Dariush Divsalar

• PhD
• Senior Researcher at California Institute of Technology

Rate-adaptive coding enables reliable communication while efficiently utilizing the available channel mutual information in free-space optical (FSO) communication. While adaptive coding has been explored in numerous articles, the effect of feedback delay is often overlooked. To adapt the code rate to current channel conditions, the transmitter must...

Recently, neural networks have improved MinSum message-passing decoders for low-density parity-check (LDPC) codes by multiplying or adding weights to the messages, where the weights are determined by a neural network. The neural network complexity to determine distinct weights for each edge is high, often limiting the application to relatively shor...

Non-uniform message quantization techniques such as reconstruction-computation-quantization (RCQ) improve error-correction performance and decrease hardware complexity of low-density parity-check (LDPC) decoders that use a flooding schedule. Layered MinSum RCQ (L-msRCQ) enables message quantization to be utilized for layered decoders and irregular...

Protograph-based Raptor-like low-density paritycheck codes (PBRL codes) are a family of easily encodable rate-compatible LDPC codes. PBRL codes have an excellent performance across all design rates. Quasi-cyclic (QC) PBRL code families permit high-speed decoder implementations. PBRL codes designed thus far, for both long and short block-lengths, ha...

Recent studies on noisy decoding for LDPC codes rely on the assumption that the noise in each component is independent and perpetual. This work examines a noisy decoding model that generalizes this approach: the noise is due to multistate channels where the channel states are governed by queuelike processes. This model is inspired by errors in deco...

Protograph-based Raptor-like low-density parity-check codes (PBRL codes) are a recently proposed family of easily encodable and decodable rate-compatible LDPC (RC-LDPC) codes. These codes have an excellent iterative decoding threshold and performance across all design rates. PBRL codes designed thus far, for both long and short block-lengths, have...

Rate-compatible (RC) codes are at the core of systems with incremental redundancy. Usually, an RC code family supports successively lower code rates by sending specific increments of additional redundancy at each rate. That is, the order of the increments is fixed. However, in some multi-hop communication systems and also in recently proposed inter...

This paper presents a general approach for optimizing the number of symbols in increments (packets of incremental redundancy) in a feedback communication system with a limited number of increments. This approach is based on a tight normal approximation on the rate for successful decoding. Applying this approach to a variety of feedback systems usin...

This paper presents a general approach for optimizing the number of symbols in increments (packets of incremental redundancy) in a feedback communication system with a limited number of increments. This approach is based on a tight normal approximation on the rate for successful decoding. Applying this approach to a variety of feedback systems usin...

It is a measure of the importance and profundity of Marvin Kenneth Simon's contributions to communication theory that this tribute article and tutorial about his life and work is of current research relevance in spite of the continually accelerating rate of evolution in this area. Marv, as the entire community affectionately knew him, was one of th...

In the last decade, great progress was made in the development of small satellites and CubeSats. Several small spacecraft were designed, fabricated, launched, and successfully operated in low Earth orbit. While more companies and space agencies are becoming interested in CubeSats and small satellite, also the mission goals for these spacecraft are...

In this paper a communication system for CubeSats in formation to operate in the vicinity of the Lunar Lagrangian L1 is proposed. CubeSats will collect lunar scientific data and will perform surface observations. An improved low complexity CDMA system for CubeSats for communications between the Lunar L1 and Earth station is considered. The complexi...

We consider the problem of constructing $(3,L)$ quasi-cyclic low-density parity-check (LDPC) codes from complete protographs. A complete protograph is a small bipartite graph with two disjoint vertex sets such that every vertex in the variable-node set is connected to every vertex in the check-node set by a unique edge. This paper analyzes the requ...

This chapter provides design, analysis, construction, and performance of the turbo codes, serially concatenated codes, and turbo-like codes including the design of interleavers in concatenation of codes. Also this chapter describes the iterative decoding algorithms for these codes. Performance of parallel versus serial concatenation using analysis...

This paper uses extrinsic-information-transfer (EXIT)-function analysis employing the reciprocal channel approximation (RCA) to obtain optimal LDPC code degree distributions for initial hard decoding (one-bit quantization of the channel output) and for decoding with the soft information provided by additional reads in both SLC (two-level cell) and...

One advantage of incremental transmissions with feedback in point-to-point memoryless channels is a reduction in average blocklength required to approach capacity. This paper optimizes the size of each incremental transmission for non-binary (NB) LDPC codes to maximize throughput in VLFT and two-phase VLF settings. The optimization problem uses an...

Digital communication coding methods for designing protograph-based bit-interleaved code modulation that is general and applies to any modulation. The general coding framework can support not only multiple rates but also adaptive modulation. The method is a two stage lifting approach. In the first stage, an original protograph is lifted to a slight...

This paper provides a comprehensive analysis of nonbinary low-density parity check (LDPC) codes built out of protographs. We consider both random and constrained edge-weight labeling, and refer to the former as the unconstrained nonbinary protograph-based LDPC codes (U-NBPB codes) and to the latter as the constrained nonbinary protograph-based LDPC...

One advantage of feedback in a point-to-point memoryless channel is the reduction of the average blocklength required to approach capacity. This paper presents a communication system with feedback that uses carefully designed non-binary LDPC (NB-LDPC) codes and incremental transmissions to achieve 92-94% of the idealized throughput of rate-compatib...

Following Poulliat et al.'s design of (2, dc) nonbinary LDPC (NB-LDPC) codes, this paper designs high-rate irregular NB-LDPC codes by addressing the problem of minimum symbol distance. The design procedure first identifies all stopping sets up to weight five in an LDPC code and enumerates them via a message passing algorithm. For each identified st...

This paper considers finite-blocklength achievability for rate-compatible codes. For a fixed number of messages, random coding analysis determines a sequence of achievable error probabilities for a sequence of blocklengths. However, traditional random coding achievability draws each code independently so that it does not show that a family of rate-...

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...

This paper proposes a class of rate-compatible LDPC codes, called protograph-based Raptor-like (PBRL) codes. The construction is focused on binary codes for BI-AWGN channels. As with the Raptor codes, additional parity bits are produced by exclusive-OR operations on the precoded bits, providing extensive rate compatibility. Unlike Raptor codes, the...

Radio Science (RS) experiments currently rely on unmodulated CW RF signal carrier for spectral purity and maximized signal-to-noise ratio. This requires missions to carefully schedule them away from periods of high rate telemetry. In the era of optical communications, current systems experience the same problem. In this paper, we derive a data proc...

Interplanetary Cubesats would enable low-cost missions for high-quality scientific and exploration programs. In particular cubeSats in formation have been proposed to operate in the vicinity of the Lunar Lagrangian L1 to collect lunar scientific data and to perform surface observation. In this paper we present a low complexity CDMA system for CubeS...

Closed form upper bounds to error probabilities of nonbinary coded systems with two and higher dimensional constellation over the additive white Gaussian noise channel are derived. Computation of these bounds do not require integrations nor parameter optimizations. These bounds are the extension of bounds derived by Divsalar in 1999 for binary code...

This letter produces a family of rate-compatible protograph-based LDPC codes approaching the independent and uniformly distributed (i.u.d.) capacity of inter-symbol interference (ISI) channels. This problem is highly nontrivial due to the joint design of structured (protograph-based) LDPC codes and the state structure of ISI channels. We describe a...

Radio Science started when it became apparent with early deep space missions that occultations by planetary atmospheres would affect the quality of radio communications. Since then the atmospheric properties and other aspects of planetary science, solar science, and fundamental physics were studied by scientists. Radio Science data was always extra...

With the advent of modern coding techniques, considerable improvement is possible over the BCH codes specified in the current Consultative Committee for Space Data Systems (CCSDS) telecommand standard. Two broad classes of applications are identified, one for low-data-rate transfer of simple commands and protocol information, and the other for tran...

This paper produces a rate-compatible protograph LDPC code at 1k information blocklength with superior performance in both waterfall and error floor regions. The design of such codes has proved difficult in the past because the constraints imposed by structured design (protographs), rate-compatibility, as well as small block length, are not easily...

Despite encouraging advances in the design of relay codes, several important challenges remain. Many of the existing LDPC relay codes are tightly optimized for fixed channel conditions and not easily adapted without extensive re-optimization of the code. Some have high encoding complexity and some need long block lengths to approach capacity. This...

A new coding scheme for image transmission over noisy channel is proposed. Similar to standard image compression, the scheme includes a linear transform followed by successive refinement scalar quantization. Unlike conventional schemes, in the proposed system the quantized transform coefficients are linearly mapped into channel symbols using system...

This paper presents two complementary constructions of finite-length non-binary protograph-based codes with the focus on the short block-length regime. The first class is based on the existing approaches of applying the copy-and-permute operations to the constituent protograph with unweighted edges, followed by assigning non-binary scales to the ed...

This paper introduces a novel class of non-binary graph-based codes, built upon graph covers of non-binary protograph LDPC codes. This new ensemble is more restrictive than previously considered constructions, but in turn is much simpler to design and implement. The simplifications in design allow for the enumeration of codeword weight, trapping se...

Coherent states achieve the Holevo capacity of a pure-loss channel when paired with an optimal measurement, but a physical realization of this measurement is unknown, and likely to be of high complexity. In this paper, we focus on the photon-counting measurement and study the photon and dimensional efficiencies attainable with modulations over clas...

This paper presents a new construction of punctured-node protograph-based Raptor-like (PN-PBRL) codes that is suitable for long-blocklength applications. As with the Raptor codes, additional parity bits can be easily produced by exclusive-OR operations on the precoded bits, providing extensive rate compatibility. The new construction provides low i...

This paper addresses the design of a protograph-based LDPC code which can approach the independent and uniformly distributed (i.u.d.) capacity of partial response channels. We propose a method to calculate the iterative decoding threshold of a joint graph between a protograph and the state structure of a partial response channel using the extrinsic...

Recent results by Chen et al. and Polyanskiy et al. explore using feedback to approach capacity with short blocklengths. This paper explores Chernoff bounding techniques to extend the rate-compatible sphere-packing (RCSP) analysis proposed by Chen et al. to scenarios involving numerous retransmissions and different step sizes in each incremental re...

Coherent states achieve the Holevo capacity of a pure-loss channel when paired with an optimal measurement, but a physical realization of this measurement is as of yet unknown, and it is also likely to be of high complexity. In this paper, we focus on the photon-counting measurement and study the photon and dimensional efficiencies attainable with...

This paper proves the existence of the typical minimum distance for certain ensembles of the protograph-based nonbinary (PB NB) LDPC codes with degree-2 variable nodes. Using recently obtained ensemble weight enumerators for the PB NB LDPC codes, we show that asymptotically in the code length N, the entries in the weight enumerators up to some weig...

This paper presents a new class of rate-compatible LDPC codes, protograph-based Raptor-like (PBRL) codes. The proposed PBRL codes are jointly decodable with an iterative belief propagation decoder. As with Raptor codes, additional parity bits can be easily produced by exclusive-or operations on the precoded bits, providing extensive rate compatibil...

Protograph-based bit-interleaved coded modulation (BICM) provides an elegant way of designing coded modulation over Rayleigh faded channels, however, to date the available designs have been limited to specific modulations and the corresponding decoding thresholds have not been known for Rayleigh faded channels. In this work, we present a simple met...

Binary LDPC codes built out of protographs constitute a class of high-performance structured codes. In this paper we carefully extend the code construction to the non-binary case. We present a method based on a newly developed EXIT-chart approach to efficiently design non-binary protograph-based LDPC codes with good properties. The results presente...

This paper presents a method for evaluating pseudocodeword weight enumerators of nonbinary LDPC codes built out of protographs. The ensemble enumerators are evaluated for both the finite-length and infinite-length regimes. Results of this type can be particularly useful for designing structured non-binary LDPC codes with good properties under messa...

This paper considers the ensemble enumerators of protograph-based nonbinary (PB NB) LDPC codes. Equipped with combinatorial definitions extended to the nonbinary domain, ensemble enumerators of codeword weight, trapping set size and stopping set size are calculated. The exact enumerators are presented in the finite-length regime, and the correspond...

A new coding scheme for image transmission over a noisy channel is proposed. Similar to the standard image encoders, the scheme includes a transform coding stage and scalar quantization. Differently, the proposed scheme considers the image as a set of parallel subsources where subsources are equal-size partitions of transform domain subbands. The s...

A prior paper introduced the waveform denoted GMSK/PN as a candidate for power-limited, single-access communications links on which simultaneous high data rate transmission and precision ranging are desired. The waveform combines traditional GMSK (Gaussian Minimum-Shift Keying) modulation and a PN (pseudonoise) spread-spectrum sequence used for ran...

A new coding scheme for image transmission over noisy channel is proposed. Similar to standard image compression, the scheme includes a linear transform followed by embedded scalar quantization. Joint source-channel coding is implemented by optimizing the rate allocation across the source subbands, treated as the components of a parallel source mod...

Dedicated to the memory of Ralf Koetter (1963-2009) Abstract—Protograph-based LDPC and generalized LDPC (G-LDPC) codes have the advantages of a simple design proce- dure and highly structured encoders and decoders. The design of such "protograph-based codes" relies on what is effectively a computer-based search. As such, following Gallager, it is p...

This paper presents and compares two iterative coded modulation techniques for deep-space optical communications using pulse-position modulation (PPM). The first code, denoted by SCPPM, consists of the serial concatenation of an outer convolutional code, an interleaver, a bit accumulator, and PPM. The second code, denoted by LDPC-PPM, consists of t...

This paper presents a simple yet powerful method for designing embedded rate-compatible families of LDPC codes. Rate compatible codes are essential for many communication applications, e.g. hybrid automatic repeat request (HARQ) systems, and their design is nontrivial due to the difficulty of simultaneously guaranteeing the quality of several relat...

This paper presents a high-performing LDPC code for the relay channel that addresses simultaneously two important issues: a code structure that allows low encoding complexity, and a flexible rate-compatible code that allows matching to various channel conditions. Most of the previous high-performance LDPC codes for the relay channel are tightly opt...

Protograph-based generalized LDPC (GLDPC) codes have the advantages of a simple design procedure and highly structured encoders and decoders. Recently, a technique for computing ensemble weight enumerators for GLDPC codes has been published. In the current paper, we investigate the existence of typical minimum distance for protograph-based GLDPC co...

In this paper, a method is presented for enumerating the trapping sets of a specific LDPC code given its Tanner graph. The technique involves augmenting the original Tanner graph with additional variable nodes, and then applying a weight-enumeration algorithm to the augmented Tanner graph. The proposed method is used to find trapping set enumerator...

In this paper we prove that, for a certain class of protograph-based LDPC codes with degree-two variable nodes, a typical minimum distance exists. We obtain a tight bound on the sum of weight enumerators, up to some weight d*, for the ensemble of finite-length protograph LDPC codes. Then we prove that this sum goes to zero as the block length goes...

Recently, pseudocodewords of Tanner graphs of LDPC codes have been used to explain the behavior of iterative decoders for these codes. In this paper, finite-length pseudocodeword weight enumerators for protograph-based generalized-LDPC code ensembles are obtained. Then asymptotic results are derived from the finite-length results by letting the blo...

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...

In this work, we study the performance of structured Low-Density Parity-Check (LDPC) Codes together with bandwidth efficient modulations. We consider protograph-based LDPC codes that facilitate high-speed hardware implementations and have minimum distances that grow linearly with block sizes. We cover various higher-order modulations such as 8-PSK,...

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 bo...

A modification to the usual iterative decoding algorithm for LDPC codes, called bounded angle iterative (BA-I) decoding, is introduced. The modified decoder erases codewords detected during iterations that fall outside a maximum decoding angle with respect to the received observation. The new algorithm is applicable in scenarios that demand a very...

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 ca...

Renewed interest in human exploration of space suggests a future need for high throughput earth-space links. Anticipating crowding within spectrum used for deep- space communications, particularly at X-band, NASA is investigating the use of bandwidth-efficient modulation (BEM). Requirements for trajectory/orbit determination and vehicle guidance wi...

NASA has undertaken a study to recommend and justify coding, modulation, and link protocol (CMLP) designs for the Space Communications and Networking (SCaN) office. This paper reports on the coding part of the CMLP study, which is chartered with identifying the forward error correction (FEC) codes suitable for NASA space exploration and science mis...

In earlier work, we presented a method for finding ensemble weight enumerator for protograph-based generalized LDPC (G-LDPC) codes, and leveraged this method to find ensemble stopping set enumerator and ensemble trapping set enumerator. The method is conceptually simple, but when the dimensionality of the constraint nodes (number of their code-word...

Protograph-based LDPC codes have the advantages of a simple design (or search) procedure and highly structured encoders and decoders. These advantages have also been exploited in the design of protograph-based generalized LDPC (G-LDPC) codes. Recently, a technique for computing ensemble weight enumerators and stopping set enumerators for protograph...

The development of error-correcting codes has been closely coupled with deep-space exploration since the early days of both. Since the discovery of turbo codes in 1993, the research community has invested a great deal of work on modern iteratively decoded codes, and naturally NASA's Jet Propulsion Laboratory (JPL) has been very much involved. This...

In this paper we design protograph-based LDPC codes with short block sizes. Mainly we consider rate 1/2 codes with input block sizes 64, 128, and 256 bits. To simplify the encoder and decoder implementations for high data rate transmission, the structure of the codes is based on protographs and circulants. These codes are designed for short block s...

Implementation of belief propagation for low-density parity-check codes involves selection of functions possessing manageable dynamic range, topologic considerations for aggregation of these functions such that nodes of varying degree can be efficiently realized, and message passing architectures that offer various alternatives for flexibility and...