Satellite modem equipment using advanced coding and modulation techniques for current and potential INTELSAT services

Error-Control Coding, Modulation and Equalization for All-Digital Advanced Television: State of the Art and Future Possibilities

All digital television broadcast schemes require some form of forward error correction. Trellis coded modulation and Reed-Solomon (RS) codes are two of the most commonly used error correction strategies. While RS codes have been used for a fairly long time in various applications and are well understood, use of trellis coded modulation has been restricted mostly to telephone modems. We explain the principles of trellis coded modulation and how trellis codes can be chosen as part of the error correction strategy for digital television broadcasting. A variety of coding and interleaving schemes that can be used to obtain the desired performance for compressed TV signal transmission is discussed. The nature of the terrestrial channel and the system performance requirements for a high definition television (HDTV) system are described, including a coding strategy called concatenated coding. >

This paper presents a comprehensive analysis and implementation of various error correction coding methods, focusing on Reed-Solomon (RS) codes and Liberation codes in RAID6 systems. RS codes are emphasized for their robust error correction capabilities, making them ideal for high-reliability environments such as enterprise data centers and mission-critical systems, where the ability to correct multiple errors or data losses is crucial. In contrast, Liberation codes are noted for their superior encoding efficiency and lower computational complexity, making them well-suited for high-performance systems with stringent speed requirements. Through experimental comparisons, this study also evaluates Cauchy Reed-Solomon (CRS) codes, EVENODD codes, and Blaum-Roth (BR) codes, identifying the strengths and weaknesses of each method in various scenarios. The findings underscore the importance of selecting the appropriate coding technique based on system-specific requirements, as different use cases benefit from different error correction schemes in terms of performance and data reliability. Additionally, this research highlights the potential of these coding methods in broader distributed storage applications and discusses the trade-offs between them. Future research directions are suggested, particularly in optimizing existing codes and expanding their application in more complex and distributed storage environments.

One of the approaches to organization of error correcting coding for multilevel flash memory is based on concatenated construction, in particular, on multidimensional lattices for inner coding. A characteristic feature of such structures is the dominance of the complexity of the outer decoder in the total decoder complexity. Therefore the concatenated construction with low-complexity outer decoder may be attractive since in practical applications the decoder complexity is the crucial limitation for the usage of the error correction coding.
 We consider a concatenated coding scheme for multilevel flash memory with the Barnes-Wall lattice based codes as an inner code and the Reed-Solomon code with correction up to 4…5 errors as an outer one.
 Performance analysis is fulfilled for a model characterizing the basic physical features of a flash memory cell with non-uniform target voltage levels and noise variance dependent on the recorded value (input-dependent additive Gaussian noise, ID-AGN). For this model we develop a modification of our approach for evaluation the error probability for the inner code. This modification uses the parallel structure of the inner code trellis which significantly reduces the computational complexity of the performance estimation. We present numerical examples of achievable recording density for the Reed-Solomon codes with correction up to four errors as the outer code for wide range of the retention time and number of write/read cycles.

Error-resilient scalable compression based on distributed video coding

The performance of a communication system having almost the same spectral efficiency as a trellis coded modulation (TCM) system with r = 2/3 convolutional encoding and 8-ary phase-shift keying (8-PSK) modulation is investigated. TCM is a common solution to the problem of adding forward error correction (FEC) coding without an attendant increase in channel bandwidth. The primary drawback to TCM is that the achievable coding gain is limited by the maximum practical number of states in the convolutional encoder. The alternative system considered uses (63, 37) Reed-Solomon (RS) encoding. The six-bit symbols at the output of the Reed-Solomon encoder undergo serial-to-parallel conversion to two three-bit symbols, which are then independently transmitted on the in-phase and quadrature components of the carrier using 8-ary biorthogonal keying. This system has a null-to-null bandwidth of 0.993R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> , which is 0.7% smaller than TCM with r = 2/3 convolutional encoding and 8-PSK modulation. The two waveforms are compared for the relatively benign case where additive white Gaussian noise is the only noise present as well as when pulse-noise interference is present.

Foschini's diagonally layered space-time transmission system known as D-BLAST is an architecture designed for a Rayleigh fading environment using multiple element antenna arrays at both the transmit and receive sites to achieve very high spectral efficiencies. In this paper, we propose a simple coding technique for D-BLAST that uses a single trellis code with finite-traceback Viterbi decoding. We examine the performance of universal trellis codes that are designed to have a distance structure that is matched to the periodic signal-to-noise ratio (SNR) variation of the channel created by D-BLAST, under the assumption that the channel is static during one burst but may change from burst to burst. We show that a universal 64-state trellis code on a 2/spl times/2 D-BLAST system with long enough block lengths displays universal behavior working on almost every 2/spl times/2 channel with at least the mutual information required by a standard 64-state AWGN trellis code. The only 2/spl times/2 channel where more mutual information is required is a certain rotation of the zero eigenvalue channel. We also present 4/spl times/4 and 8/spl times/8 examples.

The High Performance Waveform (HPW) was developed before parallel concatenated codes (PCCC) and serial concatenated codes (SCCC) were in wide use and so it makes sense to take advantage of the advancements in communication theory and processor computation speed that have taken place since its inception. In its current form, HPW transmits a Raised-Cosine Continuous Phase Modulation (1RC CPM) modulation with a trellis code that is designed to provide, with the use of a Cyclic Redundancy Check Code error detection (CRC), error free transmission over a single, narrowband UHF satellite communications channel. In this paper we present an additional set of coding and modulation schemes which take advantage of serial concatenated code (SCCC) technology to simultaneously improve throughput at the lower end of the signal-to-noise ratio (SNR) range while increasing the highest throughput at the highest SNR available on UHF satellites. The overall bit error rate and throughput of each individual modulation type is analyzed and the framework for the adaptive modulation protocol is provided. To provide for a gradual release of a newer revision of HPW, a framework for a PHY layer is provided which will allow a heterogeneous network of legacy and updated radio terminals.

In general, a concatenated RS/BCH code consists of an outer RS code and an inner BCH code with separation by an interleaver. We create a novel BCS code using a new methodology by combining an outer BCH code with an inner RS code appended by an interleaver to randomize burst errors and help the RS code in correcting the errors. Generally, BCH codes handle binary data, whereas RS codes handle non-binary data. Hence, RS (7, 1) inner code is proposed to achieve compatibility with BCH (15, 5) outer codes and ultimately create a novel BCS code to handle binary data. The proposed BCS code is compared with familiar concatenated RS/BCH codes and single codes (RS and BCH) for BPSK and QPSK modulation schemes. Results show the downlink LTE system performance using the proposed BCS code is significantly better than the uncoded LTE system and single codes (RS and BCH). Moreover, the proposed BCS code also outperforms familiar concatenated RS/BCH codes for both schemes. In contrast, the system performance is improved further when the number of antennas in the MIMO channel is increased from $$2 \times 2$$ to $$4 \times 4$$ . Therefore, the proposed BCS code can be considered a stronger code with high reliability in wireless communication systems.

With rapid growth in today’s technology, digital communication is playing a major role to provide hostile environment to meet various applications. In this communication, Coding plays a prominent role to contribute error free transmission through channel coding which improves capacity of a channel by adding some redundant bit to the original information. One way to provide a better performance of the communication system is by concatenating different types of channel coding techniques. The concatenation can be done either in parallel or serial. The primary aim of this paper is to concatenate the Reed-Solomon codes with Convolutional codes in series, which provides better results comparing with single coding techniques. The performance of the concatenation of Reed-Solomon codes with Convolutional codes can be evaluated by finding bit error rate with various values of signal-to-noise ratio over AWGN channel. The analytical result has been obtained by using MATLAB/OCTAVE.

An enhanced transmission is presented in a multiple‐input‐multiple‐output (MIMO) dense‐wavelength division multiplexed (DWDM) free‐space‐optical (FSO) communication link using diversity coding techniques under the effect of turbulent weather phenomenon. The findings show good performance with an (8 channels × 2.5 Gbps data rate/channel) 20 Gbps 1500 m transmission distance. The bit‐error‐rate (BER), outage probability (OP), and signal‐to‐noise ratio (SNR) of the diversity combining techniques using maximum‐ratio combining (MRC), selection combining (SC), and equal‐gain combining (EGC) technique are evaluated in this work. The obtained results illustrate that Alamouti, space‐time coding (STC), space‐time block coding (STBC), space‐time trellis code (STTC), orthogonal STBC (O‐STBC), and quasi‐orthogonal STBC ( QO‐STBC ) on the minimum mean‐square‐error, and MRC are worth implementing on the DWDM‐FSO wireless communication systems. The mitigation of atmospheric turbulence is achieved using MIMO diversity combining techniques coding. The simulation results for diversity coding techniques using QO‐STBC/STTC and SC/MRC in the MIMO‐DWDM FSO communication system can improve BER performance, OP, and SNR. The MRC exhibits the lowest OP and BER when compared with the SC and EGC. The numerical results demonstrate that the FSO communication link using DWDM QO‐STBC/STTC improves the power penalty at both BER values under varying atmospheric turbulence conditions for ST, MT, and WT, in comparison to FSO systems without DWDM QO‐STBC/STTC diversity coding techniques.

Protecting nonvolatile memory systems in harsh radiation environments encountered in space missions is important and error correcting schemes can extend the lifetime of those memory systems. For example, recent research has shown that LDPC codes can extend the lifetime of nonvolatile memory under space radiation environment more than Bose-Chaudhuri-Hocquenghem (BCH) or Reed-Solomon (RS) codes at fixed codeword error rates. However, conventional memory models assume that bit errors are independent, but multibit errors were reported in satellite experiments. Moreover, memory feature sizes are shrinking and multibit-per-cell structures are becoming standard so radiation will increasingly lead to multibit errors. For these reasons, we can expect that the bit errors in memory systems will be correlated. In this work, we develop a mathematical multibit-per-cell memory model under a radiation environment. In this memory model, bit errors are correlated and the probability of errors depends on radiation parameters and time. For correlated bit errors, nonbinary codes can be more effective than binary codes. We will demonstrate that nonbinary LDPC code can outperform conventional BCH and RS codes in a correlated multibit error environment.

A coset of a convolutional code may be used to generate a zero-run length limited trellis code for a 1-D partial-response channel. The free squared Euclidean distance, d/sub free//sup 2/, at the channel output is lower bounded by the free Hamming distance of the convolutional code. The lower bound suggests the use of a convolutional code with maximal free Hamming distance, d/sub max/(R,N), for given rate R and number of decoder states N. In this paper we present cosets of convolutional codes that generate trellis codes with d/sub free//sup 2/>d/sub max/(R,N) for rates 1/5/spl les/R/spl les/7/9 and (d/sub free//sup 2/=d/sub max/(R,N) for R=13/16,29/32,61/64, The tabulated convolutional codes with R/spl les/7/9 were not optimized for Hamming distance. Instead, a computer search was used to determine cosets of convolutional codes that exploit the memory of the 1-D channel to increase d/sub free//sup 2/ at the channel output. The search was limited by only considering cosets with certain structural properties. The R/spl ges/13/16 codes were obtained using a new construction technique for convolutional codes with free Hamming distance 4. Newly developed bounds on the maximum zero-run lengths of cosets were used to ensure a short maximum run length at the 1-D channel output.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The well known transfer function bounding technique for trellis codes is used to obtain an approximation for the bit error rate of a trellis coded diversity receiver over a slowly fading Rayleigh channel. The approximation accommodates diversity reception through a modification of the branch labeling of the error state diagram.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The objective has been to find memory-efficient coding/interleaving techniques and to accurately quantify their memory requirements. Toward this objective, convolutional interleaving, differential phase shift keying (DPSK) modulation, and various convolutional codes, Reed-Solomon codes, and concatenated convolutional and Reed-Solomon codes were evaluated by high-fidelity link simulations. Their interleaving memory requirements were derived as functions of data bit energy relative to channel noise-density for bit-error-rates of 10/sup -5/. Interleaving delay requirements were also derived, and code selections with the smallest interleaving memory and delay requirements were identified. >