Rate 1/2 convolutional codes with complementary generators
Rate 1/2 convolutional error correcting binary codes with complementary generators, discussing synthesis and search procedure for largest free distance
Bahl, L. R.↗
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Nonsystematic convolutional codes for sequential decoding in space applications.
Description of a class of rate 1/2 nonsystematic convolutional codes with the following desirable properties: (1) an undetected decoding error probability verified by simulation to be much smaller than for the best systematic codes of the same constraint length; (2) computation behavior with sequential decoding verified by simulation to be virtually identical to that of the best systematic codes; (3) a ?quick-look-in' feature that permits recovery of the information sequence from the hard-decisioned received data without decoding simply by modulo-two addition of the received sequences; and (4) suitability for encoding by simple circuitry requiring less hardware than encoders for the best systematic codes of the same constraint length. Theoretical analyses are given. These codes have been adopted for use in several forthcoming space missions.
Massey, J. L.↗
A simple branch synchronizer for convolutional decoders.
A simple branch synchronizer for rate 1/3, constraint length five, nonsystematic convolutional code is described. The scheme derives the sync information from the received channel bits, thus avoiding the extra formatting of the sync data at the transmitter and receiver, and increasing the data rate. The synchronizer detects the proper sync bits for both the in-phase and phase ambiguous cases. The design is adaptable to nonsystematic codes of different constraint lengths.
Taqvi, S. Z. H.↗
Real-time minimal bit error probability decoding of convolutional codes
A recursive procedure is derived for decoding of rate R=1/n binary convolutional codes which minimizes the probability of the individual decoding decisions for each information bit subject to the constraint that the decoding delay be limited to Delta branches. This new decoding algorithm is similar to, but somewhat more complex than, the Viterbi decoding algorithm. A real-time, i.e. fixed decoding delay, version of the Viterbi algorithm is also developed and used for comparison to the new algorithm on simulated channels. It is shown that the new algorithm offers advantages over Viterbi decoding in soft-decision applications such as in the inner coding system for concatenated coding.
Lee, L. N.↗
Real-time minimal-bit-error probability decoding of convolutional codes
A recursive procedure is derived for decoding of rate R = 1/n binary convolutional codes which minimizes the probability of the individual decoding decisions for each information bit, subject to the constraint that the decoding delay be limited to Delta branches. This new decoding algorithm is similar to, but somewhat more complex than, the Viterbi decoding algorithm. A real-time, i.e., fixed decoding delay, version of the Viterbi algorithm is also developed and used for comparison to the new algorithm on simulated channels. It is shown that the new algorithm offers advantages over Viterbi decoding in soft-decision applications, such as in the inner coding system for concatenated coding.
Lee, L.-N.↗
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.↗
Short, unit-memory, Byte-oriented, binary convolutional codes having maximal free distance
It is shown that (n sub 0, k sub 0) convolutional codes with unit memory always achieve the largest free distance among all codes of the same rate k sub 0/n sub 0 and same number 2MK sub 0 of encoder states, where M is the encoder memory. A unit-memory code with maximal free distance is given at each place where this free distance exceeds that of the best code with k sub 0 and n sub 0 relatively prime, for all Mk sub 0 less than or equal to 6 and for R = 1/2, 1/3, 1/4, 2/3. It is shown that the unit-memory codes are byte-oriented in such a way as to be attractive for use in concatenated coding systems.
Lee, L. N.↗
Some long, rate one-half, binary convolutional codes with an optimum distance profile and the systematic versus nonsystematic code question
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.
Johannesson, R.↗
Convolutional code performance in fading channels
The performance of convolutional codes in fading channels typical of the planetary entry channel is examined in detail. Short constraint length codes are considered in conjunction with binary phase-shift-keyed (BPSK) modulation and Viterbi maximum likelihood decoding while for longer constraint length codes we consider sequential decoding utilizing both the Fano and Zigangirov-Jelinek (ZJ) algorithms. For short constraint length codes we are primarily interested in the bit error probability performance parameterized by the fading channel parameters. For longer constraint length codes interest will center on the effect of the fading channel parameters on the computational requirements of both the Fano and ZJ algorithms. In either case the effects of simple block interleaving in combatting the memory of the channel is thoroughly explored. The approach is analytic where possible otherwise resort is made to digital computer simulation.
Modestino, J. W.↗
DSN telemetry system performance with convolutionally code data
The results obtained to date and the plans for future experiments for the DSN telemetry system were presented. The performance of the DSN telemetry system in decoding convolutionally coded data by both sequential and maximum likelihood techniques is being determined by testing at various deep space stations. The evaluation of performance models is also an objective of this activity.
Mulhall, B. D. L.↗
Comparison of rate one-half, equivalent constraint length 24, binary convolutional codes for use with sequential decoding on the deep-space channel
Virtually all previously-suggested rate 1/2 binary convolutional codes with KE = 24 are compared. Their distance properties are given; and their performance, both in computation and in error probability, with sequential decoding on the deep-space channel is determined by simulation. Recommendations are made both for the choice of a specific KE = 24 code as well as for codes to be included in future coding standards for the deep-space channel. A new result given in this report is a method for determining the statistical significance of error probability data when the error probability is so small that it is not feasible to perform enough decoding simulations to obtain more than a very small number of decoding errors.
Massey, J. L.↗
DSN telemetry system performance with convolutionally coded data: Maximum likelihood decoding
DSN telemetry system performance is analyzed based on convolutionally coded data for the short constraint length 7:1/2 codes at low bit rates, 8 to 2,048 bits per second, obtained from CTA 21 for the S-band configuration. The results indicate that a loss of one or more decibels in the system performance may be expected due to system degradation. Also, burst error lengths up to 100 bits may not be unusual in actual operational situations.
Benjauthrit, B.↗
DSN telemetry system performance with convolutionally coded data: Sequential decoding update
DSN telemetry system performance in decoding convolutionally coded data by both sequential and maximum likelihood techniques is being determined by testing at various deep space stations. This article describes corrections and refinements to the sequential decoding tests.
Greenhall, C. A.↗
Maximum likelihood convolutional decoding (MCD) performance due to system losses
A model for predicting the computational performance of a maximum likelihood convolutional decoder (MCD) operating in a noisy carrier reference environment is described. This model is used to develop a subroutine that will be utilized by the Telemetry Analysis Program to compute the MCD bit error rate. When this computational model is averaged over noisy reference phase errors using a high-rate interpolation scheme, the results are found to agree quite favorably with experimental measurements.
Webster, L.↗
Convolutional code performance in the Rician fading channel
The performance of short constraint length convolutional codes in conjunction with binary phase-shift keyed (BPSK) modulation and Viterbi maximum likelihood decoding on the classical Rician fading channel is examined in detail. Primary interest is in the bit error probability performance as a function of E sub b/N sub 0 parameterized by the fading channel parameters. Fairly general upper bounds on bit error probability performance in the presence of fading are obtained and compared with simulation results in the two extremes of zero channel memory and infinite channel memory. The efficacy of simple block interleaving in combating the memory of the channel is thoroughly explored. Results include the effects of fading on tracking loop performance and the subsequent impact on overall coded system performance. The approach is analytical where possible; otherwise resort is made to digital computer simulation.
Modestino, J. W.↗
Programmable convolution via the chirp Z-transform with CCD's
Technique filtering by convolution in frequency domain rather than in time domain presents possible solution to problem of programmable transversal filters. Process is accomplished through utilization of chip z-transform (CZT) with charge-coupled devices
Buss, D. D.↗
Convolution using guided acoustooptical interaction in thin-film waveguides
Interaction of two antiparallel acoustic surface waves (ASW) with an optical guided wave has been investigated theoretically as well as experimentally to obtain the convolution of two ASW signals. The maximum time-bandwidth product that can be achieved by such a convolver is shown to be of the order of 1000 or more. The maximum dynamic range can be as large as 83 dB.
Chang, W. S. C.↗
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.↗