Strengthened lower bound on definite decoding minimum distance for periodic convolutional codes
Binary periodic convolutional codes with lower bound everywhere stronger than Wagner on definite decoding minimum distance
Costello, D. J., Jr.↗
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Results for “minimum decoding”
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Generalized minimum distance decoding.
Generalized minimum distance decoding that permits likelihood information to be used, yielding same probability of error as maximum likelihood decoding
DISTANCE MEASURING EQUIPMENT↗
Some algebraic and distance properties of convolutional codes.
Upper and lower bounds for feedback decoding and definite decoding minimum distances of binary convolutional codes
Massey, J. L.↗
Free distance bounds for convolutional codes
The best asymptotic bounds presently known on free distance for convolutional codes are presented from a unified point of view. Upper and lower bounds for both time-varying and fixed codes are obtained. A comparison is made between bounds for nonsystematic and systematic codes which shows that more free distance is available with nonsystematic codes. This result is important when selecting codes for use with sequential or maximum-likelihood (Viterbi) decoding since the probability of decoding error is closely related to the free distance of the code. An ancillary result, used in proving the lower bound on free distance for time-varying nonsystematic codes, furnishes a generalization of two earlier bounds on the definite decoding minimum distance of convolutional codes.
Costello, D. J., Jr.↗
Rate-Compatible Protograph LDPC Codes
Digital communication coding methods resulting in rate-compatible low density parity-check (LDPC) codes built from protographs. Described digital coding methods start with a desired code rate and a selection of the numbers of variable nodes and check nodes to be used in the protograph. Constraints are set to satisfy a linear minimum distance growth property for the protograph. All possible edges in the graph are searched for the minimum iterative decoding threshold and the protograph with the lowest iterative decoding threshold is selected. Protographs designed in this manner are used in decode and forward relay channels.
Nguyen, Thuy V.↗
Variable-length codes and the Fano metric.
It is shown that the metric proposed originally by Fano for sequential decoding is precisely the required statistic for minimum-error-probability decoding of variable-length codes. The analysis shows further that the 'natural' choice of bias in the metric is the code rate and gives insight into why the Fano metric has proved to be the best practical choice in sequential decoding. The recently devised Jelinek-Zigangirov 'stack algorithm' is shown to be a natural consequence of this interpretation of the Fano metric. Finally, it is shown that the elimination of the bias in the 'truncated' portion of the code tree gives a slight reduction in average computation at the sacrifice of increased error probability.
Massey, J. L.↗
Construction of Protograph LDPC Codes with Linear Minimum Distance
A construction method for protograph-based LDPC codes that simultaneously achieve low iterative decoding threshold and linear minimum distance is proposed. We start with a high-rate protograph LDPC code with variable node degrees of at least 3. Lower rate codes are obtained by splitting check nodes and connecting them by degree-2 nodes. This guarantees the linear minimum distance property for the lower-rate codes. Excluding checks connected to degree-1 nodes, we show that the number of degree-2 nodes should be at most one less than the number of checks for the protograph LDPC code to have linear minimum distance. Iterative decoding thresholds are obtained by using the reciprocal channel approximation. Thresholds are lowered by using either precoding or at least one very high-degree node in the base protograph. A family of high- to low-rate codes with minimum distance linearly increasing in block size and with capacity-approaching performance thresholds is presented. FPGA simulation results for a few example codes show that the proposed codes perform as predicted.
Low-density parity-check (LDPC)↗
Rate-Compatible LDPC Codes with Linear Minimum Distance
A recently developed method of constructing protograph-based low-density parity-check (LDPC) codes provides for low iterative decoding thresholds and minimum distances proportional to block sizes, and can be used for various code rates. A code constructed by this method can have either fixed input block size or fixed output block size and, in either case, provides rate compatibility. The method comprises two submethods: one for fixed input block size and one for fixed output block size. The first mentioned submethod is useful for applications in which there are requirements for rate-compatible codes that have fixed input block sizes. These are codes in which only the numbers of parity bits are allowed to vary. The fixed-output-blocksize submethod is useful for applications in which framing constraints are imposed on the physical layers of affected communication systems. An example of such a system is one that conforms to one of many new wireless-communication standards that involve the use of orthogonal frequency-division modulation
Divsalar, Dariush↗
Investigation of the Use of Erasures in a Concatenated Coding Scheme
A new method for declaring erasures in a concatenated coding scheme is investigated. This method is used with the rate 1/2 K = 7 convolutional code and the (255, 223) Reed Solomon code. Errors and erasures Reed Solomon decoding is used. The erasure method proposed uses a soft output Viterbi algorithm and information provided by decoded Reed Solomon codewords in a deinterleaving frame. The results show that a gain of 0.3 dB is possible using a minimum amount of decoding trials.
Kwatra, S. C.↗
Language Model Combination and Adaptation Using Weighted Finite State Transducers
In speech recognition systems language model (LMs) are often constructed by training and combining multiple n-gram models. They can be either used to represent different genres or tasks found in diverse text sources, or capture stochastic properties of different linguistic symbol sequences, for example, syllables and words. Unsupervised LM adaption may also be used to further improve robustness to varying styles or tasks. When using these techniques, extensive software changes are often required. In this paper an alternative and more general approach based on weighted finite state transducers (WFSTs) is investigated for LM combination and adaptation. As it is entirely based on well-defined WFST operations, minimum change to decoding tools is needed. A wide range of LM combination configurations can be flexibly supported. An efficient on-the-fly WFST decoding algorithm is also proposed. Significant error rate gains of 7.3% relative were obtained on a state-of-the-art broadcast audio recognition task using a history dependently adapted multi-level LM modelling both syllable and word sequences
Liu, X.↗
An Iterative Soft-Decision Decoding Algorithm
This paper presents a new minimum-weight trellis-based soft-decision iterative decoding algorithm for binary linear block codes. Simulation results for the RM(64,22), EBCH(64,24), RM(64,42) and EBCH(64,45) codes show that the proposed decoding algorithm achieves practically (or near) optimal error performance with significant reduction in decoding computational complexity. The average number of search iterations is also small even for low signal-to-noise ratio.
Lin, Shu↗
An iterative algorithm for decoding block codes transmitted over a memoryless channel
An algorithm was developed which optimally decodes a block code for minimum probability of symbol error in an iterative manner. The initial estimate is made by looking at each bit independently and is improved by considering bits related to it through the parity check equations. The dependent bits are considered in order of interesting probability of error. Since the computation proceeds in a systematic way with the bits having the greatest effect being used first, the algorithm approaches the optimum estimate after only a fraction of the parity check equations were used.
Greenberger, H. J.↗
Soft-decision decoding techniques for linear block codes and their error performance analysis
The first paper presents a new minimum-weight trellis-based soft-decision iterative decoding algorithm for binary linear block codes. The second paper derives an upper bound on the probability of block error for multilevel concatenated codes (MLCC). The bound evaluates difference in performance for different decompositions of some codes. The third paper investigates the bit error probability code for maximum likelihood decoding of binary linear codes. The fourth and final paper included in this report is concerns itself with the construction of multilevel concatenated block modulation codes using a multilevel concatenation scheme for the frequency non-selective Rayleigh fading channel.
Lin, Shu↗
LDPC Codes with Minimum Distance Proportional to Block Size
Low-density parity-check (LDPC) codes characterized by minimum Hamming distances proportional to block sizes have been demonstrated. Like the codes mentioned in the immediately preceding article, the present codes are error-correcting codes suitable for use in a variety of wireless data-communication systems that include noisy channels. The previously mentioned codes have low decoding thresholds and reasonably low error floors. However, the minimum Hamming distances of those codes do not grow linearly with code-block sizes. Codes that have this minimum-distance property exhibit very low error floors. Examples of such codes include regular LDPC codes with variable degrees of at least 3. Unfortunately, the decoding thresholds of regular LDPC codes are high. Hence, there is a need for LDPC codes characterized by both low decoding thresholds and, in order to obtain acceptably low error floors, minimum Hamming distances that are proportional to code-block sizes. The present codes were developed to satisfy this need. The minimum Hamming distances of the present codes have been shown, through consideration of ensemble-average weight enumerators, to be proportional to code block sizes. As in the cases of irregular ensembles, the properties of these codes are sensitive to the proportion of degree-2 variable nodes. A code having too few such nodes tends to have an iterative decoding threshold that is far from the capacity threshold. A code having too many such nodes tends not to exhibit a minimum distance that is proportional to block size. Results of computational simulations have shown that the decoding thresholds of codes of the present type are lower than those of regular LDPC codes. Included in the simulations were a few examples from a family of codes characterized by rates ranging from low to high and by thresholds that adhere closely to their respective channel capacity thresholds; the simulation results from these examples showed that the codes in question have low error floors as well as low decoding thresholds. As an example, the illustration shows the protograph (which represents the blueprint for overall construction) of one proposed code family for code rates greater than or equal to 1.2. Any size LDPC code can be obtained by copying the protograph structure N times, then permuting the edges. The illustration also provides Field Programmable Gate Array (FPGA) hardware performance simulations for this code family. In addition, the illustration provides minimum signal-to-noise ratios (Eb/No) in decibels (decoding thresholds) to achieve zero error rates as the code block size goes to infinity for various code rates. In comparison with the codes mentioned in the preceding article, these codes have slightly higher decoding thresholds.
Divsalar, Dariush↗
Protograph based LDPC codes with minimum distance linearly growing with block size
We propose several LDPC code constructions that simultaneously achieve good threshold and error floor performance. Minimum distance is shown to grow linearly with block size (similar to regular codes of variable degree at least 3) by considering ensemble average weight enumerators. Our constructions are based on projected graph, or protograph, structures that support high-speed decoder implementations. As with irregular ensembles, our constructions are sensitive to the proportion of degree-2 variable nodes. A code with too few such nodes tends to have an iterative decoding threshold that is far from the capacity threshold. A code with too many such nodes tends to not exhibit a minimum distance that grows linearly in block length. In this paper we also show that precoding can be used to lower the threshold of regular LDPC codes. The decoding thresholds of the proposed codes, which have linearly increasing minimum distance in block size, outperform that of regular LDPC codes. Furthermore, a family of low to high rate codes, with thresholds that adhere closely to their respective channel capacity thresholds, is presented. Simulation results for a few example codes show that the proposed codes have low error floors as well as good threshold SNFt performance.
minimum decoding↗
Protograph LDPC Codes with Node Degrees at Least 3
In this paper we present protograph codes with a small number of degree-3 nodes and one high degree node. The iterative decoding threshold for proposed rate 1/2 codes are lower, by about 0.2 dB, than the best known irregular LDPC codes with degree at least 3. The main motivation is to gain linear minimum distance to achieve low error floor. Also to construct rate-compatible protograph-based LDPC codes for fixed block length that simultaneously achieves low iterative decoding threshold and linear minimum distance. We start with a rate 1/2 protograph LDPC code with degree-3 nodes and one high degree node. Higher rate codes are obtained by connecting check nodes with degree-2 non-transmitted nodes. This is equivalent to constraint combining in the protograph. The condition where all constraints are combined corresponds to the highest rate code. This constraint must be connected to nodes of degree at least three for the graph to have linear minimum distance. Thus having node degree at least 3 for rate 1/2 guarantees linear minimum distance property to be preserved for higher rates. Through examples we show that the iterative decoding threshold as low as 0.544 dB can be achieved for small protographs with node degrees at least three. A family of low- to high-rate codes with minimum distance linearly increasing in block size and with capacity-approaching performance thresholds is presented. FPGA simulation results for a few example codes show that the proposed codes perform as predicted.
low density parity check (LDPC)↗
Support for User Interfaces for Distributed Systems
An extensible Java(TradeMark) software framework supports the construction and operation of graphical user interfaces (GUIs) for distributed computing systems typified by ground control systems that send commands to, and receive telemetric data from, spacecraft. Heretofore, such GUIs have been custom built for each new system at considerable expense. In contrast, the present framework affords generic capabilities that can be shared by different distributed systems. Dynamic class loading, reflection, and other run-time capabilities of the Java language and JavaBeans component architecture enable the creation of a GUI for each new distributed computing system with a minimum of custom effort. By use of this framework, GUI components in control panels and menus can send commands to a particular distributed system with a minimum of system-specific code. The framework receives, decodes, processes, and displays telemetry data; custom telemetry data handling can be added for a particular system. The framework supports saving and later restoration of users configurations of control panels and telemetry displays with a minimum of effort in writing system-specific code. GUIs constructed within this framework can be deployed in any operating system with a Java run-time environment, without recompilation or code changes.
Eychaner, Glenn↗
A 1-1/2-level on-chip-decoding bubble memory chip design
Design includes multi-channel replicator which can reduce chip-writing requirement, selective annihilating switch which can effectively annihilate bubbles with minimum delay, and modified transfer switch which can be used as selective steering-type decoder.
Chen, T. T.↗