Performance Analysis of Channel Coding Techniques for 5G Networks

In this paper we propose an innovative channel coding scheme called 'Accumulate Repeat Accumulate codes' (ARA). This class of codes can be viewed as serial turbo-like codes, or as a subclass of Low Density Parity Check (LDPC) codes, thus belief propagation can be used for iterative decoding of ARA codes on a graph. The structure of encoder for this class can be viewed as precoded Repeat Accumulate (RA) code or as precoded Irregular Repeat Accumulate (IRA) code, where simply an accumulator is chosen as a precoder. Thus ARA codes have simple, and very fast encoder structure when they representing LDPC codes. Based on density evolution for LDPC codes through some examples for ARA codes, we show that for maximum variable node degree 5 a minimum bit SNR as low as 0.08 dB from channel capacity for rate 1/2 can be achieved as the block size goes to infinity. Thus based on fixed low maximum variable node degree, its threshold outperforms not only the RA and IRA codes but also the best known LDPC codes with the dame maximum node degree. Furthermore by puncturing the accumulators any desired high rate codes close to code rate 1 can be obtained with thresholds that stay close to the channel capacity thresholds uniformly. Iterative decoding simulation results are provided. The ARA codes also have projected graph or protograph representation that allows for high speed decoder implementation.

Channel coding is an important building block in communication systems since it ensures the quality of service. Irregular repeat-accumulate (IRA) codes belong to the class of low-density parity-check (LDPC) codes and even outperform the recently introduced turbo-codes of current communication standards. The advantage of IRA codes over LDPC codes is that they come with a linear-time encoding complexity. IRA codes can be represented by a Tanner graph with arbitrary connections between nodes of given degrees. The implementation complexity of IRA decoders is dominated by the randomness of these connections. In this paper, we present a scalable partly parallel IRA decoder architecture. We present a joint graph-decoder design to parallelize IRA codes which can be efficiently processed by this decoder without any RAM access conflicts. We show design examples of these IRA codes which outperform the UMTS turbo-code by 0.2 dB.

The replicate-and-mask (R&M) construction of finite-length spatially-coupled (SC) LDPC codes is proposed in this paper. The proposed R&M construction generalizes the conventional matrix unwrapping construction and contains it as a special case. The R&M construction of a class of algebraic spatially coupled (SC) quasi-cyclic (QC) LDPC codes over arbitrary finite fields is demonstrated. The girth, rank, and time-varying periodicity of the proposed R&M SC QC LDPC codes are analyzed. The error rate performance of finite-length nonbinary algebraic SC QC LDPC codes is investigated with window decoding. Compared to the conventional unwrapping construction, it is found through numerical simulations that the R&M construction resulted in SC QC LDPC codes with better block error rate performance and lower error floors. With a flooding schedule decoder, it is shown that the proposed R&M algebraic SC QC LDPC codes have better error performance than the corresponding LDPC block codes and random SC codes. The R&M construction of irregular SC QC LDPC codes is demonstrated. It is shown that low-complexity regular puncturing schemes can be deployed on these codes to construct families of rate-compatible irregular SC QC LDPC codes with good performance.

Polar codes [1] are a class of provably capacity-achieving error correcting codes (ECC) for memoryless symmetric channels with low-complexity code structures; they have been shown to enjoy better decoding performance over LDPC and Turbo codes under certain scenarios. In this work, we study the application of polar codes for NAND-based SSDs, and mainly focus on the joint source channel coding (JSCC) aspect of polar codes for flash data protection. In a practical SSD system, in addition to the host data, both flash translation layer (FTL) and host side will write on NAND a small amount of non-host data (a.k.a. metadata) for system managing purposes. We demonstrate that the metadata information can be readily and efficiently utilized by polar codes, whereas such property is lacking in LDPC-based systems. With the help of the side information provided by metadata, the decoding capability of polar codes can be further enhanced with little or no modifications on the decoder side. Simulation results verify the performance improvement of metadata-based JSCC scheme, and indicate that polar codes have competitive advantages over LDPC codes on flash memories.

Turbo codes are attractive compared with Low Density Parity Check (LDPC) codes for Forward Error Correction (FEC) applications mainly due to their superior performance, especially at low Signal-to-Noise Ratio (SNR) such as are common in Powerline channels. For example, IEEE 1901-FFT PHY used the Turbo coding scheme defined in the HomePlug AV standards. However, patent fees are usually required for each turbo-code enabled manufactured device. The objective of this paper is to examine whether unlicensed LDPC codes, with optimized choices of block lengths, could be a viable alternative for future Powerline Communications (PLC) applications. The paper shows that the performance of the LDPC codes can approximate that of the Turbo codes with higher block lengths, on channels with typical and realistic PLC characteristics. The paper also shows that the additional complexity associated with this increase in block length can be mitigated by the use of Quasi-Cyclic LDPC (QC-LDPC) codes.

DOI: 10.1049/cp:20061337 ISBN: 0 86341 644 6 Location: Hangzhou, China Conference date: 6-9 Nov. 2006 Format: PDF The BER performance of presented quasi-cyclic (QC) low-density parity-check (LDPC) codes is not good as that of randomly constructed LDPC codes, while the lack of structure of randomly constructed LDPC codes implies serious disadvantages in terms of storing and accessing a large parity-check matrix. To solve the problems, this paper proposes a design of good quasi-cyclic (QC) low-density parity-check (LDPC) codes, the obtained algebraically structured codes have large minimum distances and good BER performance. The proposed design is based on index matrices, which determines the shifts of the circulant matrices of the sparse parity-check matrices. Compared with the presented design of QC LDPC codes, the designed QC LDPC codes are free from girth 4, sometimes free from girth 6, and have much larger minimum distances. Based on the algebraic code structure, the conditions of the girth and minimum distance of the codes are found. The BER performance of the designed QC LDPC block codes compares with that of randomly constructed LDPC codes for any block lengths. Better BER performance is obtained by increasing the circulant size of the base QC code. Simulations verify the construction of the QC LDPC codes to be valid. (4 pages) Inspec keywords: AWGN channels; error statistics; channel coding; algebraic codes; parity check codes; sparse matrices Subjects: Algebra; Other topics in statistics; Codes

Polar codes were shown to be weak at finite block lengths even under maximum-likelihood (ML) decoding. To enhance polar codes, CRC-aided polar codes were proposed. It has been shown that CRC-aided polar codes under the successive cancellation list (SCL) decoder outperform LDPC codes and turbo codes. Recently, interleaved polar (i-polar) codes were proposed. By using a new bit channel selection algorithm, i-polar codes without CRC were shown to outperform the 5G LDPC codes. However, most research on polar codes focuses on the binary case. In this paper, a new family of nonbinary i-polar codes with random constellation mapping is proposed. A recursive form for calculating the average weight enumerating function (WEF) of the nonbinary i-polar code is derived. With the random constellation mapping, the upper bound on the BLER under ML decoding depends on the WEF of the nonbinary i-polar code. Then a new channel selection algorithm is proposed based on the polarization effect and the BLER upper bound. The algorithm generates a sequence, termed the i-polar sequence (IPS). Simulation results show that the nonbinary i-polar codes with the IPS outperform the 5G LDPC codes.

Channel coding plays a crucial role in enhancing the reliability and efficiency of communication systems, particularly when transmission channels are disrupted by noise and interference. This paper presents an in-depth review of various channel coding techniques, their applications, and future research directions. Key topics discussed include prevalent channel coding methods, such as repetition codes, convolutional codes, LDPC codes, turbo codes, and polar codes. The paper also delves into the selection of suitable channel coding parameters and their applications in digital TV, mobile and satellite communications, unmanned aerial vehicle data links, speech communication, and underwater acoustic channels. Moreover, the paper explores the performance analysis and comparison of different channel coding techniques, shedding light on their strengths and weaknesses. Lastly, the paper identifies emerging trends and challenges in channel coding research, providing valuable insights for researchers and practitioners in the field of communication systems. By examining these techniques and future directions, this comprehensive overview aims to contribute to the development of more robust and efficient channel coding schemes for a wide range of communication applications.

Both polar code and Low-Density Parity-Check (LDPC) code have been adopted in 3GPP eMBB scenario. Some scholars have proposed a serial concatenation structure combining these two codes. However, the inner code needs to add redundant bits to protect the redundant bits of the outer code in the serial concatenation. In this paper, we propose a parallel concatenation code combining polar code and LDPC code on the AWGN channel, which does not distinguish the inner code from the outer code. In the proposed concatenated structure, the BP algorithm is used to decode polar code, and the output soft information of BP decoder is logarithmically processed before LDPC decoding. According to the simulation results, compared with the serial concatenated code with the same code rate and code length, the parallel concatenated code has better BER(Bit-Error-Rate) performance.

Irregular-repeat-accumulate (IRA) codes are random-like codes having extremely good performance over AWGN channel. They can be viewed as special kinds of LDPC codes in the way their parity-check matrix are sparse. Like LDPC codes, they can be decoded using the messages-passing algorithm efficiently, while the existence of short length circles in their corresponding factor graph representation has a deleterious effect on the BER performance of the codes. Progressive edge-growth (PEG) algorithm is a famous method to construct factor graph without short circles. In this paper, we use PEG algorithm to construct the parity-check matrix of IRA codes firstly, and then deduce the interleaver design of the codes. Experimental results show significant improvement on the BER performance of the IRA codes with designed interleaver over the IRA codes with randomly choose interleaver.

This chapter discusses fundamentals of information theory and channel coding (error correction coding ECC, Forward error correction FEC). First, key results of Shannon, including channel capacity and the relationship between transmit power and bandwidth, are discussed. Block codes multiply a block of data with an encoding matrix. For systematic codes, the resulting codeword consists of systematic bits and parity check bits. Decoding is achieved by multiplication with a parity check matrix and determination of the syndrome vector. Correction of errors within the correction sphere can be done, e.g., through lookup tables. Convolutional codes send the source data stream through shift registers and adders, a process described by a trellis diagram. Maximum-likelihood sequence estimation (Viterbi algorithm) determines the (transmit) bit sequence with best distance metric (Hamming or Euclidean) from the received signal. Methods for combining coding and higher-order modulation include trellis coded modulation (using set partitioning for code design) and bit-interleaved coded modulation (BICM). Turbo codes are close to capacity-achieving. They are based on transmitting differently interleaved convolutional codes; receivers use soft decoding of the constituent codes and iterative exchange of soft information (log-likelihood ratios). Low-density parity check codes (LDPCC) are decoded by belief propagation (message passing), where variable nodes and constraint nodes exchange beliefs about the codeword. In fading channels, (block or convolutional) interleaving is essential to provide diversity. From an information-theoretic point of view, in fading channels we can distinguish between the ergodic capacity and the outage capacity. If the channel state information is known at the transmitter, waterfilling is the optimum power allocation strategy. Automatic Repeat Request ARQ) and Hybrid ARQ (including chase combining or incremental redundancy) are described in the appendix.

Spatially-coupled (SC) LDPC codes are constructed from a set of L regular sparse codes of length M. In the asymptotic limit of these parameters, SC codes present an excellent decoding threshold under belief propagation (BP) decoding, close to the maximum a posteriori (MAP) threshold of the underlying regular code. In the finite-length regime, we need both dimensions, L and M, to be sufficiently large, yielding a very large code length and decoding latency. In this paper, and for the erasure channel, we show that the finite-length performance of SC codes is improved if we consider the tree-structured expectation propagation (TEP) algorithm in the decoding stage. When applied to the decoding of SC LDPC codes, it allows using shorter codes to achieve similar error rates. We also propose a window-sliding scheme for the TEP decoder to reduce the decoding latency.

Polar code has been proven to obtain Shannon capacity for Binary Input Discrete Memoryless Channel (BIDMC) and its use has been proposed as the channel coding in 5G technology. However, its performance is limited in finite block length, compared to Turbo or LDPC codes. This research proposes the use of various CRC codes to complement Polar codes with finite block length and analyses the performance based on Block Error Rate (BLER) to Es/N0 (dB). The CRC codes used are of degrees 11 and 24, with 3 different polynomial generators for each degree. The number of bits in the information sequence is 32. The list sizes used are 1, 2, 4, and 8. Simulation results show that the concatenation of CRC and Polar codes will yield good BLER vs Es/N0 performance for short blocks of codeword, with rates 32/864 and 54/864. Concatenating CRC codes with Polar codes will yield a BLER performance of 10-2 with Es/N0 values of -9.1 to -7.5 dB when CRC codes of degree 11 is used, depending on the SC list used. The use of CRC codes of degree 24 enables a BLER performance of 10-2 with Es/N0 values of -7 to -6 dB when the SC list used is 1 or 2. The use of CRC codes of degree 24 combined with SC list with sizes 4 or 8 will improve the BLER performance to 10-2 with Es/N0 values of -8 to -7.5 dB

The Schalkwijk-Kailath (SK) scheme for the AWGN channel with noise-free feedback is well-known since its coding complexity grows linearly with the coding blocklength, and it is capacity-achieving and has extremely lower decoding error probability comparing with existing excellent codes such as LDPC and Polar codes. However, extension of SK scheme to more practical scenarios is challenging since it depends heavily on the feedback success. This paper aims to investigate how to design SK-type schemes for channels with intermittent feedback and establish the relationship between the coding blocklength, the desired decoding error probability, the achievable transmission rate and secrecy level of our proposed schemes. Specifically, first, for the additive white Gaussian noise (AWGN) channel with intermittent noise-free feedback, a variation of the well-known Schalkwijk-Kailath (SK) scheme for the AWGN channel with noise-free feedback is proposed, and the corresponding achievable rate is characterized for given coding blocklength and decoding error probability. Subsequently, the proposed scheme is extended to channels with noisy intermittent feedback. To quantitatively evaluate the secrecy performance, we adopt the eavesdropper's normalized equivocation as the secrecy metric and analytically characterize the achievable secrecy level of the proposed schemes. In particular, we show that perfect weak secrecy, i.e., asymptotically vanishing information leakage rate, can be achieved under certain conditions. Numerical results show that for a given decoding error probability threshold, our proposed schemes require lower signal-to-noise ratio and significantly shorter coding blocklength comparing with LDPC code. The study of this paper may provide a way to construct efficient coding scheme for channels in the presence of intermittent feedback.

A novel method to combine encryption and channel coding in such a way as to get increased security without any additional complexity is presented in this paper. A secure communication system usually consists of an encryption block followed by the channel coder. The encryption block here is a Shrinking generator which is a Linear Feedback Shift Register (LFSR) based stream cipher system. The channel coding technique used is Turbo codes or Low Density Parity Check Codes (LDPC) that performs very well and provides results near Shannon's Limit. Controlled randomness using Pseudo Random Bit Sequence (PRBS) generator is incorporated during encoding of these codes to provide additional level of security in the system without any additional complexity. To achieve optimum decoding, soft decision decoding algorithms are used rather than hard decisions. Bit Error Rate (BER) performance of the proposed channel coders with keyed randomness is well analyzed for intended and un-intended users. Security of the system is analyzed by mounting Improved Linear Consistency Attack and the results show that a significant increase in security is achieved in a stream cipher based secure communication system without any additional increase in complexity by introducing security in channel coding.