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At least 217 records · Page 12

Simplified Decoding of Convolutional Codes

Some complicated intermediate steps shortened or eliminated. Decoding of convolutional error-correcting digital codes simplified by new errortrellis syndrome technique. In new technique, syndrome vector not computed. Instead, advantage taken of newly-derived mathematical identities simplify decision tree, folding it back on itself into form called "error trellis." This trellis graph of all path solutions of syndrome equations. Each path through trellis corresponds to specific set of decisions as to received digits. Existing decoding algorithms combined with new mathematical identities reduce number of combinations of errors considered and enable computation of correction vector directly from data and check bits as received.

Truong, T. K.

Decoding convolutionally encoded images

Maximum Likelihood Convolutional Decoding, which is used by the Deep Space Network for short constraint-length convolutional codes, assumes that all strings of information bits are equally likely. In some cases, like image data, this is not the case. The use of information about an adjacent pixel in decoding convolutionally encoded Voyager images is examined. It is discovered that, in a region of interest, as much as 2 dB may be gained.

Pitt, G. H., III

Image statistics decoding for convolutional codes

It is a fact that adjacent pixels in a Voyager image are very similar in grey level. This fact can be used in conjunction with the Maximum-Likelihood Convolutional Decoder (MCD) to decrease the error rate when decoding a picture from Voyager. Implementing this idea would require no changes in the Voyager spacecraft and could be used as a backup to the current system without too much expenditure, so the feasibility of it and the possible gains for Voyager were investigated. Simulations have shown that the gain could be as much as 2 dB at certain error rates, and experiments with real data inspired new ideas on ways to get the most information possible out of the received symbol stream.

Pitt, G. H., III

Single-Chip VLSI Reed-Solomon Decoder

Efficient utilization of computing elements reduces size while preserving throughput. VLSI architecture is pipeline Reed-Solomon decoder for correction of errors and erasures. Uses transform circuit to compute syndrome polynomial. Erasure information enters decoder as binary sequence. Applied to variety of digital communications involving error-correcting RS codes.

Shao, Howard M.

On the VLSI design of a pipeline Reed-Solomon decoder using systolic arrays

A new very large scale integration (VLSI) design of a pipeline Reed-Solomon decoder is presented. The transform decoding technique used in a previous article is replaced by a time domain algorithm through a detailed comparison of their VLSI implementations. A new architecture that implements the time domain algorithm permits efficient pipeline processing with reduced circuitry. Erasure correction capability is also incorporated with little additional complexity. By using a multiplexing technique, a new implementation of Euclid's algorithm maintains the throughput rate with less circuitry. Such improvements result in both enhanced capability and significant reduction in silicon area.

Shao, H. M.

A lower bound for the decoder error probability of the linear MDS code

A lower bound for the decoder error probability (P sub E (u)) of a linear maximum distance separable (MDS) code is derived by counting the dominant types of decoding words around code words. It is shown that the lower bound derived is similar in form, and close numerically, to the upper bound derived.

Cheung, K.-M.

A software simulation study of the long constraint length VLSI Viterbi decoder

A software simulation of long constraint length Viterbi decoders was developed. This software closely follows the hardware architecture that was chosen for the Very Large Scale Integration implementation. The program is used to validate the design of the decoder and to generate test vectors for the VLSI circuits.

Arnold, S.

Decoding of 1/2-rate (24,12) Golay codes

A decoding method for a (23,12) Golay code is extended to the important 1/2-rate (24,12) Golay code so that three errors can be corrected and four errors can be detected. It is shown that the method can be extended to any decoding method which can correct three errors in the (23,12) Golay code.

Truong, T.-K.

On the VLSI design of a pipeline Reed-Solomon decoder using systolic arrays

A new very large scale integration (VLSI) design of a pipeline Reed-Solomon decoder is presented. The transform decoding technique used in a previous article is replaced by a time domain algorithm through a detailed comparison of their VLSI implementations. A new architecture that implements the time domain algorithm permits efficient pipeline processing with reduced circuitry. Erasure correction capability is also incorporated with little additional complexity. By using multiplexing technique, a new implementation of Euclid's algorithm maintains the throughput rate with less circuitry. Such improvements result in both enhanced capability and significant reduction in silicon area.

Shao, Howard M.

Multi-level trellis coded modulation and multi-stage decoding

Several constructions for multi-level trellis codes are presented and many codes with better performance than previously known codes are found. These codes provide a flexible trade-off between coding gain, decoding complexity, and decoding delay. New multi-level trellis coded modulation schemes using generalized set partitioning methods are developed for Quadrature Amplitude Modulation (QAM) and Phase Shift Keying (PSK) signal sets. New rotationally invariant multi-level trellis codes which can be combined with differential encoding to resolve phase ambiguity are presented.

Costello, Daniel J., Jr.

A hybrid M-algorithm/sequential decoder for convolutional and trellis codes

The Viterbi Algorithm (VA) is optimum in the sense of being maximum likelihood for decoding codes with a trellis structure. However, since the VA is in fact an exhaustive search of the code trellis, the complexity of the VA grows exponentially with the constraint length upsilon. This limits its application to codes with small values of upsilon and relatively modest coding gains. The M-Algorithm (MA) is a limited search scheme which carries forward M paths in the trellis, all of the same length. All successors of the M paths are extended at the next trellis depth, and all but the best M of these are dropped. Since a limited search convolutional decoder will flounder indefinitely if one of the paths in storage is not the correct one, the data are usually transmitted in blocks. It has been shown that the performance of the MA approaches the VA at high signal to noise ratios (SNR's) with an M which is far less than the 2 sup upsilon states in the full trellis. Thus the MA can be used with larger values of upsilon, making larger coding gains possible at high SNR's. However, it still requires a relatively large fixed computational effort to achieve good performance.

Wang, Fu-Quan

Study of a co-designed decision feedback equalizer, deinterleaver, and decoder

A technique that promises better quality data from band limited channels at lower received power in digital transmission systems is presented. Data transmission, in such systems often suffers from intersymbol interference (ISI) and noise. Two separate techniques, channel coding and equalization, have caused considerable advances in the state of communication systems and both concern themselves with removing the undesired effects of a communication channel. Equalizers mitigate the ISI whereas coding schemes are used to incorporate error-correction. In the past, most of the research in these two areas has been carried out separately. However, the individual techniques have strengths and weaknesses that are complementary in many applications: an integrated approach realizes gains in excess to that of a simple juxtaposition. Coding schemes have been successfully used in cascade with linear equalizers which in the absence of ISI provide excellent performance. However, when both ISI and the noise level are relatively high, nonlinear receivers like the decision feedback equalizer (DFE) perform better. The DFE has its drawbacks: it suffers from error propagation. The technique presented here takes advantage of interleaving to integrate the two approaches so that the error propagation in DFE can be reduced with the help of error correction provided by the decoder. The results of simulations carried out for both, binary, and non-binary, channels confirm that significant gain can be obtained by codesigning equalizer and decoder. Although, systems with time-invariant channels and simple DFE having linear filters were looked into, the technique is fairly general and can easily be modified for more sophisticated equalizers to obtain even larger gains.

Peile, Robert E.

VLSI architecture for a Reed-Solomon decoder

A basic single-chip building block for a Reed-Solomon (RS) decoder system is partitioned into a plurality of sections, the first of which consists of a plurality of syndrome subcells each of which contains identical standard-basis finite-field multipliers that are programmable between 10 and 8 bit operation. A desired number of basic building blocks may be assembled to provide a RS decoder of any syndrome subcell size that is programmable between 10 and 8 bit operation.

Hsu, In-Shek

A VLSI design for a trace-back Viterbi decoder

A systolic Viterbi decoder for convolutional codes is developed which uses the trace-back method to reduce the amount of data needed to be stored in registers. It is shown that this new algorithm requires a smaller chip size and achieves a faster decoding time than other existing methods.

Truong, T. K.

On the decoder error probability of block codes

By using coding and combinational techniques, an explicit formula is derived which enumerates the complete weight distribution of decodable words of block codes using partially known weight distributions. Also an approximation formula for nonbinary block codes is obtained. These results in turn give exact and approximate expressions for the decoder error probability PE(u) of block codes.

Cheung, Kar-Ming

The algebraic decoding of the (41, 21, 9) quadratic residue code

A new algebraic approach for decoding the quadratic residue (QR) codes, in particular the (41, 21, 9) QR code is presented. The key ideas behind this decoding technique are a systematic application of the Sylvester resultant method to the Newton identities associated with the code syndromes to find the error-locator polynomial, and next a method for determining error locations by solving certain quadratic, cubic and quartic equations over GF(2 exp m) in a new way which uses Zech's logarithms for the arithmetic. The algorithms developed here are suitable for implementation in a programmable microprocessor or special-purpose VLSI chip. It is expected that the algebraic methods developed here can apply generally to other codes such as the BCH and Reed-Solomon codes.

Reed, Irving S.

Add/Compare/Select Circuit For Rapid Decoding

Prototype decoding system operates at 200 Mb/s. ACS (add/compare/select) gate array is highly integrated emitter-coupled-logic circuit implementing arithmetic operations essential to Viterbi decoding of convolutionally encoded data signals. Principal advantage of circuit is speed. Operates as single unit performing eight additions and finds minimum of eight sums, or operates as two independent units, each performing four additions and finding minimum of four sums. Flexibility enables application to variety of different codes. Includes built-in self-testing circuitry, enabling unit to be tested at full speed with help of only simple test fixture.

Budinger, James M.

Soft decoding a self-dual (48, 24; 12) code

A self-dual (48,24;12) code comes from restricting a binary cyclic (63,18;36) code to a 6 x 7 matrix, adding an eighth all-zero column, and then adjoining six dimensions to this extended 6 x 8 matrix. These six dimensions are generated by linear combinations of row permutations of a 6 x 8 matrix of weight 12, whose sums of rows and columns add to one. A soft decoding using these properties and approximating maximum likelihood is presented here. This is preliminary to a possible soft decoding of the box (72,36;15) code that promises a 7.7-dB theoretical coding under maximum likelihood.

Solomon, G.