Christopher R. Jones

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.

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 preceding 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 SNR performance.

Construction of rate-compatible LDPC codes utilizing information shortening and parity puncturing

This paper proposes a method for constructing rate-compatible low-density parity-check (LDPC) codes. The construction considers the problem of optimizing a family of rate-compatible degree distributions as well as the placement of bipartite graph edges. A hybrid approach that combines information shortening and parity puncturing is proposed. Local graph conditioning techniques for the suppression of error floors are also included in the construction methodology.

Constructing LDPC codes from simple loop-free encoding modules

Inspired by recently proposed accumulate-repeat-accumulate (ARA) codes, in this paper we propose a construction method for LDPC codes using simple loop-free encoding modules. Such codes can be viewed as serial/parallel concatenations of simple modules such as accumulators, repetition codes, differentiators, and punctured single parity check codes. Examples are accumulate-repeat-accumulate (ARA) codes, accumulate-repeat-accumulate-accumulate (ARAA) codes and accumulate-repeat-check-accumulate codes, and other variations. These codes constitute a subclass of LDPC codes with very fast encoder structure. They also have a projected graph or protograph representation that allows for high-speed decoder implementation. Based on density evolution, we show through some examples that low iterative decoding thresholds close to the channel capacity limits can be achieved with low maximum variable node degrees, as the block size goes to infinity. The decoding threshold in many examples outperforms that of the best known unstructured irregular LDPC codes constrained to have the same maximum node degree. Furthermore, by puncturing the accumulator modules, any desired higher rate codes can be obtained with thresholds that stay close to their respective channel capacity thresholds uniformly.

Joint LDPC decoding and timing recovery using code constraint feedback

Timing recovery and channel decoding are traditionally performed independently. However, we show here that the information generated during the iterative decoding of low-density parity-check (LDPC) coded data can be fed back to the timing recovery circuit to enable accurate estimation of frequency and phase errors without the need for any pilot symbols. We describe a method capable of handling large offsets with complexity that grows linearly with offset size. Combining the LDPC constraint node observations with a properly calibrated phase locked loop allows successful tracking of a constant time delay, a frequency offset and a random phase walk.

Pilotless Frame Synchronization for LDPC-Coded Transmission Systems

We present a pilotless frame synchronization approach that exploits feedback from a low-density parity-check (LDPC) code decoder. The synchronizer is based on syndrome checks using hard decisions from the channel observations. The bandwidth overhead associated with pilot symbols in conventional receiver architectures is eliminated while providing sufficient synchronization performance. An LDPC decoder coupled with our synchronizer exhibits negligible frame error rate degradation over a system with perfect synchronization. The complexity of the frame synchronizer is kept relatively low due to its XOR-based approach.

Pilotless Frame Synchronization via LDPC Code Constraint Feedback

In traditional receiver architectures, frame synchronization is performed using pilot symbols and a correlation rule. In this paper we show that outputs from the constraint node side of a bipartite decoding graph can be used to achieve frame synchronization in a pilotless low-density parity-check (LDPC) coded transmission, thereby avoiding the bandwidth cost inherent in use of pilot symbols. The complexity of the frame synchronizer is kept relatively low due to its XOR-based approach.

The Universal Operation of LDPC Codes Over Scalar Fading Channels

Root and Varaiya proved the existence of a code that can communicate reliably over any linear Gaussian channel for which the channel mutual information level exceeds the transmitted rate. This paper provides several examples of scalar (single-input single-output) fading channels and shows that on these channels the performance of low-density parity-check (LDPC) codes lies in close proximity to the performance limits identified by Root and Varaiya. Specifically, we consider periodic fading channels and partial-band jamming (PBJ) channels. A special case of periodic fading is the variation of signal-to-noise ratio across orthogonal frequency division modulation subchannels. The robustness of LDPC codes to periodic fading and PBJ across parameterizations of these different channels is demonstrated through the consistency of the required mutual information to provide a specified bit error rate. For the periodic fading case, the Gaussian approximation to density evolution has been adapted such that asymptotic threshold measures can be compared to simulated code performance in various periodic fading scenarios