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At least 163 records · Page 9

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NASA NTRS1980

Spectral characteristics of convolutionally coded digital signals

The power spectral density of the output symbol sequence of a convolutional encoder is computed for two different input symbol stream source models, namely, an NRZ signaling format and a first-order Markov source. The effects of alternate symbol inversion on this spectrum are also considered. The mathematical results are illustrated with many examples corresponding to optimal performance codes. It is demonstrated that only for the case of a purely random input source (e.g., NRZ data with equiprobable symbols) and a particular class of codes is the output spectrum identical to the input spectrum except for a frequency scaling (expansion) by the reciprocal of the code rate.

Divsalar, D.↗

NASA NTRS1981

Telemetry degradation due to a CW RFI induced carrier tracking error for the block IV receiving system with maximum likelihood convolution decoding

Models to characterize the behavior of the Deep Space Network (DSN) Receiving System in the presence of a radio frequency interference (RFI) are considered. A simple method to evaluate the telemetry degradation due to the presence of a CW RFI near the carrier frequency for the DSN Block 4 Receiving System using the maximum likelihood convolutional decoding assembly is presented. Analytical and experimental results are given.

Sue, M. K.↗

NASA NTRS1981

A Simulation System for Validating the Analytical Prediction of Performance of the Convolutional Encoded and Symbol Interleaved TDRSS S-band Return Link Service in a Pulsed RFI Environment

A hardware integrated convolutional coding/symbol interleaving and integrated symbol deinterleaving/Viterbi decoding simulation system is described. Validation on the system of the performance of the TDRSS S-band return link with BPSK modulation, operating in a pulsed RFI environment is included. The system consists of three components, the Fast Linkabit Error Rate Tester (FLERT), the Transition Probability Generator (TPG), and a modified LV7017B which includes rate 1/3 capability as well as a periodic interleaver/deinterleaver. Operating and maintenance manuals for each of these units are included.

Source record↗

NASA NTRS1983

NRZ Data Asymmetry Corrector and Convolutional Encoder

Circuit compensates for timing, amplitude and symmetry perturbations. Data asymmetry corrector and convolutional encoder regenerate data and clock signals in spite of signal variations such as data or clock asymmetry, phase errors, and amplitude variations, then encode data for transmission.

Pfiffner, H. J.↗

NASA NTRS1983

VLSI Unit for Two-Dimensional Convolutions

Universal logic structure allows same VLSI chip to be used for variety of computational functions required for two dimensional convolutions. Fast polynomial transform technique is extended into tree computational structure composed of two units: fast polynomial transform (FPT) unit and Chinese remainder theorem (CRT) computational unit.

Liu, K. Y.↗

NASA NTRS1983

Simplified Syndrome Decoding of (n, 1) Convolutional Codes

A new syndrome decoding algorithm for the (n, 1) convolutional codes (CC) that is different and simpler than the previous syndrome decoding algorithm of Schalkwijk and Vinck is presented. The new algorithm uses the general solution of the polynomial linear Diophantine equation for the error polynomial vector E(D). This set of Diophantine solutions is a coset of the CC space. A recursive or Viterbi-like algorithm is developed to find the minimum weight error vector cirumflex E(D) in this error coset. An example illustrating the new decoding algorithm is given for the binary nonsymmetric (2,1)CC.

I. S. Reed↗

NASA NTRS1983

New Syndrome Decoding Techniques for the (n, K) Convolutional Codes

This paper presents a new syndrome decoding algorithm for the (n,k) convolutional codes (CC) which differs completely from an earlier syndrome decoding algorithm of Schalkwijk and Vinck. The new algorithm is based on the general solution of the syndrome equation, a linear Diophantine equation for the error polynomial vector E(D). The set of Diophantine solutions is a coset of the CC. In this error coset a recursive, Viterbi-like algorithm is developed to find the minimum weight error vector (circumflex)E(D). An example, illustrating the new decoding algorithm, is given for the binary nonsystemmatic (3,1)CC.

Reed, I. S.↗

NASA NTRS1983

New syndrome decoder for (n, 1) convolutional codes

The letter presents a new syndrome decoding algorithm for the (n, 1) convolutional codes (CC) that is different and simpler than the previous syndrome decoding algorithm of Schalkwijk and Vinck. The new technique uses the general solution of the polynomial linear Diophantine equation for the error polynomial vector E(D). A recursive, Viterbi-like, algorithm is developed to find the minimum weight error vector E(D). An example is given for the binary nonsystematic (2, 1) CC.

Reed, I. S.↗

NASA NTRS1984

Effects of NRZ-M Modulation on Convolutional Codes Performance

Non-return-to-zero mark (NRZ-M) modulation is often used to resolve data sense in suppressed carrier telemetry systems because such systems are subject to half cycle slips that result in complementing the encoded data stream. The performance of coded telemetry systems with NRZ-M is sensitive to the order in which the various operations are done. A system that demodulates the NRZ-M waveform and then decodes performs differently from a system that does the decoding first. The performance of the NASA standard (7, 1/2) convolutional codes is determined for several systems using NRZ-M. Several different demodulation schemes for NRZ-M are considered. It is shown that, even for the best soft-decision method examined, there is a 2.7 dB loss at a decoded bit error rate of 0.005 if the NRZ-M demodulation occurs before rather than after Viterbi decoding.

Deutsch, L. J.↗

NASA NTRS1984

New Short Constraint Length, Rate 1/N Convolutional Codes which Minimize Required E Sub B/n Sub o for Given Bit Error Rate

Instead of using the criterion of maximum free distance, (df) or the maximum (df) with minimizing a few first distance profiles, short constraint length rate 1/N convolution codes were searched using a criterion of minimizing required bit energy-to-noise density ratio, E(b)/N(o), for a given value of desired bit error rate (BER), for the goodness of a code. The considered channel was binary antipodal signaling over additive white Gaussian noise and no quantization at the channel output. For the BER calculations, the transfer function bounding technique was used. Partial searches were performed using some known facts and a very useful idea that "good codes generate good codes.'' That is, for a given constraint length K, good rate 1/(N + 1) codes can be found by extending the code generator matrices of good rate 1/N codes. The code search results are tabulated for 3 or = K or = 7 and 2 or = N or = 8. For many pairs of K and N, the new codes are shown to save 0.1 to 0.4 dB in the required E(b)/N(o) compared to previously reported codes. Additionally, the benefits of coding bandwidth expansion are confirmed with the new codes.

Lee, P. J.↗

NASA NTRS1984

New syndrome decoding techniques for the (n, k) convolutional codes

This paper presents a new syndrome decoding algorithm for the (n, k) convolutional codes (CC) which differs completely from an earlier syndrome decoding algorithm of Schalkwijk and Vinck. The new algorithm is based on the general solution of the syndrome equation, a linear Diophantine equation for the error polynomial vector E(D). The set of Diophantine solutions is a coset of the CC. In this error coset a recursive, Viterbi-like algorithm is developed to find the minimum weight error vector (circumflex)E(D). An example, illustrating the new decoding algorithm, is given for the binary nonsystemmatic (3, 1)CC. Previously announced in STAR as N83-34964

Reed, I. S.↗

NASA NTRS1984

Tomography by iterative convolution - Empirical study and application to interferometry

An algorithm for computer tomography has been developed that is applicable to reconstruction from data having incomplete projections because an opaque object blocks some of the probing radiation as it passes through the object field. The algorithm is based on iteration between the object domain and the projection (Radon transform) domain. Reconstructions are computed during each iteration by the well-known convolution method. Although it is demonstrated that this algorithm does not converge, an empirically justified criterion for terminating the iteration when the most accurate estimate has been computed is presented. The algorithm has been studied by using it to reconstruct several different object fields with several different opaque regions. It also has been used to reconstruct aerodynamic density fields from interferometric data recorded in wind tunnel tests.

Vest, C. M.↗

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 NTRS1984

Sequential Syndrome Decoding of Convolutional Codes

The algebraic structure of convolutional codes are reviewed and sequential syndrome decoding is applied to those codes. These concepts are then used to realize by example actual sequential decoding, using the stack algorithm. The Fano metric for use in sequential decoding is modified so that it can be utilized to sequentially find the minimum weight error sequence.

Reed, I. S.↗

NASA NTRS1985

Further Results on Rate 1/N Convolutional Code Constructions with Minimum Required SNR Criterion

New good (K, 1/N) convolutional codes for 8 or = to K or = to 13 and 2 or = to N or = to 8 were found and tabulated which require minimum signal-to-noise ratio (SNR) for given desired bit error rates (BER) with Viterbi decoding. The transfer function bound was used for the BER evaluations. These low-rate codes are expected to have a number of applications, especially for systems having large bandwidth-bit time products such as deep space and spread spectrum communication systems.

Lee, P. J.↗

NASA NTRS1985

Symbol Stream Combining in a Convolutionally Coded System

Symbol stream combining has been proposed as a method for arraying signals received at different antennas. If convolutional coding and Viterbi decoding are used, it is shown that a Viterbi decoder based on the proposed weighted sum of symbol streams yields maximum likelihood decisions.

Mceliece, R. J.↗

NASA NTRS1984

Rate 3/4 convolutional coding of 16-PSK - Code design and performance study

Convolutional coding coupled with 16-PSK modulation is investigated for bandwidth efficient transmission. Rate 3/4, small memory codes are found which are optimized in the free-distance sense on the Gaussian channel. These codes provide up to 4.8 dB of coding gain with 32 states over uncoded 8-PSK, a scheme having the same spectral efficiency as the codes described. The performance is compared with earlier findings of Ungerboeck and some recent results on R = 2/3 coded 8-PSK. In addition, results of a channel transmission study to assess the performance of the four-state code on the band-limited nonlinear channel are presented, and it is found that performance of the coded scheme degrades comparably with uncoded 8-PSK, i.e., coding gain is roughly preserved.

Wilson, S. G.↗

NASA NTRS1985

Convolutional coding combined with continuous phase modulation

Background theory and specific coding designs for combined coding/modulation schemes utilizing convolutional codes and continuous-phase modulation (CPM) are presented. In this paper the case of r = 1/2 coding onto a 4-ary CPM is emphasized, with short-constraint length codes presented for continuous-phase FSK, double-raised-cosine, and triple-raised-cosine modulation. Coding buys several decibels of coding gain over the Gaussian channel, with an attendant increase of bandwidth. Performance comparisons in the power-bandwidth tradeoff with other approaches are made.

Pizzi, S. V.↗