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New class of codes with desirable properties constructed from block codes. Finite-state encoder is machine that has finite number of internal states. Receives k parallel information symbols and transmits n parallel code symbols at each clock pulse. Finite-state codes include both block and convolutional codes. Theory of finite-state codes used to study properties of error-correcting codes in general and to design new codes to various specifications.
Laser communication and ranging experiments were successfully conducted from the satellite laser ranging (SLR) station at NASA Goddard Space Flight Center (GSFC) to the Lunar Reconnaissance Orbiter (LRO) in lunar orbit. The experiments used 4096-ary pulse position modulation (PPM) for the laser pulses during one-way LRO Laser Ranging (LR) operations. Reed-Solomon forward error correction codes were used to correct the PPM symbol errors due to atmosphere turbulence and pointing jitter. The signal fading was measured and the results were compared to the model.
Floquet codes are a novel form of quantum error correcting codes, where the logical degrees of freedom appear in a dynamical form. The first example of such a code was constructed by Hastings and Haah on a honeycomb lattice. Specifically, they showed how to Floquetify the Kitaev honeycomb model, which when viewed as a subsystem code, encodes no logical qubits. However, by choosing a particular measurement schedule of the check operators, this model leads to dynamically encoded logical qubits. Since this initial work, several examples of Floquet codes have been constructed, mainly on trivalent lattices. Here, we report progress on understanding when such codes can be implemented on lattices of different connectivities.
This slide presentation reviews the progress that the workgroup on Low-Density Parity-Check (LDPC) for space link coding. The workgroup is tasked with developing and recommending new error correcting codes for near-Earth, Lunar, and deep space applications. Included in the presentation is a summary of the technical progress of the workgroup. Charts that show the LDPC decoder sensitivity to symbol scaling errors are reviewed, as well as a chart showing the performance of several frame synchronizer algorithms compared to that of some good codes and LDPC decoder tests at ESTL. Also reviewed is a study on Coding, Modulation, and Link Protocol (CMLP), and the recommended codes. A design for the Pseudo-Randomizer with LDPC Decoder and CRC is also reviewed. A chart that summarizes the three proposed coding systems is also presented.
Although ACTS (Advanced Communications Technology Satellite) provides an almost error-free channel during much of the day and under most conditions, there are times when it is not suitable for reliably error-free data communications when operating in the uncoded mode. Because coded operation is not always available to every earth station, measures must be taken in the end system to maintain adequate throughput when transferring data under adverse conditions. The most effective approach that we tested to improve performance was the addition of an 'outer' Reed-Solomon code through use of CCSDS (Consultative Committee for Space Data Systems) GOS 2 (a forward error correcting code). This addition can benefit all users of an ACTS channel including those applications that do not require totally reliable transport, but it is somewhat expensive because additional hardware is needed. Although we could not characterize the link noise statistically (it appeared to resemble uncorrelated white noise, the type that block codes are least effective in correcting), we did find that CCSDS GOS 2 gave an essentially error-free link at BER's (bit error rate) as high as 6x10(exp -4). For users that demand reliable transport, an ARQ (Automatic Repeat Queuing) protocol such as TCP (Transmission Control Protocol) or TP4 (Transport Protocol, Class 4) will probably be used. In this category, it comes as no surprise that the best choice of the protocol suites tested over ACTS was TP4 using CCSDS GOS 2. TP4 behaves very well over an error-free link which GOS 2 provides up to a point. Without forward error correction, however, TP4 service begins to degrade in the 10(exp -7)-10(exp -6) range and by 4x10(exp -6), it barely gives any throughput at all. If Congestion Avoidance is used in TP4, the degradation is even more pronounced. Fortunately, as demonstrated here, this effect can be more than compensated for by choosing the Selective Acknowledgment option. In fact, this option can enable TP4 to deliver some throughput at error rates as high as 10(exp -5).
Error correcting coding is required for 50 Mbps data link from the Shuttle Orbiter through the Tracking and Data Relay Satellite System (TDRSS) to the ground because of severe power limitations. Convolutional coding has been chosen because the decoding algorithms (sequential and Viterbi) provide significant coding gains at the required bit error probability of one in 10 to the sixth power and can be implemented at 50 Mbps with moderate hardware. While a 50 Mbps sequential decoder has been built, the highest data rate achieved for a Viterbi decoder is 10 Mbps. Thus, five multiplexed 10 Mbps Viterbi decoders must be used to provide a 50 Mbps data rate. This paper discusses the tradeoffs which were considered when selecting the multiplexed Viterbi decoder approach for this application.
The results of a study on a class of error correcting codes called partial unit memory (PUM) codes are presented. This class of codes, though not entirely new, has until now remained relatively unexplored. The possibility of using the well developed theory of block codes to construct a large family of promising PUM codes is shown. The performance of several specific PUM codes are compared with that of the Voyager standard (2, 1, 6) convolutional code. It was found that these codes can outperform the Voyager code with little or no increase in decoder complexity. This suggests that there may very well be PUM codes that can be used for deep space telemetry that offer both increased performance and decreased implementational complexity over current coding systems.
In the late seventies and early eighties a technique known as Trellis Coded Modulation (TCM) was developed for providing spectrally efficient error correction coding. Instead of adding redundant information in the form of parity bits, redundancy is added at the modulation stage thereby increasing bandwidth efficiency. A digital communications system can be designed to use bandwidth-efficient multilevel/phase modulation such as Amplitude Shift Keying (ASK), Phase Shift Keying (PSK), Differential Phase Shift Keying (DPSK) or Quadrature Amplitude Modulation (QAM). Performance gain can be achieved by increasing the number of signals over the corresponding uncoded system to compensate for the redundancy introduced by the code. A considerable amount of research and development has been devoted toward developing good TCM codes for severely bandlimited applications. More recently, the use of TCM for satellite and deep space communications applications has received increased attention. This report describes the general approach of using a concatenated coding scheme that features TCM and RS coding. Results have indicated that substantial (6-10 dB) performance gains can be achieved with this approach with comparatively little bandwidth expansion. Since all of the bandwidth expansion is due to the RS code we see that TCM based concatenated coding results in roughly 10-50% bandwidth expansion compared to 70-150% expansion for similar concatenated scheme which use convolution code. We stress that combined coding and modulation optimization is important for achieving performance gains while maintaining spectral efficiency.
This paper describes algorithms implemented by the Magellan High Rate Processor to recover radar data corrupted by the failure of an onboard tape recorder that dropped bits. For data with error correction coding, an algorithm was developed that decodes data in the presence of bit errors and missing bits.
Addressed in this paper is the dependence of telecommunication channel, forward error correcting coding and source data compression coding on integrated circuit technology. Emphasis is placed on real time high speed Reed Solomon (RS) decoding using full custom VLSI technology. Performance curves of NASA's standard channel coder and a proposed standard lossless data compression coder are presented.
The Bose, Chaudhuri, and Hocquenghem (BCH) codes form a large class of powerful error-correcting cyclic codes. Among the non-binary BCH codes, the most important subclass is the Reed Solomon (RS) codes. Reed Solomon codes have the ability to correct random and burst errors. It is well known that an (n,k) RS code can correct up to (n-k)/2 random errors. When burst errors are involved, the error correcting ability of the RS code can be increased beyond (n-k)/2. It has previously been show that RS codes can reliably correct burst errors of length greater than (n-k)/2. In this paper, a new decoding algorithm is given which can also correct a burst error of length greater than (n-k)/2.
The application of error-detecting or error-correcting codes in digital computer design requires studies of cost and effectiveness tradeoffs to supplement the knowledge of their theoretical properties. General criteria for cost and effectiveness studies of error codes are developed, and results are presented for arithmetic error codes with the low-cost check modulus 2 super a - 1. Both separate (residue) and nonseparate (AN) codes are considered. The class of multiple arithmetic error codes is developed as an extension of low-cost single codes.
Work on partial unit memory codes continued; it was shown that for a given virtual state complexity, the maximum free distance over the class of all convolutional codes is achieved within the class of unit memory codes. The effect of phase-lock loop (PLL) tracking error on coding system performance was studied by using the channel cut-off rate as the measure of quality of a modulation system. Optimum modulation signal sets for a non-white Gaussian channel considered an heuristic selection rule based on a water-filling argument. The use of error correcting codes to perform data compression by the technique of syndrome source coding was researched and a weight-and-error-locations scheme was developed that is closely related to LDSC coding.
Ford Aerospace has developed a proof-of-concept satellite 8 phase shift keying (PSK) modulation and coding system operating in the Time Division Multiple Access (TDMA) mode at a data range of 200 Mbps using rate 5/6 forward error correction coding. The 80 Msps 8 PSK modem was developed in a mostly digital form and is amenable to an ASIC realization in the next phase of development. The codec was developed as a paper design only. The power efficiency goal was to be within 2 dB of theoretical at a bit error rate (BER) of 5x10(exp 7) while the measured implementation loss was 4.5 dB. The bandwidth efficiency goal was 2 bits/sec/Hz while the realized bandwidth efficiency was 1.8 bits/sec/Hz. The burst format used a preamble of only 40 8 PSK symbol times including 32 symbols of all zeros and an eight symbol unique word. The modem and associated special test equipment (STE) were fabricated mostly on a specially designed stitch-weld board although a few of the highest rate circuits were built on printed circuit cards. All the digital circuits were ECL to support the clock rates of from 80 MHz to 360 MHz. The transmitter and receiver matched filters were square-root Nyquist bandpass filters realized at the 3.37 GHz i.f. The modem operated as a coherent system although no analog phase locked (PLL) loop was employed. Within the budgetary constraints of the program, the approach to the demodulator has been proven and is eligible to proceed to the next phase of development of a satellite demodulator engineering model. This would entail the development of an ASIC version of the digital portion of the demodulator, and MMIC version of the quadrature detector, and SAW Nyquist filters to realize the bandwidth efficiency.
This paper addresses the carrier-phase estimation problem under low SNR conditions as are typical of turbo- and LDPC-coded applications. In previous publications by the first author, closed-loop carrier synchronization schemes for error-correction coded BPSK and QPSK modulation were proposed that were based on feeding back hard data decisions at the input of the loop, the purpose being to remove the modulation prior to attempting to track the carrier phase as opposed to the more conventional decision-feedback schemes that incorporate such feedback inside the loop. In this paper, we consider an alternative approach wherein the extrinsic soft information from the iterative decoder of turbo or LDPC codes is instead used as the feedback.
A technique proposed by Chase (1972) is used to evaluate the performance of several fairly long binary block codes on a wideband additive Gaussian channel. Considerations leading to the use of Chase's technique are discussed. Chase's concepts are first applied to the most powerful practical class of binary codes, the BCH codes with Berlekamp's (1972) decoding algorithm. Chase's algorithm is then described along with proposed selection of candidate codes. Results are presented of applying Chase's algorithm to four binary codes: (23, 12) Golay code, (32, 16) second-order Reed-Muller code, (63, 36) 5-error correcting BCH code, and (95, 39) 9-error correcting shortened BCH code. It is concluded that there are many block codes of length not exceeding 100 with extremely attractive maximum likelihood decoding performance on a Gaussian channel. BCH codes decoded via Berlekamp's binary decoding algorithm and Chase's idea are close to being practical competitors to short-constraint length convolutional codes with Viterbi decoding.
NASA publication second in series on data-coding techniques for noiseless channels. Techniques used even in noisy channels, provided data further processed with Reed-Solomon or other error-correcting code. Techniques discussed in context of transmission of monochrome imagery from Voyager II spacecraft but applicable to other streams of data. Objective of this type coding to "compress" data; that is, to transmit using as few bits as possible by omitting as much as possible of portion of information repeated in subsequent samples (or picture elements).
In proposed communication system, digital signals transmitted efficiently over fading channel by combination of trellis coding and multiple-phase-shift keying with addition of asymmetry to signal set. Coding and modulation schemes not designed separately as in previous systems but integrated to yield bandwidth-efficient modulation and forward-error-correction coding. Helps to satisfy need for reliable high-quality transmission of voice and data between land-mobile units via satellites, where limitations of power and bandwidth imposed simultaneously. Also applicable to ionospheric communications between fixed or mobile units.