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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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NASA NTRS1989

Mixture block coding with progressive transmission in packet video. Appendix 1: Item 2

Video transmission will become an important part of future multimedia communication because of dramatically increasing user demand for video, and rapid evolution of coding algorithm and VLSI technology. Video transmission will be part of the broadband-integrated services digital network (B-ISDN). Asynchronous transfer mode (ATM) is a viable candidate for implementation of B-ISDN due to its inherent flexibility, service independency, and high performance. According to the characteristics of ATM, the information has to be coded into discrete cells which travel independently in the packet switching network. A practical realization of an ATM video codec called Mixture Block Coding with Progressive Transmission (MBCPT) is presented. This variable bit rate coding algorithm shows how a constant quality performance can be obtained according to user demand. Interactions between codec and network are emphasized including packetization, service synchronization, flow control, and error recovery. Finally, some simulation results based on MBCPT coding with error recovery are presented.

Chen, Yun-Chung↗
NASA NTRS1998

Trellises and Trellis-Based Decoding Algorithms for Linear Block Codes: A Recursive Maximum Likelihood Decoding - Part 3

The Viterbi algorithm is indeed a very simple and efficient method of implementing the maximum likelihood decoding. However, if we take advantage of the structural properties in a trellis section, other efficient trellis-based decoding algorithms can be devised. Recently, an efficient trellis-based recursive maximum likelihood decoding (RMLD) algorithm for linear block codes has been proposed. This algorithm is more efficient than the conventional Viterbi algorithm in both computation and hardware requirements. Most importantly, the implementation of this algorithm does not require the construction of the entire code trellis, only some special one-section trellises of relatively small state and branch complexities are needed for constructing path (or branch) metric tables recursively. At the end, there is only one table which contains only the most likely code-word and its metric for a given received sequence r = (r(sub 1), r(sub 2),...,r(sub n)). This algorithm basically uses the divide and conquer strategy. Furthermore, it allows parallel/pipeline processing of received sequences to speed up decoding.

Lin, Shu↗
NASA NTRS1999

Map Algorithms for Decoding Linear Block codes Based on Sectionalized Trellis Diagrams

The MAP algorithm is a trellis-based maximum a posteriori probability decoding algorithm. It is the heart of the turbo (or iterative) decoding which achieves an error performance near the Shannon limit. Unfortunately, the implementation of this algorithm requires large computation and storage. Furthermore, its forward and backward recursions result in long decoding delay. For practical applications, this decoding algorithm must be simplified and its decoding complexity and delay must be reduced. In this paper, the MAP algorithm and its variations, such as Log-MAP and Max-Log-MAP algorithms, are first applied to sectionalized trellises for linear block codes and carried out as two-stage decodings. Using the structural properties of properly sectionalized trellises, the decoding complexity and delay of the MAP algorithms can be reduced. Computation-wise optimum sectionalizations of a trellis for MAP algorithms are investigated. Also presented in this paper are bi-directional and parallel MAP decodings.

Lin, Shu↗
NASA NTRS2000

MAP Algorithms for Decoding Linear Block Codes Based on Sectionalized Trellis Diagrams

The maximum a posteriori probability (MAP) algorithm is a trellis-based MAP decoding algorithm. It is the heart of turbo (or iterative) decoding that achieves an error performance near the Shannon limit. Unfortunately, the implementation of this algorithm requires large computation and storage. Furthermore, its forward and backward recursions result in long decoding delay. For practical applications, this decoding algorithm must be simplified and its decoding complexity and delay must be reduced. In this paper, the MAP algorithm and its variations, such as log-MAP and max-log-MAP algorithms, are first applied to sectionalized trellises for linear block codes and carried out as two-stage decodings. Using the structural properties of properly sectionalized trellises, the decoding complexity and delay of the MAP algorithms can be reduced. Computation-wise optimum sectionalizations of a trellis for MAP algorithms are investigated. Also presented in this paper are bidirectional and parallel MAP decodings.

Lui, Ye↗
NASA NTRS1991

Suboptimum decoding of block codes

This paper investigates a class of decomposable codes, their distance and structural properties. it is shown that this class includes several classes of well known and efficient codes as subclasses. Several methods for constructing decomposable codes or decomposing codes are presented. A two-stage soft decision decoding scheme for decomposable codes, their translates or unions of translates is devised. This two-stage soft-decision decoding is suboptimum, and provides an excellent trade-off between the error performance and decoding complexity for codes of moderate and long block length.

Lin, Shu↗
NASA NTRS1996

Bit Error Probability for Maximum Likelihood Decoding of Linear Block Codes

In this paper, the bit error probability P(sub b) for maximum likelihood decoding of binary linear codes is investigated. The contribution of each information bit to P(sub b) is considered. For randomly generated codes, it is shown that the conventional approximation at high SNR P(sub b) is approximately equal to (d(sub H)/N)P(sub s), where P(sub s) represents the block error probability, holds for systematic encoding only. Also systematic encoding provides the minimum P(sub b) when the inverse mapping corresponding to the generator matrix of the code is used to retrieve the information sequence. The bit error performances corresponding to other generator matrix forms are also evaluated. Although derived for codes with a generator matrix randomly generated, these results are shown to provide good approximations for codes used in practice. Finally, for decoding methods which require a generator matrix with a particular structure such as trellis decoding or algebraic-based soft decision decoding, equivalent schemes that reduce the bit error probability are discussed.

Lin, Shu↗
NASA NTRS1972

Burst decoding of binary block codes on Q-ary output channels.

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.

Wainberg, S.↗
NASA NTRS1973

Algebraic decoding of block codes over a q-ary input, Q-ary output channel, Q greater than q.

Decoding algorithms designed for one output alphabet are shown to be effectively usable for channels with a different output alphabet. The described technique that makes this possible can be used in conjunction with an arbitrary distance measure between input and output vectors. Thus, Hamming distance, Lee distance, or a burst distance can be assumed. Examples are presented for each of these distances.

Wainberg, S.↗
NASA NTRS1979

Approximate maximum likelihood decoding of block codes

Approximate maximum likelihood decoding algorithms, based upon selecting a small set of candidate code words with the aid of the estimated probability of error of each received symbol, can give performance close to optimum with a reasonable amount of computation. By combining the best features of various algorithms and taking care to perform each step as efficiently as possible, a decoding scheme was developed which can decode codes which have better performance than those presently in use and yet not require an unreasonable amount of computation. The discussion of the details and tradeoffs of presently known efficient optimum and near optimum decoding algorithms leads, naturally, to the one which embodies the best features of all of them.

Greenberger, H. J.↗
NASA NTRS1994

Convolutional encoding of self-dual block codes (2)

Solomon and van Tilborg have developed convolutional encoding algorithms for quadratic residue (QR) codes of lengths 47 and beyond. For these codes and reasonable constraint lengths, there are sequential 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 (48, 24; 12) QR code was lower to K = 8 by Solomon. In our search for the smallest possible constraint lengths K for (80, 40; 16) self-dual quadratic residue and nonquadratic residue codes, we have found the constraint lengths K = 14 and K = 13, respectively. We have discovered a K = 21 convolutional encoding for the (104, 52; 20) QR code; there may be a smaller K for a (104, 52; 20) self-dual code that is not a quadratic residue code. The smaller the K, the less complex the sequential or Viterbi decoder.

Solomon, G.↗
NASA NTRS1997

Complementary Reliability-Based Decodings of Binary Linear Block Codes

This correspondence presents a hybrid reliability-based decoding algorithm which combines the reprocessing method based on the most reliable basis and a generalized Chase-type algebraic decoder based on the least reliable positions. It is shown that reprocessing with a simple additional algebraic decoding effort achieves significant coding gain. For long codes, the order of reprocessing required to achieve asymptotic optimum error performance is reduced by approximately 1/3. This significantly reduces the computational complexity, especially for long codes. Also, a more efficient criterion for stopping the decoding process is derived based on the knowledge of the algebraic decoding solution.

Fossorier, Marc P. C.↗