Channel Coding for Energy Harvesting Communications Using Run Length Limited Codes

This paper addresses a new scheme by Vasic and Pedagani to combine low-density parity-check (LDPC) codes with run length limited (RLL) constraints. In this method, the RLL constraints are embedded into the LDPC codewords by deliberately flipping the bits of LDPC codewords that violate the RLL constraints. It is important to keep the number of flipped bits small in order to not overburden the LDPC decoder. In this paper, we introduce a method to control the number of flipped bits by using pseudorandom sequences. We present a new low-complexity iterative decoding and detection scheme to correct both the flipped bits and channel errors in a partial response channel. Analyses and simulation results show that the proposed method has good performance and reasonable complexity for (0,k) RLL constraints.

Visible light communication (VLC) uses run-length limited (RLL) code to avoid flickering and support different dimming ranges. In this paper, we design an error control coding scheme for VLC using polar code as a forward error correction (FEC) code in serial concatenation with an RLL code. We propose to use soft iterative decoding between RLL code and polar code. Extrinsic information transfer (EXIT) chart is also used to illustrate the proposed serial concatenated scheme's iterative decoding behavior. We will show improvement in bit error rate (BER) performance as compared to the hard decoding based polar code proposed in the literature for VLC.

In this paper, we investigate the soft iterative decoding technique for ternary recoding systems with run-length-limited (RLL) constraints. We employ a simple binary-to-ternary RLL encoder following the LDPC (low density parity check) encoder. In the decoder, the iteratively passing of soft information between the LDPC decoder and a detector is used, where the detector is constructed for a combination of the RLL encoder, PLM (pulse length modulation) precoder and the partial response channel. We provide two different decoding algorithms. For one of the decoding algorithm, we are able to obtain bit-error-rate performance which is inferior to the comparable system without considering the RLL constraint for the high sign-to-noise ratio (SNR) regime and is better for the low-to-moderate SNR regime.

This dissertation presents a systematic exposition on finite-block-length coding theory and practice. We begin with the task of identifying the maximum achievable rates over noisy, finite-block-length constrained channels, referred to as (e, n)-capacity Cen, with e denoting target block-error probability and n the block length. We characterize how the optimum codes look like over finite-block-length constrained channels. Constructing good, short-block-length error-correcting codes defined on sparse graphs is the focus of the thesis. We propose a new, general method for constructing Tanner graphs having a large girth by progressively establishing edges or connections between symbol and check nodes in an edge-by-edge manner, called progressive edge-growth (PEG) construction. Lower bounds on the girth of PEG Tanner graphs and on the minimum distance of the resulting low-density parity-check (LDPC) codes are derived in terms of parameters of the graphs. The PEG construction attains essentially the same girth as Gallager's explicit construction for regular graphs, both of which meet or exceed an extension of the Erdos-Sachs bound. The PEG construction proves to be powerful for generating good, short-block-length binary LDPC codes. Furthermore, we show that the binary interpretation of GF(2b) codes on the cycle Tanner graph TG(2, dc), if b grows sufficiently large, can be used over the binary-input additive white Gaussian noise (AWGN) channel as good code for optimum and good code for iterative decoding. Codes on sparse graphs are often decoded iteratively by a sum-product algorithm (SPA) with low complexity. We investigate efficient digital implementations of the SPA for decoding binary LDPC codes from both the architectural and algorithmic point of view, and describe new reduced-complexity derivatives thereof. The unified treatment of decoding techniques for LDPC codes provides flexibility in selecting the appropriate design point in high-speed applications from a performance, latency, and computational complexity perspective.

The joint Viterbi detector/decoder (JVDD) has been proposed as an alternative to the powerful and ubiquitous low-density parity check (LDPC) coding schemes, that are used in the majority of channel coding applications today. At shorter block lengths, the JVDD is able to outperform the state-of-the-art LDPC decoder that can be found in many of today’s systems, from deep-space communications to the digital video broadcasting standard, to the advanced television standard committee 3.0. Researchers have developed the tools to analyze the performance of the LDPC decoder, which is known as the sum-product algorithm or message passing algorithm. These tools include density evolution (DE) and extrinsic information transfer (EXIT) charts. To date, no similar such analysis exists for the JVDD. In the current paper we perform a similar preliminary analysis on the JVDD algorithm akin to what DE and EXIT charts are for the LDPC decoder. The current new analysis of the JVDD allows prediction of its probability of error based on the probability distribution functions of the metrics used within the algorithm. Our analysis plays a similar role to the abovementioned tools developed for the LDPC decoder: it allows us to predict the performance of the JVDD under various conditions (such as varying SNR’s, thresholds, and block lengths), it improves our understanding of the JVDD algorithm and the match against Monte-Carlo simulations verifies our assumptions on the main error-causing mechanisms within the JVDD.

Runlength-limited (RLL) codes, also known as (d,k) RLL codes, are used in digital magnetic recording and have potential use in soliton optical communication. We show how our approach to RLL coding can naturally incorporate multilevel error correction coding. It allows us not only to correct shift errors but also insertions and deletions of zeros. The main method for achieving this is to use Lee-metric codes. The component codes of the multilevel block code are chosen such that this code has a large minimum Lee distance and such that the (d,k) RLL code combined with the error correction multilevel code provides the highest possible rate. We emphasize that multilevel (d,k) RLL coding combined with multilevel block coding for error correction is well suited to multistage decoding. We also show that for an appropriate choice of the normalised thresholds of these parallel codes, the rate of the corresponding (d,k) RLL code converges to the capacity of the (d,k) constraint, as the dimension of each of the parallel codes goes to infinity.

EXtrinsic Information Transfer (EXIT) chart is a graphical tool for analysis of low density parity check (LDPC) and other codes with iterative decoding. In this paper, we propose the design of LDPC codes for coded modulation schemes by application of linear programming with conditions derived from EXIT charts. Points on the EXIT curve for bit and check node operations are first computed either using analysis or by simulation. The entire EXIT curve is then obtained by linear interpolation. Finally, the EXIT curves are optimized to obtain the maximum possible rate for the code under a given threshold condition. To demonstrate the design procedure, we consider the cases of M-PAM and 8-PSK over the additive white Gaussian noise (AWGN) channel. The optimization method presented is versatile, and can be extended to other constellations and situations easily.

This paper investigates an iterative multiuser detection for nonbinary low density parity check (LDPC) coded multicarrier multiple level frequency shift keying system to increase system performance under specific signal-to-noise ratio and data rate. We propose three-level hard-limited detection probabilities over both additive white Gaussian noise (AWGN) channels and Rayleigh fading channels. During multiuser detection (MUD) process, the hard-limited detection probabilities are computed in advanced and stored in tables. By using table looking up, the MUD soft outputs can be computed efficiently. We test the reliability of soft outputs from nonbinary LDPC channel decoder for all users. If the soft output exceeds a reliability threshold, the user is declared as a reliable user. For each symbol, we count the number of reliable users on it, and, use this information to update the soft output of MUD during the iterative multiuser detection and decoding process, which cancel multiple access interference iteratively. Numerical results show that the performances of three-level hard-limited systems outperform two-level hard-limited systems over AWGN channels and Rayleigh fading channels.

Ultra low bit error rate (BER) is required in high speed communications such as the 100 Gbit/s long haul optic communications. In this paper, a type of simple product codes is proposed using low density parity check (LDPC) codes with very high rate algebraic block codes by exploiting the sparsity of LDPC decoding failure and sparse error distribution in an LDPC frame with errors. Specifically, different with traditional product codes, the information bits are first encoded with very high rate algebraic block codes of low encoding and decoding complexity. Even the block codes correcting a single error using algebraic decoding method can be used. Then, LDPC codes are used as the inner code to obtain a low decoding threshold using iterative decoding. This design scheme can achieve the ultra low bit error rate at relatively low signal-to-noise ratios. The cost of the proposed scheme is the relatively large latency, which is not so critical for the ultra high speed communications.

In Japan, the next generation of Integrated Services Digital Broadcasting — Terrestrial (ISDB-T) system is being developed for transmission of large-volume content services such as ultra high definition television (UHDTV). The system uses low density parity check (LDPC) code as the forward error correction (FEC) to improve its robustness. In particular, the performance of the system's FEC should be evaluated not only in additive white Gaussian noise (AWGN) environments, but also in multipath environments. Moreover, it would be desirable for the new FEC to have better performance than the previous one even in multipath environments. Previous research evaluated the transmission performance of LDPC code by using computer simulations of the propagation model. The actual propagation characteristics were not evaluated. In this paper, we describe the transmission performance of convolutional coded orthogonal frequency division multiplexing (CC-OFDM) and LDPC coded OFDM (LDPC-OFDM) in computer simulations using the same OFDM frame structure and propagation channels as measured in an outdoor experiment conducted in an urban area. We show that LDPC code outperforms CC in multipath environments and how the transmission performance depends on the code rate. In addition, we analyze the correlation between transmission performance and propagation channels.

This paper explains the structure of a newly designed quarter-rate low density parity check (LDPC) code for the cloud transmission system, and presents its truncated performance under additive white Gaussian noise (AWGN) channel. Since new quarter-rate LDPC code has fountain code's property, at the receiver, it can be decoded with truncated codeword for power saving and less latency under high signal to noise ratio (SNR) regions. By computer simulation, the truncated LDPC code shows the same or worse performance compared with the dedicated DVB-T2/S2 LDPC code.

Low-density parity-check (LDPC) codes over finite fields GF(q) have a better performance than those of the binary low-density parity-check codes, at short and medium block lengths, but the decoder of GF(q)-LDPC has more complexity. In this paper, we present a new reduced-complexity belief propagation (BP) decoding algorithm for GF(q)-LDPC codes by analyzing the reliability of code symbols. Instead of update all the variable nodes during iteration, we just update variable nodes which are mostly to be in an error. The algorithm also shows a property to reduce the effects of oscillating on decoding. The simulations prove that we could improve performance and reduce complexity at the same time for short and medium GF(q)-LDPC codes.

Probabilistic amplitude shaping (PAS) combines an outer shaping layer with an inner, systematic forward error correction (FEC) layer to close the shaping gap. Proposed for PAS, constant composition distribution matching (CCDM) produces amplitude sequences with a fixed empirical distribution. We show that CCDM suffers from high rate losses for small block lengths, and we propose to use Enumerative Sphere Shaping (ESS) instead. ESS minimizes the rate loss at any block length. Furthermore, we discuss the computational complexity of ESS and demonstrate that it is significantly smaller than shell mapping (SM), which is another method to perform sphere shaping. We then study the choice of design parameters for PAS. Following Wachsmann et al., we show that for a given constellation and target rate, there is an optimum balance between the FEC code rate and the entropy of the Maxwell-Boltzmann distribution that minimizes the gap-to-capacity. Moreover, we demonstrate how to utilize the non-systematic convolutional code from IEEE 802.11 in PAS. Simulations over the additive white Gaussian noise (AWGN) and frequency-selective channels exhibit that ESS is up to 1.6 and 0.7 dB more energy-efficient than uniform signaling at block lengths as small as 96 symbols, respectively, with convolutional and low-density parity-check (LDPC) codes.

Rate-compatible LDPC codes with short block lengths based on puncturing and extension techniques

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.