR channel coding scheme.Grado en Ingeniería en Sistemas de Telecomunicació

Polar-Coded OFDM with Index Modulation

Polar codes, as the first error-correcting codes with an explicit construction to provably achieve thesymmetric capacity of memoryless channels, which are constructed based on channel polarization, have recently become a primary contender in communication networks for achieving tighter requirements with relatively low complexity. As one of the contributions in this thesis, three modified polar decoding schemes are proposed. These schemes include enhanced versions of successive cancellation-flip (SC-F), belief propagation (BP), and sphere decoding (SD). The proposed SC-F utilizes novel potential incorrect bits selection criteria and stack to improve its error correction performance. Next, to make the decoding performance of BP better, permutation and feedback structure are utilized. Then, in order to reduce the complexity without compromising performance, a SD by using novel decoding strategies according to modified path metric (PM) and radius extension is proposed. Additionally, to solve the problem that BP has redundant iterations, a new stopping criterion based on bit different ratio (BDR) is proposed. According to the simulation results and mathematical proof, all proposed schemes can achieve corresponding performance improvement or complexity reduction compared with existing works. Beside applying polar coding, to achieve a reliable and flexible transmission in a wireless communication system, a modified version of orthogonal frequency division multiplexing (OFDM) modulation based on index modulation, called OFDM-in-phase/quadrature-IM (OFDM-I/Q-IM), is applied. This modulation scheme can simultaneously improve spectral efficiency and bit-error rate (BER) performance with great flexibility in design and implementation. Hence, OFDM-I/Q-IM is considered as a potential candidate in the new generation of cellular networks. As the main contribution in this work, a polar-coded OFDM-I/Q-IM system is proposed. The general design guidelines for overcoming the difficulties associated with the application of polar codes in OFDM-I/Q-IM are presented. In the proposed system, at the transmitter, we employ a random frozen bits appending scheme which not only makes the polar code compatible with OFDM-I/Q-IM but also improves the BER performance of the system. Furthermore, at the receiver, it is shown that the \textit{a posteriori} information for each index provided by the index detector is essential for the iterative decoding of polar codes by the BP algorithm. Simulation results show that the proposed polar-coded OFDM-I/Q-IM system outperforms its OFDM counterpart in terms of BER performance

System Development and VLSI Implementation of High Throughput and Hardware Efficient Polar Code Decoder

Polar code is the first channel code which is provable to achieve the Shannon capacity. Additionally, it has a very good performance in terms of low error floor. All these merits make it a potential candidate for the future standard of wireless communication or storage system. Polar code is received increasing research interest these years. However, the hardware implementation of hardware decoder still has not meet the expectation of practical applications, no matter from neither throughput aspect nor hardware efficient aspect. This dissertation presents several system development approaches and hardware structures for three widely known decoding algorithms. These algorithms are successive cancellation (SC), list successive cancellation (LSC) and belief propagation (BP). All the efforts are in order to maximize the throughput meanwhile minimize the hardware cost. Throughput centric successive cancellation (TCSC) decoder is proposed for SC decoding. By introducing the concept of constituent code, the decoding latency is significantly reduced with a negligible decoding performance loss. However, the specifically designed computation unites dramatically increase the hardware cost, and how to handle the conventional polar code sets and constituent codes sets makes the hardware implementation more complicated. By exploiting the natural property of conventional SC decoder, datapaths for decoding constituent codes are compatibly built via computation units sharing technique. This approach does not incur additional hardware cost expect some multiplexer logic, but can significantly increase the decoding throughput. Other techniques such as pre-computing and gate-level optimization are used as well in order to further increase the decoding throughput. A specific designed partial sum generator (PSG) is also investigated in this dissertation. This PSG is hardware efficient and timing compatible with proposed TCSC decoder. Additionally, a polar code construction scheme with constituent codes optimization is also presents. This construction scheme aims to reduce the constituent codes based SC decoding latency. Results show that, compared with the state-of-art decoder, TCSC can achieve at least 60% latency reduction for the codes with length n = 1024. By using Nangate FreePDK 45nm process, TCSC decoder can reach throughput up to 5.81 Gbps and 2.01 Gbps for (1024, 870) and (1024, 512) polar code, respectively. Besides, with the proposed construction scheme, the TCSC decoder generally is able to further achieve at least around 20% latency deduction with an negligible gain loss. Overlapped List Successive Cancellation (OLSC) is proposed for LSC decoding as a design approach. LSC decoding has a better performance than LS decoding at the cost of hardware consumption. With such approach, the l (l > 1) instances of successive cancellation (SC) decoder for LSC with list size l can be cut down to only one. This results in a dramatic reduction of the hardware complexity without any decoding performance loss. Meanwhile, approaches to reduce the latency associated with the pipeline scheme are also investigated. Simulation results show that with proposed design approach the hardware efficiency is increased significantly over the recently proposed LSC decoders. Express Journey Belief Propagation (XJBP) is proposed for BP decoding. This idea origins from extending the constituent codes concept from SC to BP decoding. Express journey refers to the datapath of specific constituent codes in the factor graph, which accelerates the belief information propagation speed. The XJBP decoder is able to achieve 40.6% computational complexity reduction with the conventional BP decoding. This enables an energy efficient hardware implementation. In summary, all the efforts to optimize the polar code decoder are presented in this dissertation, supported by the careful analysis, precise description, extensively numerical simulations, thoughtful discussion and RTL implementation on VLSI design platforms