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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Method for Veterbi decoding of large constraint length convolutional codes

A new method of Viterbi decoding of convolutional codes lends itself to a pipline VLSI architecture using a single sequential processor to compute the path metrics in the Viterbi trellis. An array method is used to store the path information for NK intervals where N is a number, and K is constraint length. The selected path at the end of each NK interval is then selected from the last entry in the array. A trace-back method is used for returning to the beginning of the selected path back, i.e., to the first time unit of the interval NK to read out the stored branch metrics of the selected path which correspond to the message bits. The decoding decision made in this way is no longer maximum likelihood, but can be almost as good, provided that constraint length K in not too small. The advantage is that for a long message, it is not necessary to provide a large memory to store the trellis derived information until the end of the message to select the path that is to be decoded; the selection is made at the end of every NK time unit, thus decoding a long message in successive blocks.

Hsu, In-Shek↗
NASA NTRS1992

Error control techniques for satellite and space communications

Worked performed during the reporting period is summarized. Construction of robustly good trellis codes for use with sequential decoding was developed. The robustly good trellis codes provide a much better trade off between free distance and distance profile. The unequal error protection capabilities of convolutional codes was studied. The problem of finding good large constraint length, low rate convolutional codes for deep space applications is investigated. A formula for computing the free distance of 1/n convolutional codes was discovered. Double memory (DM) codes, codes with two memory units per unit bit position, were studied; a search for optimal DM codes is being conducted. An algorithm for constructing convolutional codes from a given quasi-cyclic code was developed. Papers based on the above work are included in the appendix.

Costello, Daniel J., Jr.↗
NASA NTRS1994

Error control techniques for satellite and space communications

The unequal error protection capabilities of convolutional and trellis codes are studied. In certain environments, a discrepancy in the amount of error protection placed on different information bits is desirable. Examples of environments which have data of varying importance are a number of speech coding algorithms, packet switched networks, multi-user systems, embedded coding systems, and high definition television. Encoders which provide more than one level of error protection to information bits are called unequal error protection (UEP) codes. In this work, the effective free distance vector, d, is defined as an alternative to the free distance as a primary performance parameter for UEP convolutional and trellis encoders. For a given (n, k), convolutional encoder, G, the effective free distance vector is defined as the k-dimensional vector d = (d(sub 0), d(sub 1), ..., d(sub k-1)), where d(sub j), the j(exp th) effective free distance, is the lowest Hamming weight among all code sequences that are generated by input sequences with at least one '1' in the j(exp th) position. It is shown that, although the free distance for a code is unique to the code and independent of the encoder realization, the effective distance vector is dependent on the encoder realization.

Costello, Daniel J., Jr.↗
NASA NTRS1997

Soft-Decision Decoding of Binary Linear Block Codes Based on an Iterative Search Algorithm

This correspondence presents a suboptimum soft-decision decoding scheme for binary linear block codes based on an iterative search algorithm. The scheme uses an algebraic decoder to iteratively generate a sequence of candidate codewords one at a time using a set of test error patterns that are constructed based on the reliability information of the received symbols. When a candidate codeword is generated, it is tested based on an optimality condition. If it satisfies the optimality condition, then it is the most likely (ML) codeword and the decoding stops. If it fails the optimality test, a search for the ML codeword is conducted in a region which contains the ML codeword. The search region is determined by the current candidate codeword and the reliability of the received symbols. The search is conducted through a purged trellis diagram for the given code using the Viterbi algorithm. If the search fails to find the ML codeword, a new candidate is generated using a new test error pattern, and the optimality test and search are renewed. The process of testing and search continues until either the MEL codeword is found or all the test error patterns are exhausted and the decoding process is terminated. Numerical results show that the proposed decoding scheme achieves either practically optimal performance or a performance only a fraction of a decibel away from the optimal maximum-likelihood decoding with a significant reduction in decoding complexity compared with the Viterbi decoding based on the full trellis diagram of the codes.

Lin, Shu↗
NASA NTRS2009

Hardware Implementation of Serially Concatenated PPM Decoder

A prototype decoder for a serially concatenated pulse position modulation (SCPPM) code has been implemented in a field-programmable gate array (FPGA). At the time of this reporting, this is the first known hardware SCPPM decoder. The SCPPM coding scheme, conceived for free-space optical communications with both deep-space and terrestrial applications in mind, is an improvement of several dB over the conventional Reed-Solomon PPM scheme. The design of the FPGA SCPPM decoder is based on a turbo decoding algorithm that requires relatively low computational complexity while delivering error-rate performance within approximately 1 dB of channel capacity. The SCPPM encoder consists of an outer convolutional encoder, an interleaver, an accumulator, and an inner modulation encoder (more precisely, a mapping of bits to PPM symbols). Each code is describable by a trellis (a finite directed graph). The SCPPM decoder consists of an inner soft-in-soft-out (SISO) module, a de-interleaver, an outer SISO module, and an interleaver connected in a loop (see figure). Each SISO module applies the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm to compute a-posteriori bit log-likelihood ratios (LLRs) from apriori LLRs by traversing the code trellis in forward and backward directions. The SISO modules iteratively refine the LLRs by passing the estimates between one another much like the working of a turbine engine. Extrinsic information (the difference between the a-posteriori and a-priori LLRs) is exchanged rather than the a-posteriori LLRs to minimize undesired feedback. All computations are performed in the logarithmic domain, wherein multiplications are translated into additions, thereby reducing complexity and sensitivity to fixed-point implementation roundoff errors. To lower the required memory for storing channel likelihood data and the amounts of data transfer between the decoder and the receiver, one can discard the majority of channel likelihoods, using only the remainder in operation of the decoder. This is accomplished in the receiver by transmitting only a subset consisting of the likelihoods that correspond to time slots containing the largest numbers of observed photons during each PPM symbol period. The assumed number of observed photons in the remaining time slots is set to the mean of a noise slot. In low background noise, the selection of a small subset in this manner results in only negligible loss. Other features of the decoder design to reduce complexity and increase speed include (1) quantization of metrics in an efficient procedure chosen to incur no more than a small performance loss and (2) the use of the max-star function that allows sum of exponentials to be computed by simple operations that involve only an addition, a subtraction, and a table lookup. Another prominent feature of the design is a provision for access to interleaver and de-interleaver memory in a single clock cycle, eliminating the multiple clock-cycle latency characteristic of prior interleaver and de-interleaver designs.

Moision, Bruce↗
NASA NTRS1996

New Bandwidth Efficient Parallel Concatenated Coding Schemes

We propose a new solution to parallel concatenation of trellis codes with multilevel amplitude/phase modulations and a suitable iterative decoding structure. Examples are given for throughputs 2 bits/sec/Hz with 8PSK and 16QAM signal constellations.

trellis codes multilevel amplitude modulations dec↗
NASA NTRS1972

Thermally stable structural framework

Development of structural framework with zero or negligible thermal expansion is discussed. Combination of two types of metallic materials in binary trellis to compensate for thermal expansion is explained. Construction details are presented and illustration is included.

Schuerch, H. U.↗
NASA NTRS1972

On the structure of rate 1/n convolutional codes.

It is shown what choice there is in assigning output digits to transitions of binary rate 1/n code trellis so that the latter will correspond to a convolutional code. A new upper bound on free distance of rate 1/n convolutional codes is also derived, and the results obtained are used to determine the length of the largest input sequence that can conceivably result in an output whose weight is equal to the free distance of a code of rate 1/2.

Bahl, L.↗
NASA NTRS1974

Convolutional codes. II - Maximum-likelihood decoding. III - Sequential decoding

Maximum-likelihood decoding is characterized as the determination of the shortest path through a topological structure called a trellis. Aspects of code structure are discussed along with questions regarding maximum-likelihood decoding on memoryless channels. A general bounding technique is introduced. The technique is used to obtain asymptotic bounds on the probability of error for maximum-likelihood decoding and list-of-2 decoding. The basic features of sequential algorithms are discussed along with a stack algorithm, questions of computational distribution, and the martingale approach to computational bounds.

Forney, G. D., Jr.↗
NASA NTRS1975

Application of satellite remote-sensing data to land selection and management

A pilot project conducted to demonstrate the utility and economy of satellite data in preparing thematic maps of a wilderness area emphasizing those resources of greatest interest to the potential owner is described. Vegetation maps delineating potential commercial timber and maps of suggested mineral prospecting areas of seven scattered regions were prepared by interpretation of LANDSAT images, coupled with a limited amount of ground truth. Images acquired both in winter and summer seasons were registered to township maps and used in making interpretations of the areal extent of commercial timber potentials. The amount of snow cover visible through the forest canopies was found to be a useful indicator of timber potentials. Identification was made of characteristic topographic features which are typical of flood plain deposits or of the well developed trellis drainage patterns which can indicate the strike of structural grain of underlying Cretaceous sedimentary rocks. The presence of igneous and mixed igneous and metamorphic rocks were indicated by combinations of spectral differences and anomalous interruptions of local radial drainage patterns.

Stringer, W. J.↗
NASA NTRS1980

A generalized formulation of minimum shift keying modulation

The modulator structure consisting of a single-input two-output sequential transducer whose output sequences control the modulated signal in the manner s(t) = x(i)p(t) + y(i)q(t) is considered. Here, iT is less than or equal to t, which is less than iT + T, where T is the modulation bit duration and where x(i) and y(i) take values in /+1, -1, 0/. The behavior of a sequential transducer is characterized by means of a 'trellis'. It is shown that, provided only that the 'carriers' p(t) and q(t) have the same energy in every bit interval, the optimum demodulator for the additive white Gaussian noise channel need process the received signal over only two bit intervals in making each data bit decision. It is demonstrated that particular choices of the sequential transducer yield differential minimum shift keying and differential staggered quadriphase shift keying. Possible generalizations of this approach are discussed.

Massey, J. L.↗
NASA NTRS1982

Quadratic integer programming for large scale banded matrices

This paper is concerned with the integer quadratic program where the variables are constrained to belong to a given set of discrete values. This quadratic integer program is shown to be equivalent to a problem of finding the shortest path in a particular directed graph called a trellis when the matrix is a positive-definite symmetric banded matrix. An efficient procedure for solving this shortest path problem is presented which allows the solution of the integer quadratic program. This method is particularly effective when the half-bandwidth of the matrix is significantly smaller than its dimension.

Yan, T. Y.↗
NASA NTRS1987

Error control coding for satellite and space communications

The optical direct detection channel is discussed. It is shown how simple trellis coded modulation can be used to improve performance or increase throughput (in bits per second) without a bandwidth expansion and no performance loss. In fact, a modest performance gain can be achieved. The concentration is on signals derived from the pulse-position modulation format by allowing overlap.

Georghiades, Costas N.↗
NASA NTRS1987

Soft-decision decoding of some block codes

The performance of certain binary block codes with soft-decision decoding is evaluated by simulation. A construction is proposed to introduce memory on block codes, and simulation results are shown for a trellis code derived from the Nordstrom-Robinson code.

Pollara, F.↗
NASA NTRS1986

Near-toll quality digital speech transmission in the mobile satellite service

This paper discusses system considerations for near-toll quality digital speech transmission in a 5 kHz mobile satellite system channel. Tradeoffs are shown for power performance versus delay for a 4800 bps speech compression system in conjunction with a 16 state rate 2/3 trellis coded 8PSK modulation system. The suggested system has an additional 150 ms of delay beyond the propagation delay and requires an E(b)/N(0) of about 7 dB for a Ricean channel assumption with line-of-sight to diffuse component ratio of 10 assuming ideal synchronization. An additional loss of 2 to 3 dB is expected for synchronization in fading environment.

Townes, S. A.↗
NASA NTRS1987

Bandwidth efficient block codes for M-ary PSK modulation

A class of bandwidth efficient block codes for M-ary PSK modulation is presented. A soft-decision decoding for this class of codes is devised. Some specific short codes for Quad Phase Shift Key (QPSK), 8-PSK and 16-PSK modulations are constructed. These codes have good minimum squared Euclidean distances and provide 2 to 5.8 dB coding gains over uncoded QPSK modulation without (or with little) bandwidth expansion. The complete weight distributions of these specific codes are determined. Based on these weight distributions, their error probabilities are evaluated. Some of these codes have simple trellis structures and hence can be decoded by Viterbi decoding algorithm with relatively simple implementation. Moreover, the codes are very suitable for use as inner codes for various cascaded coding schemes with Reed-Solomon codes as outer codes.

Lin, Shu↗
NASA NTRS1988

A concatenated coded modulation scheme for error control

A concatenated coded modulation scheme for error control in data communications is presented. The scheme is achieved by concatenating a Reed-Solomon outer code and a bandwidth efficient block inner code for M-ary PSK modulation. Error performance of the scheme is analyzed for an AWGN channel. It is shown that extremely high reliability can be attained by using a simple M-ary PSK modulation inner code and relatively powerful Reed-Solomon outer code. Furthermore, if an inner code of high effective rate is used, the bandwidth expansion required by the scheme due to coding will be greatly reduced. The proposed scheme is particularly effective for high speed satellite communication for large file transfer where high reliability is required. Also presented is a simple method for constructing block codes for M-ary PSK modulation. Some short M-ary PSK codes with good minimum squared Euclidean distance are constructed. These codes have trellis structure and hence can be decoded with a soft decision Viterbi decoding algorithm.

Kasami, Tadao↗