Low-Density Parity Check (LDPC) is one of the contemporary error-correcting codes that has shown near Shannon capacity performance; it has been implemented into various stan-dards such as the second-generation Digital Video Broadcasting for Satellite (DVB-S2) and eventually made its way toward the 5G New Radio (NR) for the data channel. In an effort to enhance the LDPC decoding performance without a significant increase in the decoding complexity, in this paper, a receiver-based concatenated decoding approach is proposed, which is composed of the soft-input soft-output (SISO) repetition and offset min-sum (OMS) algorithm representing outer and inner decoders, respectively. At the receiver, the received signal is oversampled with an oversampling rate (OSR) faster than multiple integers of the Nyquist rate to produce repeated symbols. Moreover, the repetition employed at the receiver to handle the repeated symbols will not impact the coding rate. Finally, the simulation results revealed that the proposed scheme could accomplish faster-decoding convergence compared to the conventional LDPC decoders and achieve coding gain up to 2.3 dB with OSR = 2. Additionally, the computational complexity does not increase significantly; on the contrary, the achieved gain can be exploited to reduce the number of iterations.
Low-Density Parity Check (LDPC) is one of the contemporary error-correcting codes that has shown near Shannon capacity performance; it has been implemented into various stan-dards such as the second-generation Digital Video Broadcasting for Satellite (DVB-S2) and eventually made its way toward the 5G New Radio (NR) for the data channel. In an effort to enhance the LDPC decoding performance without a significant increase in the decoding complexity, in this paper, a receiver-based concatenated decoding approach is proposed, which is composed of the soft-input soft-output (SISO) repetition and offset min-sum (OMS) algorithm representing outer and inner decoders, respectively. At the receiver, the received signal is oversampled with an oversampling rate (OSR) faster than multiple integers of the Nyquist rate to produce repeated symbols. Moreover, the repetition employed at the receiver to handle the repeated symbols will not impact the coding rate. Finally, the simulation results revealed that the proposed scheme could accomplish faster-decoding convergence compared to the conventional LDPC decoders and achieve coding gain up to 2.3 dB with OSR = 2. Additionally, the computational complexity does not increase significantly; on the contrary, the achieved gain can be exploited to reduce the number of iterations.
The development of the Fifth Generation (5G) New Radio (NR) provides several significant advantages when compared to the fourth generation (4G) Long Term Evolution (LTE) in mobile communications. Due to the outstanding characteristics of Low-Density Parity-Check (LDPC) codes such as high decoding performance, high throughput, low complexity, they have been accepted as the standard codes for the 5G NR. In this paper, we propose two LDPC decoding algorithms: Hybrid Offset Min-Sum (HOMS) and Variable Offset Min-Sum (VOMS), which are aimed at improving the error correction performance. The main idea of the HOMS/VOMS algorithm is to apply modified factors to both variable-nodes and check-nodes updated processing in order to compensate the extrinsic messages overestimation of the MS-based algorithms and increase the protection ability for degree-1 variable-nodes. The simulation results show that at the Bit-Error-Rate (BER) of 10-5, the proposed HOMS/VOMS algorithm achieves the decoding gain up to 0.2 dB compared to the Offset Min-Sum (OMS) algorithm, with a slight increase in decoding complexity.
In this work, iterative decoders for Low-Density Parity-Check (LDPC) codes are analyzed and optimized for low computational complexity. LDPC block codes are now widely used in industry standards such as Wi-Fi or 5G New Radio (NR). Hence, there is a strong need for decoder concepts suitable for hardware designs. In addition, terminated LDPC convolutional codes are promising candidates for next-generation communication systems. The main theme of this work is to investigate low-overhead strategies for reducing the computational complexity of iterative decoders. Two aspects are considered for fast decoding of the LDPC block codes in 5G NR. Firstly, an efficient but simple-to determine update schedule for the iterative decoding process, i.e., the sequence of updates on different parts of a codeword, is proposed. Secondly, Early Termination (ET), i.e., an option to stop decoding before a maximal number of iterations is exhausted, is improved in two ways: On the one hand, a partial evaluation of the code’s Parity-Check (PC) equations speeds up the detection of valid codewords. On the other hand, a novel criterion detects when the decoding process is unlikely to converge and stops the decoding before a lot of resources are wasted on futile iterations. The combination of all techniques results in a decoder with significant reduction of the computational complexity compared to a decoder without these methods. Still, only few additional residual decoding errors are produced. This work also contains an analysis of various aspects of a Windowed Decoder (WD), which is a specialized decoder design for LDPC convolutional codes. A WD can be configured in even more ways than a decoder for block codes. The analysis in this work assumes a normalization of the computational complexity to a certain maximal value. With this setup, it is shown that a larger size of the decoding window may be preferable over a smaller size to minimize the computational complexity. Furthermore, various window update strategies (determining in which way the code symbol reliabilities are updated in each window) and variations of ET are compared to identify a well-suited WD configuration. Lastly, strategies with Dynamic Scheduling (DS) are considered to further reduce the computational complexity. A novel fixed approach derived from several DS strategies performs well without actual dynamic knowledge of the decoder state. All in all, the optimized WD configuration halves the computational complexity of a block decoder while maintaining an acceptable loss in the decoding performance measured by the number of residual decoding errors. A comparison of systems with Hybrid Automatic Repeat reQuest (HARQ) expands the scope of this work into the domain of error control by retransmissions. The analyzed systems make use of the decoder output, e.g., the final code-symbol reliabilities, to assemble dynamic retransmissions that are as short as possible and contain specifically selected code symbols. These systems stand in contrast to contemporary implementations of HARQ that only use imprecise feedback messages. Still, some compatibility with existing systems is achieved by assuming a limited feedback channel, which requires clever compression of the feedback information. A novel HARQ system is proposed, which evaluates the code’s PC equations to avoid the computational overhead of soft-value processing. The throughput with the proposed system is found to be improved compared to a reference system that evaluates code-symbol reliabilities. Finally, approximations of the accurate message-update rules of the Sum–Product Algorithm (SPA) are analyzed. With fixed-point arithmetic, Look-Up Tables (LUTs) are a promising approach to approximate functions that are costly to compute. It is shown that an optimized LUT with just nine entries can be used in a fixed-point decoder such that the decoding performance is close to that of a floating-point decoder with accurate message updates.
Channel coding technique is a fundamental building block in any modern communication system to realize reliable, fast, and secure data transmission. At the same time, it is a challenging and crucial task, as the data transmission happens in a channel where noise, fading, and other impairments are present. The Low-Density Parity-Check (LDPC) codes give substantial results close to the Shannon limit when the complexity and processing delay time are unlimited. In this paper, the performance of the LDPC decoding with four algorithms was investigated. The investigated four algorithms were Belief Propagation (BP), Layered Belief Propagation (LBP), Normalized min-sum (NMS), and Offset min-sum (OMS). These algorithms were examined for code rates ranging from 1/3 to 9/10 and message block lengths (64, 512, 1024, and 5120) bits. The simulation results revealed the flexibility of these decoders in supporting these code rates and block lengths, which enables their usage in a wide range of applications and scenarios for fifth-generation (5G) wireless communication. In addition, the effect of the maximum number of decoding iterations on the error correction performance was investigated, and a gain of 5.6 dB can be obtained by using 32 decoding iterations at BER=2*10-3 instead of one decoding iteration. The results showed that the decoders performed better for longer message blocks than for short message blocks, and less power was required for transmitting longer messages. Finally, the comparison results of their performance in terms of bit error rate (BER) under the same conditions showed a gain of 0.8 dB using LBP at BER= 10-5 compared with the NMS decoding algorithm.
In conventional satellite broadcasting systems,e.g.DVB-S2,the error-correction schemes are often based on the concatenation of BCH and low-density parity-check(LDPC) codes,so as to obtain excellent bit error rate(BER) performance.As the inner codes,LDPC codes are traditionally decoded by iterative algorithms with many iteration cycles.In virtue of the concatenated structure of BCH and LDPC codes,a novel iterative decoding structure involving the embedment of BCH error-check function into each iterative cycle of LDPC is proposed.Computer simulations show that the iteration number of LDPC decoding with the proposed algorithm is obviously smaller than with traditional algorithm,thus greatly lowering the additional complexity of BCH error-check codes.Therefore,the total complexity and latency of the iterative decoding could be sufficiently reduced,while the similar system BER performance is maintained.
Despite the performance of 5th Generation Low Density Parity Check (5G-LDPC) codes close to the capacity limit, the near-optimal floating-point BP decoding will lead to excessive use of hardware and high complexity of calculation. Thus, the quantized min-sum decoder with limited-precision is usually used in practical implementations. No matter using high or low precision quantization, some 5G-LDPC codes always suffer from the problem of high error floor, which affects their applications in future ultra-reliable scenarios. Using Reed-Solomon (RS) codes as the outer codes can significantly lower the error floor of 5G-LDPC codes due to their Hamming distance properties and excellent error-correction capability. In order to further improve the overall performance, an efficient iterative decoding algorithm of RS-LDPC concatenated codes is proposed in this paper. The proposed iterative algorithm of RS-LDPC codes can achieve noticeable gains over the 5G-LDPC codes at lower FER.
Concatenated codes are effectively used in different approaches of error-correcting theory. We suggest new concatenated code construction that is composed of outer LDPC code and a particular designed inner LDPC code. Special optimization procedure was developed to obtain inner code with specific error-correcting characteristics. We apply the decoder of woven codes to this construction, while reducing the complexity of decoding procedure compared to a classic decoder of LDPC code. Furthermore, we improve the performance of our scheme with puncturing the code symbols. The resulting concatenated construction outperforms low-rate LDPC from the 5G standard. Besides this, we demonstrate the performance of code with a special parity-check matrix consisting of parity-check matrices of inner and outer codes from our suggested construction.