Kenneth Andrews

Capacity-approaching protograph codes

This paper discusses construction of protograph-based low-density parity-check (LDPC) codes. Emphasis is placed on protograph ensembles whose typical minimum distance grows linearly with block size. Asymptotic performance analysis for both weight enumeration and iterative decoding threshold determination is provided and applied to a series of code constructions. Construction techniques that yield both low thresholds and linear minimum distance growth are introduced by way of example throughout. The paper also examines implementation strategies for high throughput decoding derived from first principles of belief propagation on bipartite graphs.

Encoders for block-circulant LDPC codes

In this paper, we present two encoding methods for block-circulant LDPC codes. The first is an iterative encoding method based on the erasure decoding algorithm, and the computations required are well organized due to the block-circulant structure of the parity check matrix. The second method uses block-circulant generator matrices, and the encoders are very similar to those for recursive convolutional codes. Some encoders of the second type have been implemented in a small field programmable gate array (FPGA) and operate at 100 Msymbols/second

Methodologies for designing LDPC codes using protographs and circulants

A method is presented for constructing LDPC codes with excellent performance, simple hardware implementation, low encoder complexity, and which can be concisely documented. The simple code structure is achieved by using a base graph, expanded with circulants. The base graph is chosen by computer search using simulated annealing, driven by density evolutions decoding threshold as determined by the reciprocal channel approximation. To build a full parity check matrix, each edge of the base graph is replaced by a circulant permutation, chosen to maximize loop length by using a Viterbi-like algorithm.

Optical array receiver for communication through atmospheric turbulence

An optical array receiver concept is developed and analyzed. It is shown that for ground-based reception, the number of array elements can be increased without incurring performance degradation, provided the array telescope diameters exceed the coherence-length of the atmosphere. Maximum likelihood detection of turbulence-degraded signal fields is developed for the case of pulse-position modulated signals observed in the presence of background radiation. Performance of optical array receivers is compared to single-aperture receivers with diameters ranging from 4 to 8 m, both in the presence of turbulence and in a turbulence-free environment such as space. It is shown that in the absence of atmospheric turbulence, single-aperture receivers outperform receiver arrays when significant background radiation is present. However, it is also demonstrated that for ground-based reception of deep-space signals, the number of array elements can be as great as several thousand without incurring any performance degradation relative to a large single-aperture receiver.

A scalable architecture of a structured LDPC decoder

We present a scalable decoding architecture for a certain class of structured LDPC codes. The codes are designed using a small (n, r) protograph that is replicated Z times to produce a decoding graph for a (Z/spl times/n, Z/spl times/r) code. Using this architecture, we have implemented a decoder for a (4096, 2048) LDPC code on a Xilinx Virtex-II 2000 FPGA, and achieved decoding speeds of 31 Mbps with 10 fixed iterations. The implemented message-passing algorithm uses an optimized 3-bit nonuniform quantizer that allows near floating point performance in the waterfall region, with drastically smaller hardware implementation requirements.

Deep Space Network turbo decoder implementation

A new decoder is being developed by the Jet Propulsion Laboratory for NASAs Deep Space Network. This unit will decode the new turbo codes, which have recently been approved by the Consultative Committee for Space Data Systems (CCSDS). Turbo codes provide up to 0.8 dB improvement in E/sub b//N/sub 0/ over the current best codes used by deep space missions. The new decoder is being implemented in software running on commercial DSP chips, removing the need to design complicated and expensive hardware as was the case with the previous generation of codes. The decoder will time-tag the data frames, perform frame synchronization in the symbol domain (as opposed to the current bit domain synchronization), decode the turbo coded frames, and output the decoded bits in the CCSDS Standard Formatted Data Units format. The decoder is initially designed to operate up to 365 kbps, but will increase in rate as DSP clock rates increase. The implementation will go operational in October, 2003.

Adaptive optics correction into single mode fiber for a low Earth orbiting space to ground optical communication link using the OPALS downlink.

An adaptive optics (AO) testbed was integrated to the Optical PAyload for Lasercomm Science (OPALS) ground station telescope at the Optical Communications Telescope Laboratory (OCTL) as part of the free space laser communications experiment with the flight system on board the International Space Station (ISS). Atmospheric turbulence induced aberrations on the optical downlink were adaptively corrected during an overflight of the ISS so that the transmitted laser signal could be efficiently coupled into a single mode fiber continuously. A stable output Strehl ratio of around 0.6 was demonstrated along with the recovery of a 50 Mbps encoded high definition (HD) video transmission from the ISS at the output of the single mode fiber. This proof of concept demonstration validates multi-Gbps optical downlinks from fast slewing low-Earth orbiting (LEO) spacecraft to ground assets in a manner that potentially allows seamless space to ground connectivity for future high data-rates network.

LDPC decoding using multiple representations

For a particular block code, a multitude of different parity check matrices could be chosen to represent the code constraints. We demonstrate that belief propagation decoders based on different parity check matrices often respond in different ways, and that for a given complexity, it may be preferable to use several decoders for fewer iterations, than to run a single decoder for many iterations. We also propose some additional decoder architectures that use multiple representations of the parity constraints.

Bounds on error probability of block codes with bounded-angle maximum-likelihood incomplete decoding

Recently, Dolinar et al. obtained extremely tight bounds on the probabilities of decoding error and undetected error for block codes using bounded-angle maximum-likelihood (BA-ML) incomplete decoding. Unfortunately, these bounds are complex and difficult to compute for large block sizes. In this paper we obtain simple exponential upper bounds on both the word error probability and the undetected error probability of block codes using BA-ML decoding.

The limits of coding with joint constraints on detected and undetected error rates

We develop a remarkably tight upper bound on the performance of a parameterized family of bounded angle maximum-likelihood (BA-ML) incomplete decoders. The new bound for this class of incomplete decoders is calculated from the codepsilas weight enumerator, and is an extension of Poltyrev-type bounds developed for complete ML decoders. This bound can also be applied to bound the average performance of random code ensembles in terms of an ensemble average weight enumerator. We also formulate conditions defining a parameterized family of optimal incomplete decoders, defined to minimize both the total codeword error probability and the undetected error probability for any fixed capability of the decoder to detect errors. We illustrate the gap between optimal and BA-ML incomplete decoding via simulation of a small code.