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A digital communication decoding method for low-density parity-check coded messages. The decoding method decodes the low-density parity-check coded messages within a bipartite graph having check nodes and variable nodes. Messages from check nodes are partially hard limited, so that every message which would otherwise have a magnitude at or above a certain level is re-assigned to a maximum magnitude.
Digital communication coding methods resulting in rate-compatible low density parity-check (LDPC) codes built from protographs. Described digital coding methods start with a desired code rate and a selection of the numbers of variable nodes and check nodes to be used in the protograph. Constraints are set to satisfy a linear minimum distance growth property for the protograph. All possible edges in the graph are searched for the minimum iterative decoding threshold and the protograph with the lowest iterative decoding threshold is selected. Protographs designed in this manner are used in decode and forward relay channels.
Language structure and message decoding for interplanetary decoding
In this paper we propose an innovative coded modulation scheme called 'Accumulate Repeat Accumulate Coded Modulation' (ARA coded modulation). This class of codes can be viewed as serial turbo-like codes, or as a subclass of Low Density Parity Check (LDPC) codes that are combined with high level modulation. Thus at the decoder belief propagation can be used for iterative decoding of ARA coded modulation on a graph, provided a demapper transforms the received in-phase and quadrature samples to reliability of the bits.
Inspired by recently proposed Accumulate-Repeat-Accumulate (ARA) codes [15], in this paper we propose a channel coding scheme called Accumulate-Repeat-Accumulate-Accumulate (ARAA) codes. These codes can be seen as serial turbo-like codes or as a subclass of Low Density Parity Check (LDPC) codes, and they have a projected graph or protograph representation; this allows for a high-speed iterative decoder implementation using belief propagation. An ARAA code can be viewed as a precoded Repeat-and-Accumulate (RA) code with puncturing in concatenation with another accumulator, where simply an accumulator is chosen as the precoder; thus ARAA codes have a very fast encoder structure. Using density evolution on their associated protographs, we find examples of rate-lJ2 ARAA codes with maximum variable node degree 4 for which a minimum bit-SNR as low as 0.21 dB from the channel capacity limit can be achieved as the block size goes to infinity. Such a low threshold cannot be achieved by RA or Irregular RA (IRA) or unstructured irregular LDPC codes with the same constraint on the maximum variable node degree. Furthermore by puncturing the accumulators we can construct families of higher rate ARAA codes with thresholds that stay close to their respective channel capacity thresholds uniformly. Iterative decoding simulation results show comparable performance with the best-known LDPC codes but with very low error floor even at moderate block sizes.
Loss of the command function of the Telstar satellite first occurred on Novemb 4, 1962. There had been earlier indications of degraded performance. Facts are presented which led to the conclusion that the malfunction of the command system was due to surface damage to certain transistors in the redundant command decoders by the enhanced radiation in the inner Van Allen belt. Correction steps have included laboratory experiments to gain a better understanding of the cause of failure, the use of continuous normal commands, commands transmitted from Johannesburg, South Africa, and specially modified commands to circumvent failure of the more vulnerable transistors. The operations which aided in the gradual rejuvenation of both command decoders are described. Also covered are the subsequent reappearance of the command system malfunction on February 21, 1963, and its correlation with the variation of the average radiation intensity seen by the satellite.
Instrument, designed for mounting in aircraft instrument panels, decodes identification signals received in Morse from VOR or ILS transmitters as they are received and displays the literal equivalent. Without elaboration it cannot decode numbers.
Upper and lower bounds for feedback decoding and definite decoding minimum distances of binary convolutional codes
Majority logic decodability of product of two majority logic decodable cyclic codes
Coding systems for high data rates were examined from the standpoint of potential application in space-station telemetry links. Approaches considered included convolutional codes with sequential, Viterbi, and cascaded-Viterbi decoding. It was concluded that a high-speed (40 Mbps) sequential decoding system best satisfies the requirements for the assumed growth potential and specified constraints. Trade-off studies leading to this conclusion are viewed, and some sequential (Fano) algorithm improvements are discussed, together with real-time simulation results.
In deep space communications with distant planets, the data rate as well as the operating SNR may be very low. To maintain the error rate also at a very low level, it is necessary to use a sophisticated coding system (longer code) without excessive decoding complexity. The concatenated coding has been shown to meet such requirements in that the error rate decreases exponentially with the overall length of the code while the decoder complexity increases only algebraically. Three methods of concatenating an inner code with an outer code are considered. Performance comparison of the three concatenated codes is made.
A highly efficient, all-digital communications signal design employing convolutional coding and PN spectrum spreading is described for two-way transmission of voice and data between a manned spacecraft and ground. Variable-slope delta modulation is selected for analog/digital conversion of the voice signal, and a convolutional decoder utilizing the Viterbi decoding algorithm is selected for use at each receiving terminal. A PN spread spectrum technique is implemented to protect against multipath effects and to reduce the energy density (per unit bandwidth) impinging on the earth's surface to a value within the guidelines adopted by international agreement. Performance predictions are presented for transmission via a TDRS (tracking and data relay satellite) system and for direct transmission between the spacecraft and earth. Hardware estimates are provided for a flight-qualified communications system employing the coded digital signal design.
It is important to define and evaluate measures which incorporate most, if not all, of the quantities affecting the overall system reliability. For the simple types of block codes normally employed in space communication systems, the complexity of the encoder and decoder is of little consequence, since the use of integrated circuit technology allows the construction of the basic components in an inexpensive fashion. The complexity is essentially independent of the particular code-decoder used. The processing speed is generally a function of the type of logic used and the technology in the construction of the integrated circuits.
Three coding schemes designed for improved data communication are evaluated. Four block codes are evaluated relative to a quality function, which is a function of both the amount of data rejected and the error rate. The Viterbi maximum likelihood decoding algorithm as a decoding procedure is reviewed. This evaluation is obtained by simulating the system on a digital computer. Short constraint length rate 1/2 quick-look codes are studied, and their performance is compared to general nonsystematic codes.
The degradation of the performance of digital communication systems because of ionospheric scintillation effects can be reduced either by diversity techniques or by coding. The effectiveness of traditional space-diversity, frequency-diversity and time-diversity techniques is reviewed and design considerations isolated. Time-diversity signaling is then treated as an extremely simple form of coding. More advanced coding methods, such as diffuse threshold decoding and burst-trapping decoding, which appear attractive in combatting scintillation effects are discussed and design considerations noted. Finally, adaptive coding techniques appropriate when the general state of the channel is known are discussed.
The planetary entry channel is modeled for communication purposes representing turbulent atmospheric scattering effects. The performance of short and long constraint length convolutional codes is investigated in conjunction with coherent BPSK modulation and Viterbi maximum likelihood decoding. Algorithms for sequential decoding are studied in terms of computation and/or storage requirements as a function of the fading channel parameters. The performance of the coded coherent BPSK system is compared with the coded incoherent MFSK system. Results indicate that: some degree of interleaving is required to combat time correlated fading of channel; only modest amounts of interleaving are required to approach performance of memoryless channel; additional propagational results are required on the phase perturbation process; and the incoherent MFSK system is superior when phase tracking errors are considered.
The performance of convolutional codes in fading channels typical of the planetary entry channel is examined in detail. The signal fading is due primarily to turbulent atmospheric scattering of the RF signal transmitted from an entry probe through a planetary atmosphere. Short constraint length convolutional codes are considered in conjunction with binary phase-shift keyed modulation and Viterbi maximum likelihood decoding, and for longer constraint length codes sequential decoding utilizing both the Fano and Zigangirov-Jelinek (ZJ) algorithms are considered. Careful consideration is given to the modeling of the channel in terms of a few meaningful parameters which can be correlated closely with theoretical propagation studies. For short constraint length codes the bit error probability performance was investigated as a function of E sub b/N sub o parameterized by the fading channel parameters. For longer constraint length codes the effect was examined of the fading channel parameters on the computational requirements of both the Fano and ZJ algorithms. The effects of simple block interleaving in combatting the memory of the channel is explored, using the analytic approach or digital computer simulation.
A tabulation is given of long systematic and long quick-look-in (QLI) nonsystematic rate R = 1/2 binary convolutional codes with an optimum distance profile (ODP). These codes appear attractive for use with sequential decoders. Simulations for two of the new codes are reported and confirm Massey's conjecture that systematic and non-systematic codes of the same rate yield nearly identical computational and error probability performance with sequential decoding when the number of digits transmitted in the tail of the encoded frame is the same for both codes.