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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)

Optical communication with laser diode arrays

The performance of a direct-detection optical communication system in which the laser transmitter sends short optical pulses of selected nonoverlapping center frequencies is analysed. This modulation format, in which a single light pulse is sent in one of M time slots at one of N optical center frequencies, is referred to as color coded optical pulse position modulation (CCPPM). The optimum energy-efficiency of this system, as measured by the channel capacity in nats per photon, exceeds that of ordinary optical pulse position modulation which uses a pulsed laser of fixed optical frequency. Reliable communication at optimal energy efficiency is easily achieved through the use of modest block length Reed-Solomon codes with the code words represented as CCPPM symbols.

Davidson, F.

Error control techniques for satellite and space communications

The performance anlaysis of NASA's telecommand systems was summarized. It is assumed that the decoded frames are scrambled prior to decoding by the outer code. The average decoded bit error rate are examined which allows the possibility of evaluating many different frame coding options. The capacity and cutoff rate of the outer channel formed by the combination of the actual physical channel and the inner encoder and decoder in a concatenated coding system were analyzed. The best combination of inner and outer codes to use in a concatenated coding system were determined. It was established that in general: (1) it is better not to interleave between the inner and outer codes; and (2) for a fixed overall code rate, it is better to use higher rate inner codes and lower rate outer codes. Inner convolutional codes are considered. The analysis is more difficult in this case because the inner decoder error events do not appear in blocks of fixed length but can be of many different lengths.

Costello, D. J., Jr.

Testing of Error-Correcting Sparse Permutation Channel Codes

A computer program performs Monte Carlo direct numerical simulations for testing sparse permutation channel codes, which offer strong error-correction capabilities at high code rates and are considered especially suitable for storage of digital data in holographic and volume memories. A word in a code of this type is characterized by, among other things, a sparseness parameter (M) and a fixed number (K) of 1 or "on" bits in a channel block length of N.

Shcheglov, Kirill, V.

Random coding strategies for minimum entropy

This paper proves that there exists a fixed random coding strategy for block coding a memoryless information source to achieve the absolute epsilon entropy of the source. That is, the strategy can be chosen independent of the block length. The principal new tool is an easy result on the semicontinuity of the relative entropy functional of one probability distribution with respect to another. The theorem generalizes a result from rate-distortion theory to the 'zero-infinity' case.

Posner, E. C.

Bit-wise arithmetic coding for data compression

This article examines the problem of compressing a uniformly quantized independent and identically distributed (IID) source. We present a new compression technique, bit-wise arithmetic coding, that assigns fixed-length codewords to the quantizer output and uses arithmetic coding to compress the codewords, treating the codeword bits as independent. We examine the performance of this method and evaluate the overhead required when used block-adaptively. Simulation results are presented for Gaussian and Laplacian sources. This new technique could be used as the entropy coder in a transform or subband coding system.

Kiely, A. B.

An investigation of messy genetic algorithms

Genetic algorithms (GAs) are search procedures based on the mechanics of natural selection and natural genetics. They combine the use of string codings or artificial chromosomes and populations with the selective and juxtapositional power of reproduction and recombination to motivate a surprisingly powerful search heuristic in many problems. Despite their empirical success, there has been a long standing objection to the use of GAs in arbitrarily difficult problems. A new approach was launched. Results to a 30-bit, order-three-deception problem were obtained using a new type of genetic algorithm called a messy genetic algorithm (mGAs). Messy genetic algorithms combine the use of variable-length strings, a two-phase selection scheme, and messy genetic operators to effect a solution to the fixed-coding problem of standard simple GAs. The results of the study of mGAs in problems with nonuniform subfunction scale and size are presented. The mGA approach is summarized, both its operation and the theory of its use. Experiments on problems of varying scale, varying building-block size, and combined varying scale and size are presented.

Goldberg, David E.

Estimating the size of Huffman code preambles

Data compression via block-adaptive Huffman coding is considered. The compressor consecutively processes blocks of N data symbols, estimates source statistics by computing the relative frequencies of each source symbol in the block, and then synthesizes a Huffman code based on these estimates. In order to let the decompressor know which Huffman code is being used, the compressor must begin the transmission of each compressed block with a short preamble or header file. This file is an encoding of the list n = (n(sub 1), n(sub 2)....,n(sub m)), where n(sub i) is the length of the Hufffman codeword associated with the ith source symbol. A simple method of doing this encoding is to individually encode each n(sub i) into a fixed-length binary word of length log(sub 2)l, where l is an a priori upper bound on the codeword length. This method produces a maximum preamble length of mlog(sub 2)l bits. The object is to show that, in most cases, no substantially shorter header of any kind is possible.

Mceliece, R. J.

Design and Modeling of a Coded-Interleaving System in the Presence of Fading

Future deep space links are migrating towards higher frequency bands such as Ka band and optical. These links are susceptible to non linear effects (e.g. cloud coverage, atmospheric turbulence, scintillation, antenna mis-pointing, jitter, relative motion, etc.) that cause various degrees of fading loss over various time scales. We consider a channel experiencing block fading where the channel coherence time is a lot longer than the length of a codeword. As long as the fading duration is not excessive, an interleaver can be used in a coded-communication system that randomizes the fades among symbols of multiple codewords. This achieves an “averaging” effect that spreads the signal energy more evenly among the codewords, and improves the likelihood that each of them can be decoded correctly. For simplicity, we consider a block interleaver where adjacent symbols of a codeword have a fixed delay (or separation) with each other, and investigate the error-rate performance of a coded-interleaving system (with fixed and finite interleaving depth) in the presence of block fading. Unlike prior research which assumes theoretical channel coherence models, we aim to build upon our analysis using empirical spacecraft signal measurements obtained with the Deep Space Network, and to use the fundamental theories of probability and statistics (e.g. variations of Law of Large Numbers) to quantify the error-rate performance of the coded-interleaving system. We propose to utilize these results in the design of a two-dimensional coded-interleaving system for fading channels.

Sanchez-Net, Marc

Effects of cavity dimensions, boundary layer, and temperature on cavity noise with emphasis on benchmark data to validate computational aeroacoustic codes

This report documents the results of an experimental investigation on the response of a cavity to external flowfields. The primary objective of this research was to acquire benchmark of data on the effects of cavity length, width, depth, upstream boundary layer, and flow temperature on cavity noise. These data were to be used for validation of computational aeroacoustic (CAA) codes on cavity noise. To achieve this objective, a systematic set of acoustic and flow measurements were made for subsonic turbulent flows approaching a cavity. These measurements were conducted in the research facilities of the Georgia Tech research institute. Two cavity models were designed, one for heated flow and another for unheated flow studies. Both models were designed such that the cavity length (L) could easily be varied while holding fixed the depth (D) and width (W) dimensions of the cavity. Depth and width blocks were manufactured so that these dimensions could be varied as well. A wall jet issuing from a rectangular nozzle was used to simulate flows over the cavity.

Ahuja, K. K.

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

A VLSI decomposition of the deBruijn graph

A new Viterbi decoder for convolutional codes with constraint lengths up to 15, called the Big Viterbi Decoder, is under development for the Deep Space Network. It will be demonstrated by decoding data from the Galileo spacecraft, which has a rate 1/4, constraint-length 15 convolutional encoder on board. Here, the mathematical theory underlying the design of the very-large-scale-integrated (VLSI) chips that are being used to build this decoder is explained. The deBruijn graph B sub n describes the topology of a fully parallel, rate 1/v, constraint length n+2 Viterbi decoder, and it is shown that B sub n can be built by appropriately wiring together (i.e., connecting together with extra edges) many isomorphic copies of a fixed graph called a B sub n building block. The efficiency of such a building block is defined as the fraction of the edges in B sub n that are present in the copies of the building block. It is shown, among other things, that for any alpha less than 1, there exists a graph G which is a B sub n building block of efficiency greater than alpha for all sufficiently large n. These results are illustrated by describing a special hierarchical family of deBruijn building blocks, which has led to the design of the gate-array chips being used in the Big Viterbi Decoder.

Collins, O.

Two-Equation Turbulence Models for Prediction of Heat Transfer on a Transonic Turbine Blade

Two versions of the two-equation k-omega model and a shear stress transport (SST) model are used in a three-dimensional, multi-block, Navier-Stokes code to compare the detailed heat transfer measurements on a transonic turbine blade. It is found that the SST model resolves the passage vortex better on the suction side of the blade, thus yielding a better comparison with the experimental data than either of the k-w models. However, the comparison is still deficient on the suction side of the blade. Use of the SST model does require the computation of distance from a wall, which for a multiblock grid, such as in the present case, can be complicated. However, a relatively easy fix for this problem was devised. Also addressed are issues such as (1) computation of the production term in the turbulence equations for aerodynamic applications, and (2) the relation between the computational and experimental values for the turbulence length scale, and its influence on the passage vortex on the suction side of the turbine blade.

Garg, Vijay K.

The Utilization Profiles of the CCSDS Unified Space Link Protocol (USLP)

The purpose of this paper is to identify the utilization profiles for interfacing the Data Protocol Sublayer using the Unified Space Link Protocols (USLP) (reference 1) with the space link coding procedures as specified in the CCSDS Coding & Synchronization Blue Books (references 2 through 5), used in both telecommand and telemetry applications. This paper describes how the USLP Protocol utilizes the coding and synchronization sublayer to support: a. Direct to Earth (DTE) telemetry links for engineering and science data b. Direct to Earth (DTE) telemetry links for very high rate science data c. Direct from Earth (DFE) command, sequencing and flight software loads d. Space to Space Links (Proximity) utilized by orbiters for data exchange to/from surface bound assets. The CCSDS has divided the functions of the Data Link Layer into two sublayers: the Data Link Protocol Sublayer (DLP-SL) and the Coding and Synchronization Sublayer (CS-SL). The Data Link Protocol Sublayer (DLP-SL) interfaces to the users, accepting the data that is to be transported, on the sending side of the link, and delivering that data on the receiving end. The Transfer Frame is the data unit that is transferred across the Data Link Protocol Sublayer and the Coding and Synchronization Sublayer boundary. The Coding and Synchronization Sublayer (CS-SL) provides the encoding, randomization, and frame synchronization functions that prepares the USLP Transfer Frame for transport across the space link. The CS-SL is divided into 2 processes: 1) The Frame Interface Processes (FIP) performs the interface functions required to prepare the data for delivery to the Coding/Decoding Process (CDP). This process includes prepending a Frame Start Marker to the provided frame, when management has designated that the frame is not to be aligned to the codeblock or when there is no block code used. 2) The Coding/Decoding Process (CDP) performs the forward error correction processes that are used to optimize the performance of the link and minimize the error rate. The CDP creates the symbol stream that is delivered to the Physical Layer. The transfer of the USLP transfer frames across different types of space links is the focus of this paper. The Protocol Data Unit (PDU) that is passed in both directions between the Data Link Protocol Sublayer (DLP-SL) and Coding and Synchronization Sublayer (CS-SL) is the transfer frame. The USLP frame structure provides flexibility that can be constrained by the functions utilized within the CS-SL that prepare the transfer frame for transit. For example, the USLP transfer frame contains a length field that enables the frame to be of variable length but CS-SL under certain conditions may constrain the frame to be fixed in length. This paper describes 5 operational modes available for use by the Data Link Layer to provide data exchange across the USLP space link. These modes are different because different operational requirements apply to vastly different types of space links and thus the communications implementation requirements differ. The environmental issues include the power or energy available, the distance between the end points of the link, the complexity of the equipment available at those end points, the atmospheric conditions and radiometric frequency selection. The CS-SL utilizes different forward error correcting codes supported by specific operational modes to configure the data for transit. This paper describes all of the operational modes in a series of data models which decompose the functionality between the Data Link Protocol Sublayer and the Coding and Synchronization sublayer. The operational modes described are: 1. Uncoded Mode: has been used for short links that contain significant available power to provide an acceptable frame error rate. The frames in this mode can be variable in length and typically use an error detection algorithm (i.e., CRC) to determine if there are errors in the received frame. 2. Convolutional Only Mode: is currently the prime forward error correction coding used for the proximity links. The frames in this mode can be variable in length and typically use an error detection algorithm (i.e., CRC) to determine if there are errors in the received frame. 3. Variable Length Frame Aligned to Variable Length Codeblock (TC): is used for Direct from Earth links were power levels are high and the simple, least complex code i.e., the BCH code is used. This mode has been in use since the early 1970s. The BCH code is a short code and the decoder is easy to implement. 4. Fixed Length Frame Aligned to Fixed Length Codeblock (AOS/TM): was introduced when the concatenated Convolutional and Reed-Solomon Code was formulated to provide significant reduction in link data error rate and the ability to determine if there was an error in the decoded codeblock. The frame is aligned to the codeblock so that there is a one to one relationship of frame errors to codeblock errors without additional error detection coding being added. This mode requires the protocol frames to be the exact size of the message portion of the codeblock. 5. Frames Unaligned to Fixed Length Codeblocks (Currently used for very high rates and space to space links): This mode is currently used for missions that have a very high data rate that can be controlled adaptively as the environment changes and as the next generation operating mode for the proximity link. This mode from a coded data stream point of view is exactly like that described in 4. above, except that the frame need not be aligned to the codeblock. There is no requirement on frame length when using this mode. Thus when using USLP it can be used to support links that require short or long frames. There is also no mandatory requirement that frames cannot be separated by idle data reducing the tight data rate connection requirements between the data link protocol sublayer and the coding & synchronization sublayer. In conclusion, how these operational modes can be put to use in mission operational scenarios is described for Direct from Earth links (DFE), Direct to Earth links (DTE), and Proximity links.

Greenberg, E.

The CCSDS Next Generation Space Data Link Protocol (NGSLP)

The CCSDS space link protocols i.e., Telemetry (TM), Telecommand (TC), Advanced Orbiting Systems (AOS) were developed in the early growth period of the space program. They were designed to meet the needs of the early missions, be compatible with the available technology and focused on the specific link environments. Digital technology was in its infancy and spacecraft power and mass issues enforced severe constraints on flight implementations. Therefore the Telecommand protocol was designed around a simple Bose, Hocquenghem, Chaudhuri (BCH) code that provided little coding gain and limited error detection but was relatively simple to decode on board. The infusion of the concatenated Convolutional and Reed-Solomon codes5 for telemetry was a major milestone and transformed telemetry applications by providing them the ability to more efficiently utilize the telemetry link and its ability to deliver user data. The ability to significantly lower the error rates on the telemetry links enabled the use of packet telemetry and data compression. The infusion of the high performance codes for telemetry was enabled by the advent of digital processing, but it was limited to earth based systems supporting telemetry. The latest CCSDS space link protocol, Proximity-1 was developed in early 2000 to meet the needs of short-range, bi-directional, fixed or mobile radio links characterized by short time delays, moderate but not weak signals, and short independent sessions. Proximity-1 has been successfully deployed on both NASA and ESA missions at Mars and is planned to be utilized by all Mars missions in development. A new age has arisen, one that now provides the means to perform advanced digital processing in spacecraft systems enabling the use of improved transponders, digital correlators, and high performance forward error correcting codes for all communications links. Flight transponders utilizing digital technology have emerged and can efficiently provide the means to make the next leap in performance for space link communications. Field Programmable Gate Arrays (FPGAs) provide the capability to incorporate high performance forward error correcting codes implemented within software transponders providing improved performance in data transfer, ranging, link security, and time correlation. Given these synergistic technological breakthroughs, the time has come to take advantage of them in applying them to both on going (e.g., command, telemetry) and emerging (e.g., space link security, optical communication) space link applications. However one of the constraining factors within the Data Link Layer in realizing these performance gains is the lack of a generic transfer frame format and common supporting services amongst the existing CCSDS link layer protocols. Currently each of the four CCSDS link layer protocols (TM, TC, AOS, and Proximity-1) have unique formats and services which prohibits their reuse across the totality of all space link applications of CCSDS member space agencies. For example, Mars missions. These missions implement their proximity data link layer using the Proximity-1 frame format and the services it supports but is still required to support the direct from Earth (TC) protocols and the Direct To Earth (AOS/TM) protocols. The prime purpose of this paper, is to describe a new general purpose CCSDS Data Link layer protocol, the NGSLP that will provide the required services along with a common transfer frame format for all the CCSDS space links (ground to/from space and space to space links) targeted for emerging missions after a CCSDS agency-wide coordinated date. This paper will also describe related options that can be included for the Coding and Synchronization sub-layer of the Data Link layer to extend the capacities of the link and additionally provide an independence of the transfer frame sub-layer from the coding sublayer. This feature will provide missions the option of running either the currently performed synchronous coding and transfer frame data link or an asynchronous coding/frame data link, in which the transfer frame length is independent of the block size of the code. The benefits from the elimination of this constraint (frame synchronized to the code block) will simplify the interface between the transponder and the data handling equipment and reduce implementation costs and complexities. The benefits include: inclusion of encoders/decoders into transmitters and receivers without regard to data link protocols, providing the ability to insert latency sensitive messages into the link to support launch, landing/docking, telerobotics. and Variable Coded Modulation (VCM). In addition the ability to transfer different sized frames can provide a backup for delivering stored anomaly engineering data simultaneously with real time data, or relaying of frames from various sources onto a trunk line for delivery to Earth.

Kazz, Greg J.