Concatenation of short constraint length convolutional codes
Viterbi algorithm for decoding convolutional codes for space channel application
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Viterbi algorithm for decoding convolutional codes for space channel application
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Rate 1/2 convolutional error correcting binary codes with complementary generators, discussing synthesis and search procedure for largest free distance
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.
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.
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.
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.
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.
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.
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.