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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1998

Trellises and Trellis-Based Decoding Algorithms for Linear Block Codes: The Map and Related Decoding Algirithms - Part 3

In a coded communication system with equiprobable signaling, MLD minimizes the word error probability and delivers the most likely codeword associated with the corresponding received sequence. This decoding has two drawbacks. First, minimization of the word error probability is not equivalent to minimization of the bit error probability. Therefore, MLD becomes suboptimum with respect to the bit error probability. Second, MLD delivers a hard-decision estimate of the received sequence, so that information is lost between the input and output of the ML decoder. This information is important in coded schemes where the decoded sequence is further processed, such as concatenated coding schemes, multi-stage and iterative decoding schemes. In this chapter, we first present a decoding algorithm which both minimizes bit error probability, and provides the corresponding soft information at the output of the decoder. This algorithm is referred to as the MAP (maximum aposteriori probability) decoding algorithm.

Lin, Shu↗
NASA NTRS1990

Cross-over component code construction for multi-level block modulation codes

This paper investigates the multilevel technique for combining block coding and modulation. Several specific methods for constructing multilevel block modulation codes with interdependency among component codes are presented. Given a multilevel block modulation code C with no interdependency among the binary component codes, the proposed methods give a multilevel block modulation code C-prime which has the same rate as C, a minimum squared Euclidean distance not less than that of C, a trellis diagram with the same number of states as that of C, and a smaller number of nearest neighbor codewords than that of C.

Kasami, Tadao↗
NASA NTRS1995

Joint Synchronization Of Viterbi And Reed-Solomon Decoders

Synchronization times reduced to reduce loss of data. Scheme for decoding received doubly encoded binary-data signal provides for joint synchronization of two decoders. Applies to concatenated error-correcting channel coding communication system in which, at transmitter, data first encoded by interleaved Reed-Solomon code (block code), then by convolutional code.

Statman, Joseph I.↗
NASA NTRS1996

Multilevel Concatenated Block Modulation Codes for the Frequency Non-selective Rayleigh Fading Channel

This paper is concerned with construction of multilevel concatenated block modulation codes using a multi-level concatenation scheme for the frequency non-selective Rayleigh fading channel. In the construction of multilevel concatenated modulation code, block modulation codes are used as the inner codes. Various types of codes (block or convolutional, binary or nonbinary) are being considered as the outer codes. In particular, we focus on the special case for which Reed-Solomon (RS) codes are used as the outer codes. For this special case, a systematic algebraic technique for constructing q-level concatenated block modulation codes is proposed. Codes have been constructed for certain specific values of q and compared with the single-level concatenated block modulation codes using the same inner codes. A multilevel closest coset decoding scheme for these codes is proposed.

Lin, Shu↗
NASA NTRS1972

Multispectral data compression through transform coding and block quantization

Transform coding and block quantization techniques are applied to multispectral aircraft scanner data, and digitized satellite imagery. The multispectral source is defined and an appropriate mathematical model proposed. The Karhunen-Loeve, Fourier, and Hadamard encoders are considered and are compared to the rate distortion function for the equivalent Gaussian source and to the performance of the single sample PCM encoder.

Ready, P. J.↗
NASA NTRS1989

Multi-level bandwidth efficient block modulation codes

The multilevel technique is investigated for combining block coding and modulation. There are four parts. In the first part, a formulation is presented for signal sets on which modulation codes are to be constructed. Distance measures on a signal set are defined and their properties are developed. In the second part, a general formulation is presented for multilevel modulation codes in terms of component codes with appropriate Euclidean distances. The distance properties, Euclidean weight distribution and linear structure of multilevel modulation codes are investigated. In the third part, several specific methods for constructing multilevel block modulation codes with interdependency among component codes are proposed. Given a multilevel block modulation code C with no interdependency among the binary component codes, the proposed methods give a multilevel block modulation code C which has the same rate as C, a minimum squared Euclidean distance not less than that of code C, a trellis diagram with the same number of states as that of C and a smaller number of nearest neighbor codewords than that of C. In the last part, error performance of block modulation codes is analyzed for an AWGN channel based on soft-decision maximum likelihood decoding. Error probabilities of some specific codes are evaluated based on their Euclidean weight distributions and simulation results.

Lin, Shu↗
NASA NTRS1991

On multilevel block modulation codes

The multilevel (ML) technique for combining block coding and modulation is investigated. A general formulation is presented for ML modulation codes in terms of component codes with appropriate distance measures. A specific method for constructing ML block modulation codes (MLBMCs) with interdependency among component codes is proposed. Given an MLBMC C with no interdependency among the binary component codes, the proposed method gives an MLBC C-prime that has the same rate as C, a minimum squared Euclidean distance not less than that of C, a trellis diagram with the same number of states as that of C, and a smaller number of nearest-neighbor codewords than that of C. Finally, a technique is presented for analyzing the error performance of MLBMCs for an additive white Gaussian noise channel based on soft-decision maximum-likelihood decoding.

Kasami, Tadao↗
NASA NTRS1989

The weight distribution and randomness of linear codes

Finding the weight distributions of block codes is a problem of theoretical and practical interest. Yet the weight distributions of most block codes are still unknown except for a few classes of block codes. Here, by using the inclusion and exclusion principle, an explicit formula is derived which enumerates the complete weight distribution of an (n,k,d) linear code using a partially known weight distribution. This expression is analogous to the Pless power-moment identities - a system of equations relating the weight distribution of a linear code to the weight distribution of its dual code. Also, an approximate formula for the weight distribution of most linear (n,k,d) codes is derived. It is shown that for a given linear (n,k,d) code over GF(q), the ratio of the number of codewords of weight u to the number of words of weight u approaches the constant Q = q(-)(n-k) as u becomes large. A relationship between the randomness of a linear block code and the minimum distance of its dual code is given, and it is shown that most linear block codes with rigid algebraic and combinatorial structure also display certain random properties which make them similar to random codes with no structure at all.

Cheung, K.-M.↗
NASA NTRS1999

Investigation of Near Shannon Limit Coding Schemes

Turbo codes can deliver performance that is very close to the Shannon limit. This report investigates algorithms for convolutional turbo codes and block turbo codes. Both coding schemes can achieve performance near Shannon limit. The performance of the schemes is obtained using computer simulations. There are three sections in this report. First section is the introduction. The fundamental knowledge about coding, block coding and convolutional coding is discussed. In the second section, the basic concepts of convolutional turbo codes are introduced and the performance of turbo codes, especially high rate turbo codes, is provided from the simulation results. After introducing all the parameters that help turbo codes achieve such a good performance, it is concluded that output weight distribution should be the main consideration in designing turbo codes. Based on the output weight distribution, the performance bounds for turbo codes are given. Then, the relationships between the output weight distribution and the factors like generator polynomial, interleaver and puncturing pattern are examined. The criterion for the best selection of system components is provided. The puncturing pattern algorithm is discussed in detail. Different puncturing patterns are compared for each high rate. For most of the high rate codes, the puncturing pattern does not show any significant effect on the code performance if pseudo - random interleaver is used in the system. For some special rate codes with poor performance, an alternative puncturing algorithm is designed which restores their performance close to the Shannon limit. Finally, in section three, for iterative decoding of block codes, the method of building trellis for block codes, the structure of the iterative decoding system and the calculation of extrinsic values are discussed.

Kwatra, S. C.↗
DOE OSTI2023

Graphics processor unit with opportunistic inter-path reconvergence

A graphics processing unit and methods for comping and executing instructions with opportunistic inter-path reconvergence are provided. A graphics processing unit may access computer executable instructions mapped to code blocks of a control flow for a warp. The code blocks may include an immediate dominator block and an intermediate post dominator block. The graphics processing unit may store a first thread mask associated with the first code block. The first thread mask may include a plurality of bits indicative of the active or non-active status for the threads of the warp, respectively. The graphics processing unit may a second thread mask corresponding to an intermediate code block between the immediate dominator block and intermediate post dominator block. The graphics processing unit may execute, with threads indicated as active by the first thread mask, instructions of the intermediate code block with a first operand or a second operand depending on the second thread mask.

Kulkarni, Milind↗
NASA NTRS1991

Multi-stage decoding for multi-level block modulation codes

Various types of multistage decoding for multilevel block modulation codes, in which the decoding of a component code at each stage can be either soft decision or hard decision, maximum likelihood or bounded distance are discussed. Error performance for codes is analyzed for a memoryless additive channel based on various types of multi-stage decoding, and upper bounds on the probability of an incorrect decoding are derived. It was found that, if component codes of a multi-level modulation code and types of decoding at various stages are chosen properly, high spectral efficiency and large coding gain can be achieved with reduced decoding complexity. It was found that the difference in performance between the suboptimum multi-stage soft decision maximum likelihood decoding of a modulation code and the single stage optimum decoding of the overall code is very small, only a fraction of dB loss in SNR at the probability of an incorrect decoding for a block of 10(exp -6). Multi-stage decoding of multi-level modulation codes really offers a way to achieve the best of three worlds, bandwidth efficiency, coding gain, and decoding complexity.

Lin, Shu↗
NASA NTRS2008

JPEG 2000 Encoding with Perceptual Distortion Control

An alternative approach has been devised for encoding image data in compliance with JPEG 2000, the most recent still-image data-compression standard of the Joint Photographic Experts Group. Heretofore, JPEG 2000 encoding has been implemented by several related schemes classified as rate-based distortion-minimization encoding. In each of these schemes, the end user specifies a desired bit rate and the encoding algorithm strives to attain that rate while minimizing a mean squared error (MSE). While rate-based distortion minimization is appropriate for transmitting data over a limited-bandwidth channel, it is not the best approach for applications in which the perceptual quality of reconstructed images is a major consideration. A better approach for such applications is the present alternative one, denoted perceptual distortion control, in which the encoding algorithm strives to compress data to the lowest bit rate that yields at least a specified level of perceptual image quality. Some additional background information on JPEG 2000 is prerequisite to a meaningful summary of JPEG encoding with perceptual distortion control. The JPEG 2000 encoding process includes two subprocesses known as tier-1 and tier-2 coding. In order to minimize the MSE for the desired bit rate, a rate-distortion- optimization subprocess is introduced between the tier-1 and tier-2 subprocesses. In tier-1 coding, each coding block is independently bit-plane coded from the most-significant-bit (MSB) plane to the least-significant-bit (LSB) plane, using three coding passes (except for the MSB plane, which is coded using only one "clean up" coding pass). For M bit planes, this subprocess involves a total number of (3M - 2) coding passes. An embedded bit stream is then generated for each coding block. Information on the reduction in distortion and the increase in the bit rate associated with each coding pass is collected. This information is then used in a rate-control procedure to determine the contribution of each coding block to the output compressed bit stream.

Watson, Andrew B.↗
NASA NTRS1994

Convolutional Encoding of Self-Dual Codes

Self-dual block codes of rate 1/2 are constructed here, The codes are of length 8m with weights w, w = 0 mod 4. The codes have a convolutional portion of length 8m-2 and non-systematic information length 4m-1.

self↗
NASA NTRS1994

Convolutional encoding of self-dual codes

There exist almost complete convolutional encodings of self-dual codes, i.e., block codes of rate 1/2 with weights w, w = 0 mod 4. The codes are of length 8m with the convolutional portion of length 8m-2 and the nonsystematic information of length 4m-1. The last two bits are parity checks on the two (4m-1) length parity sequences. The final information bit complements one of the extended parity sequences of length 4m. Solomon and van Tilborg have developed algorithms to generate these for the Quadratic Residue (QR) Codes of lengths 48 and beyond. For these codes and reasonable constraint lengths, there are sequential decodings for both hard and soft decisions. There are also possible Viterbi-type decodings that may be simple, as in a convolutional encoding/decoding of the extended Golay Code. In addition, the previously found constraint length K = 9 for the QR (48, 24;12) Code is lowered here to K = 8.

Solomon, G.↗
NASA NTRS1994

A Planar Approximation for the Least Reliable Bit Log-likelihood Ratio of 8-PSK Modulation

The optimum decoding of component codes in block coded modulation (BCM) schemes requires the use of the log-likelihood ratio (LLR) as the signal metric. An approximation to the LLR for the least reliable bit (LRB) in an 8-PSK modulation based on planar equations with fixed point arithmetic is developed that is both accurate and easily realizable for practical BCM schemes. Through an error power analysis and an example simulation it is shown that the approximation results in 0.06 dB in degradation over the exact expression at an E(sub s)/N(sub o) of 10 dB. It is also shown that the approximation can be realized in combinatorial logic using roughly 7300 transistors. This compares favorably to a look up table approach in typical systems.

Thesling, William H.↗
NASA NTRS1992

Least reliable bits coding (LRBC) for high data rate satellite communications

LRBC, a bandwidth efficient multilevel/multistage block-coded modulation technique, is analyzed. LRBC uses simple multilevel component codes that provide increased error protection on increasingly unreliable modulated bits in order to maintain an overall high code rate that increases spectral efficiency. Soft-decision multistage decoding is used to make decisions on unprotected bits through corrections made on more protected bits. Analytical expressions and tight performance bounds are used to show that LRBC can achieve increased spectral efficiency and maintain equivalent or better power efficiency compared to that of BPSK. The relative simplicity of Galois field algebra vs the Viterbi algorithm and the availability of high-speed commercial VLSI for block codes indicates that LRBC using block codes is a desirable method for high data rate implementations.

Vanderaar, Mark↗
NASA NTRS1991

Multi-stage decoding for multi-level block modulation codes

In this paper, we investigate various types of multi-stage decoding for multi-level block modulation codes, in which the decoding of a component code at each stage can be either soft-decision or hard-decision, maximum likelihood or bounded-distance. Error performance of codes is analyzed for a memoryless additive channel based on various types of multi-stage decoding, and upper bounds on the probability of an incorrect decoding are derived. Based on our study and computation results, we find that, if component codes of a multi-level modulation code and types of decoding at various stages are chosen properly, high spectral efficiency and large coding gain can be achieved with reduced decoding complexity. In particular, we find that the difference in performance between the suboptimum multi-stage soft-decision maximum likelihood decoding of a modulation code and the single-stage optimum decoding of the overall code is very small: only a fraction of dB loss in SNR at the probability of an incorrect decoding for a block of 10(exp -6). Multi-stage decoding of multi-level modulation codes really offers a way to achieve the best of three worlds, bandwidth efficiency, coding gain, and decoding complexity.

Lin, Shu↗