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NASA NTRS1993

A low-complexity and high performance concatenated coding scheme for high-speed satellite communications

This report presents a low-complexity and high performance concatenated coding scheme for high-speed satellite communications. In this proposed scheme, the NASA Standard Reed-Solomon (RS) code over GF(2(exp 8) is used as the outer code and the second-order Reed-Muller (RM) code of Hamming distance 8 is used as the inner code. The RM inner code has a very simple trellis structure and is decoded with the soft-decision Viterbi decoding algorithm. It is shown that the proposed concatenated coding scheme achieves an error performance which is comparable to that of the NASA TDRS concatenated coding scheme in which the NASA Standard rate-1/2 convolutional code of constraint length 7 and d sub free = 10 is used as the inner code. However, the proposed RM inner code has much smaller decoding complexity, less decoding delay, and much higher decoding speed. Consequently, the proposed concatenated coding scheme is suitable for reliable high-speed satellite communications, and it may be considered as an alternate coding scheme for the NASA TDRS system.

Lin, Shu↗
NASA NTRS1995

Further Developments in the Communication Link and Error Analysis (CLEAN) Simulator

During the period 1 July 1993 - 30 June 1994, significant developments to the Communication Link and Error ANalysis (CLEAN) simulator were completed. Many of these were reported in the Semi-Annual report dated December 1993 which has been included in this report in Appendix A. Since December 1993, a number of additional modules have been added involving Unit-Memory Convolutional codes (UMC). These are: (1) Unit-Memory Convolutional Encoder module (UMCEncd); (2) Hard decision Unit-Memory Convolutional Decoder using the Viterbi decoding algorithm (VitUMC); and (3) a number of utility modules designed to investigate the performance of LTMC's such as LTMC column distance function (UMCdc), UMC free distance function (UMCdfree), UMC row distance function (UMCdr), and UMC Transformation (UMCTrans). The study of UMC's was driven, in part, by the desire to investigate high-rate convolutional codes which are better suited as inner codes for a concatenated coding scheme. A number of high-rate LTMC's were found which are good candidates for inner codes. Besides the further developments of the simulation, a study was performed to construct a table of the best known Unit-Memory Convolutional codes. Finally, a preliminary study of the usefulness of the Periodic Convolutional Interleaver (PCI) was completed and documented in a Technical note dated March 17, 1994. This technical note has also been included in this final report.

Ebel, William J.↗
NASA NTRS1989

Method and apparatus for implementing a traceback maximum-likelihood decoder in a hypercube network

A method and a structure to implement maximum-likelihood decoding of convolutional codes on a network of microprocessors interconnected as an n-dimensional cube (hypercube). By proper reordering of states in the decoder, only communication between adjacent processors is required. Communication time is limited to that required for communication only of the accumulated metrics and not the survivor parameters of a Viterbi decoding algorithm. The survivor parameters are stored at a local processor's memory and a trace-back method is employed to ascertain the decoding result. Faster and more efficient operation is enabled, and decoding of large constraint length codes is feasible using standard VLSI technology.

Pollara-Bozzola, Fabrizio↗
NASA NTRS1976

Convolutional coding at 50 Mbps for the Shuttle Ku-band return link

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.

Batson, B. H.↗
NASA NTRS1974

Evaluation of three coding schemes designed for improved data communication

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.

Snelsire, R. W.↗
NASA NTRS1974

Convolutional code performance in planetary entry channels

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.

Modestino, J. W.↗
NASA NTRS1977

The proposed coding standard at GSFC

As part of the continuing effort to introduce standardization of spacecraft and ground equipment in satellite systems, NASA's Goddard Space Flight Center and other NASA facilities have supported the development of a set of standards for the use of error control coding in telemetry subsystems. These standards are intended to ensure compatibility between spacecraft and ground encoding equipment, while allowing sufficient flexibility to meet all anticipated mission requirements. The standards which have been developed to date cover the application of block codes in error detection and error correction modes, as well as short and long constraint length convolutional codes decoded via the Viterbi and sequential decoding algorithms, respectively. Included are detailed specifications of the codes, and their implementation. Current effort is directed toward the development of standards covering channels with burst noise characteristics, channels with feedback, and code concatenation.

Morakis, J. C.↗
NASA NTRS1984

A Very Efficient Transfer Function Bounding Technique on Bit Error Rate for Viterbi Decoded, Rate 1/N Convolutional Codes

For rate 1/N convolutional codes, a recursive algorithm for finding the transfer function bound on bit error rate (BER) at the output of a Viterbi decoder is described. This technique is very fast and requires very little storage since all the unnecessary operations are eliminated. Using this technique, we find and plot bounds on the BER performance of known codes of rate 1/2 with K 18, rate 1/3 with K 14. When more than one reported code with the same parameter is known, we select the code that minimizes the required signal to noise ratio for a desired bit error rate of 0.000001. This criterion of determining goodness of a code had previously been found to be more useful than the maximum free distance criterion and was used in the code search procedures of very short constraint length codes. This very efficient technique can also be used for searches of longer constraint length codes.

Lee, P. J.↗
NASA NTRS1993

Enhanced decoding for the Galileo S-band mission

A coding system under consideration for the Galileo S-band low-gain antenna mission is a concatenated system using a variable redundancy Reed-Solomon outer code and a (14,1/4) convolutional inner code. The 8-bit Reed-Solomon symbols are interleaved to depth 8, and the eight 255-symbol codewords in each interleaved block have redundancies 64, 20, 20, 20, 64, 20, 20, and 20, respectively (or equivalently, the codewords have 191, 235, 235, 235, 191, 235, 235, and 235 8-bit information symbols, respectively). This concatenated code is to be decoded by an enhanced decoder that utilizes a maximum likelihood (Viterbi) convolutional decoder; a Reed Solomon decoder capable of processing erasures; an algorithm for declaring erasures in undecoded codewords based on known erroneous symbols in neighboring decodable words; a second Viterbi decoding operation (redecoding) constrained to follow only paths consistent with the known symbols from previously decodable Reed-Solomon codewords; and a second Reed-Solomon decoding operation using the output from the Viterbi redecoder and additional erasure declarations to the extent possible. It is estimated that this code and decoder can achieve a decoded bit error rate of 1 x 10(exp 7) at a concatenated code signal-to-noise ratio of 0.76 dB. By comparison, a threshold of 1.17 dB is required for a baseline coding system consisting of the same (14,1/4) convolutional code, a (255,223) Reed-Solomon code with constant redundancy 32 also interleaved to depth 8, a one-pass Viterbi decoder, and a Reed Solomon decoder incapable of declaring or utilizing erasures. The relative gain of the enhanced system is thus 0.41 dB. It is predicted from analysis based on an assumption of infinite interleaving that the coding gain could be further improved by approximately 0.2 dB if four stages of Viterbi decoding and four levels of Reed-Solomon redundancy are permitted. Confirmation of this effect and specification of the optimum four-level redundancy profile for depth-8 interleaving is currently being done.

Dolinar, S.↗
NASA NTRS2000

Full Duplex, Spread Spectrum Radio System

The goal of this project was to support the development of a full duplex, spread spectrum voice communications system. The assembly and testing of a prototype system consisting of a Harris PRISM spread spectrum radio, a TMS320C54x signal processing development board and a Zilog Z80180 microprocessor was underway at the start of this project. The efforts under this project were the development of multiple access schemes, analysis of full duplex voice feedback delays, and the development and analysis of forward error correction (FEC) algorithms. The multiple access analysis involved the selection between code division multiple access (CDMA), frequency division multiple access (FDMA) and time division multiple access (TDMA). Full duplex voice feedback analysis involved the analysis of packet size and delays associated with full loop voice feedback for confirmation of radio system performance. FEC analysis included studies of the performance under the expected burst error scenario with the relatively short packet lengths, and analysis of implementation in the TMS320C54x digital signal processor. When the capabilities and the limitations of the components used were considered, the multiple access scheme chosen was a combination TDMA/FDMA scheme that will provide up to eight users on each of three separate frequencies. Packets to and from each user will consist of 16 samples at a rate of 8,000 samples per second for a total of 2 ms of voice information. The resulting voice feedback delay will therefore be 4 - 6 ms. The most practical FEC algorithm for implementation was a convolutional code with a Viterbi decoder. Interleaving of the bits of each packet will be required to offset the effects of burst errors.

Harvey, Bruce A.↗
NASA NTRS1980

Viterbi/algebraic hybrid decoder

Decoder computer program is hybrid between optimal Viterbi and optimal algebraic decoders. Tests have shown that hybrid decoder outperforms any strictly Viterbi or strictly algebraic decoder and effectively handles compound channels. Algorithm developed uses syndrome-detecting logic to direct two decoders to assume decoding load alternately, depending on real-time channel characteristics.

Boyd, R. W.↗
NASA NTRS1982

The effects of Viterbi decoder node synchronization losses on the telemetry receiving system

The Viterbi decoders currently used by the Deep space Network (DSN) use an algorithm for maintaining node synchronization that breaks down at bit signal-to-noise ratios (SNRs) of about 2.0 dB. It is shown that this can become an important consideration when the effects of noisy carrier referencing are combined with the lower SNRs that are expected at Voyager 2 Uranus and Neptune encounters. Depending on the available carrier power, node synchronization losses of between 0.85 and 1.25 dB can be expected in addition to the radio loss.

Deutsch, L. J.↗
NASA NTRS1982

Viterbi decoder node synchronization losses in the Reed-Solomon/Veterbi concatenated channel

The Viterbi decoders currently used by the Deep Space Network (DSN) employ an algorithm for maintaining node synchronization that significantly degrades at bit signal-to-noise ratios (SNRs) of below 2.0 dB. In a recent report by the authors, it was shown that the telemetry receiving system, which uses a convolutionally encoded downlink, will suffer losses of 0.85 dB and 1.25 dB respectively at Voyager 2 Uranus and Neptune encounters. This report extends the results of that study to a concatenated (255,223) Reed-Solomon/(7, 1/2) convolutionally coded channel, by developing a new radio loss model for the concatenated channel. It is shown here that losses due to improper node synchronization of 0.57 dB at Uranus and 1.0 dB at Neptune can be expected if concatenated coding is used along with an array of one 64-meter and three 34-meter antennas.

Deutsch, L. J.↗
NASA NTRS1988

Long decoding runs for Galileo's convolutional codes

Decoding results are described for long decoding runs of Galileo's convolutional codes. A 1 k-bit/sec hardware Viterbi decoder is used for the (15, 1/4) convolutional code, and a software Viterbi decoder is used for the (7, 1/2) convolutional code. The output data of these long runs are stored in data files using a data compression format which can reduce file size by a factor of 100 to 1 typically. These data files can be used to replicate the long, time-consuming runs exactly and are useful to anyone who wants to analyze the burst statistics of the Viterbi decoders. The 1 k-bit/sec hardware Viterbi decoder was developed in order to demonstrate the correctness of certain algorithmic concepts for decoding Galileo's experimental (15, 1/4) code, and for the long-constraint-length codes in general. The hardware decoder can be used both to search for good codes and to measure accurately the performance of known codes.

Lahmeyer, C. R.↗
NASA NTRS1990

Finding the complete path and weight enumerators of convolutional codes

A method for obtaining the complete path enumerator T(D, L, I) of a convolutional code is described. A system of algebraic equations is solved, using a new algorithm for computing determinants, to obtain T(D, L, I) for the (7,1/2) NASA standard code. Generating functions, derived from T(D, L, I) are used to upper bound Viterbi decoder error rates. This technique is currently feasible for constraint length K less than 10 codes. A practical, fast algorithm is presented for computing the leading nonzero coefficients of the generating functions used to bound the performance of constraint length K less than 20 codes. Code profiles with about 50 nonzero coefficients are obtained with this algorithm for the experimental K = 15, rate 1/4, code in the Galileo mission and for the proposed K = 15, rate 1/6, 2-dB code.

Onyszchuk, I.↗
NASA NTRS1992

Node synchronization schemes for the Big Viterbi Decoder

The Big Viterbi Decoder (BVD), currently under development for the DSN, includes three separate algorithms to acquire and maintain node and frame synchronization. The first measures the number of decoded bits between two consecutive renormalization operations (renorm rate), the second detects the presence of the frame marker in the decoded bit stream (bit correlation), while the third searches for an encoded version of the frame marker in the encoded input stream (symbol correlation). A detailed account of the operation is given, as well as performance comparison, of the three methods.

Cheung, K.-M.↗