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A new decoder is being developed by the Jet Propulsion Laboratory for NASA's Deep Space Network. This unit will decode the new turbo codes, which have recently been approved by the Consultative Committee for Space Data Systems (CCSDS). Turbo codes provide up to 0.8 dB improvement in Eb/No over the current best codes used by deep space missions.
We describe novel interleaver and deinterleaver architectures that support bandwidth efficient memory access for decoders of turbo-like codes that are used in conjunction with high order modulations. The presentation focuses on a decoder for serially concatenated pulse-position modulation (SCPPM), which is a forward-error-correction code designed by NASA to support laser communications from Mars at more than 50 megabits-per-second (Mbps). For 64-ary PPM, the new architectures effectively triple the fan-in of the interleaver and fan-out of the deinterleaver, enabling parallelization that doubles the overall throughput. The techniques described here can be readily modified for other PPM orders.
Error correcting binary block code decoding on Q-ary output channels /weighted erasure decoding/, considering applications
Operation of sequential decoding of data at high rates using Fano algorithm is discussed. Actions followed by decoder in systematically searching branches are described. Technique of diagonal steps is explained and illustrated.
Learning decoder was developed which operates at system data rate without limiting data rate. Decoder is much simpler than those in existence, operates near Shannon's channel capacity, and automatically recovers operation after loss of signal.
A decoding technique is described for the conversion of delay-modulated digital data to nonreturn to zero (NRZ) data. A potential time-phase ambiguity in reception and decoding of delay-modulated data is resolved in real time, through monitoring the data stream for a unique waveform inherent in delay-modulated data. Statistical backup is provided.
The burst-b distance between two binary vectors is defined and shown to be a metric. This definition is applied to a binary-input, Q-ary output channel where errors occur in bursts. A decoding algorithm is presented for such a channel that is an extension of Weldon's (1971) weighted erasure decoding. Examples are presented illustrating the techniques.
This paper presents the best obtainable random coding and expurgated upper bounds on the probabilities of undetectable error, of t-order failure (advance to depth t into an incorrect subset), and of likelihood rise in the incorrect subset, applicable to sequential decoding when the metric bias G is arbitrary. Upper bounds on the Pareto exponent are also presented. The G-values optimizing each of the parameters of interest are determined, and are shown to lie in intervals that in general have nonzero widths. The G-optimal expurgated bound on undetectable error is shown to agree with that for maximum likelihood decoding of convolutional codes, and that on failure agrees with the block code expurgated bound. Included are curves evaluating the bounds for interesting choices of G and SNR for a binary-input quantized-output Gaussian additive noise channel.
The design and fabrication of an extremely low-power, constraint-length 7, rate 1/3 Viterbi decoder brassboard capable of operating at information rates of up to 100 kb/s is presented. The brassboard is partitioned to facilitate a later transition to an LSI version requiring even less power. The effect of soft-decision thresholds, path memory lengths, and output selection algorithms on the bit error rate is evaluated. A branch synchronization algorithm is compared with a more conventional approach. The implementation of the decoder and its test set (including all-digital noise source) are described along with the results of various system tests and evaluations. Results and recommendations are presented.
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.
Fourier-like transforms over GF(F sub n), where F sub n = 2(2n) + 1 is a Fermat prime, are applied in decoding Reed-Solomon codes. It is shown that such transforms can be computed using high-radix fast Fourier transform (FFT) algorithms requiring considerably fewer multiplications than the more usual radix 2 FFT algorithm. A special 256-symbol, 16-symbol-error-correcting, Reed-Solomon (RS) code for space communication-link applications can be encoded and decoded using this high-radix FFT algorithm over GF(F sub 3).
The very low error probability obtained with long error-correcting codes results in a very small number of observed errors in simulation studies of practical size and renders the usual confidence interval techniques inapplicable to the observed error probability. A natural extension of the notion of a 'confidence interval' is made and applied to such determinations of error probability by simulation. An example is included to show the surprisingly great significance of as few as two decoding errors in a very large number of decoding trials.
An upper bound on the average probability of error for maximum-likelihood decoding of the ensemble of random L-branch binary trellis codes of rate R = 1/n with distinction between memory length and tail length is given. It is shown that the bound is independent of the length L of the information sequence if the memory length exceeds the tail length by a specified amount that depends on L. Sequential decoding simulations using the stack algorithm were conducted to test the dependence of the undetected error probability on tail length and memory length, and the results corroborated the theory.
Results are described of telemetry system performance testing using DSN equipment and a Maximum Likelihood Convolutional Decoder (MCD) for code rates 1/2 and 1/3, constraint length 7 and special test software. The test results confirm the superiority of the rate 1/3 over that of the rate 1/2. The overall system performance losses determined at the output of the Symbol Synchronizer Assembly are less than 0.5 db for both code rates. Comparison of the performance is also made with existing mathematical models. Error statistics of the decoded data are examined. The MCD operational threshold is found to be about 1.96 db.
An algorithm for computing a Fourier-like transform over GF(2 to the (second power) to the n power), where n = 1,2,3,4,5, was developed to encode and decode and Reed-Solomon (RS) codes of length 2 to the (second power) to the n power. Such as RS detector is considerably faster than a decoder that uses the conventional fast transform over GF(2 to the (second power) to the n power).
Recent applications have developed for spread spectrum communications, hardware data transfer, high rate digital systems, etc. that use channels for which errors tend to occur in short bursts in addition to those at random, i.e., compound channels. Viterbi decoding algorithms are generally very good for random error channels but are not as efficient for burst errors or for compound channels. This paper presents the results of a computer simulation study of the performance of various Viterbi decoders when receiving data corrupted with burst and random errors on the same channel. Simulations were performed using hard-decision CPSK.
Through the use of continuing fractions, a simplified algorithm for decoding B.C.H. and R.S. codes is developed that corrects both erasures and errors on a finite field GF(q to the m). It is noted that the decoding method is a modification of the Forney-Belekamp technique. Finally, it is believed that the present scheme is both simpler to understand and to implement than more conventional algorithms.
A mathematical model of Viterbi decoder burst error performance is presented. This model allows for computer generation of Viterbi-like error sequences quickly and inexpensively for applications where large amounts of data are required. The model is corroborated through comparisons with actual software decoder simulations.