Gianluigi Liva

Graph-Based Analysis and Optimization of Contention Resolution Diversity Slotted ALOHA

Contention resolution diversity slotted ALOHA (CRDSA) is a simple but effective improvement of slotted ALOHA. CRDSA relies on MAC bursts repetition and on interference cancellation (IC), achieving a peak throughput T ≅ 0.55, whereas for slotted ALOHA T ≅ 0.37. In this paper we show that the IC process of CRDSA can be conveniently described by a bipartite graph, establishing a bridge between the IC process and the iterative erasure decoding of graph-based codes. Exploiting this analogy, we show how a high throughput can be achieved by selecting variable burst repetition rates according to given probability distributions, leading to irregular graphs. A framework for the probability distribution optimization is provided. Based on that, we propose a novel scheme, named irregular repetition slotted ALOHA, that can achieve a throughput T ≅ 0.97 for large frames and near to T ≅ 0.8 in practical implementations, resulting in a gain of ~ 45% w.r.t. CRDSA. An analysis of the normalized efficiency is introduced, allowing performance comparisons under the constraint of equal average transmission power. Simulation results, including an IC mechanism described in the paper, substantiate the validity of the analysis and confirm the high efficiency of the proposed approach down to a signal-to-noise ratio as a low as Eb/N0=2 dB.

Protograph LDPC Codes Design Based on EXIT Analysis

In this paper, a novel extrinsic information transfer (EXIT) analysis is presented for protograph-based and multi- edge type low-density parity-check (LDPC) codes. A protograph defines a subset of an LDPCC ensemble (identified by the degree distributions of the bipartite graph), introducing further constraints about the edge connections. For many codes belonging to this class, the conventional approach based on EXIT charts cannot be applied. The proposed EXIT analysis takes into account edge connections, permitting the decoding convergence evaluation for protograph-based LDPC codes, allowing the design of highly-structured capacity approaching LDPC codes.

Quasi-Cyclic Generalized LDPC Codes With Low Error Floors

In this paper, a novel methodology for designing structured generalized LDPC (G-LDPC) codes is presented. The proposed design results in quasi-cyclic G-LDPC codes for which efficient encoding is feasible through shift-register-based circuits. The structure imposed on the bipartite graphs, together with the choice of simple component codes, leads to a class of codes suitable for fast iterative decoding. A pragmatic approach to the construction of G-LDPC codes is proposed. The approach is based on the substitution of check nodes in the protograph of a low-density parity-check code with stronger nodes based, for instance, on Hamming codes. Such a design approach, which we call LDPC code doping, leads to low-rate quasi-cyclic G-LDPC codes with excellent performance in both the error floor and waterfall regions on the additive white Gaussian noise channel.

Coded Slotted ALOHA: A Graph-Based Method for Uncoordinated Multiple Access

In this paper, a random access scheme is introduced, which relies on the combination of packet erasure correcting codes and successive interference cancellation (SIC). The scheme is named coded slotted ALOHA. A bipartite graph representation of the SIC process, resembling iterative decoding of generalized low-density parity-check codes over the erasure channel, is exploited to optimize the selection probabilities of the component erasure correcting codes through a density evolution analysis. The capacity (in packets per slot) of the scheme is then analyzed in the context of the collision channel without feedback. Moreover, a capacity bound is developed, and component code distributions tightly approaching the bound are derived.

Performance versus overhead for fountain codes over F q

Fountain codes for packet erasure recovery are investigated over Galois fields of order q ¿ 2. It is shown through development of tight upper and lower bounds on the decoding failure probability under maximum likelihood decoding, that the adoption of higher order Galois fields is beneficial, in terms of performance, for linear random fountain codes. Moreover, it is illustrated how Raptor codes can provide performances very close to those of random fountain codes, with an affordable encoding and decoding complexity. Non-binary Raptor codes turn out to represent an appealing option for applications requiring severe constraints in terms of performance versus overhead, especially for small source block sizes.

Non-Linear Interference Mitigation for Broadband Multimedia Satellite Systems

This contribution explores the use of interference mitigation techniques applied to broadband satellite systems with co-channel interference. In particular, our focus is on nonlinear precoding techniques, borrowing ideas from the theory of broadcast MIMO channels. A number of schemes are compared, including several implementations of Tomlinson-Harashima precoding and their linear precoding counterparts. Simulations on realistic scenarios show potential improvements of non-linear precoding with respect to linear interference mitigation and classical countermeasures based on frequency division among beams. Also, we identify several practical issues related to the implementation of Tomlinson-Harashima Precoding in satellite communication systems.

Coded random access: applying codes on graphs to design random access protocols

The rise of machine-to-machine communications has rekindled interest in random access protocols as a support for a massive number of uncoordinatedly transmitting devices. The legacy ALOHA approach is developed under a collision model, where slots containing collided packets are considered as waste. However, if the common receiver (e.g. base station) is able to store the collision slots and use them in a transmission recovery process based on successive interference cancellation, the design space for access protocols is radically expanded. We present the paradigm of coded random access, in which the structure of the access protocol can be mapped to a structure of an erasure-correcting code defined on a graph. This opens the possibility to use coding theory and tools for designing efficient random access protocols, offering markedly better performance than ALOHA. Several instances of coded random access protocols are described, as well as a case study on how to upgrade a legacy ALOHA system using the ideas of coded random access.

Generalized IRA Erasure Correcting Codes for Hybrid Iterative/Maximum Likelihood Decoding

The design of low-density parity-check (LDPC) codes under hybrid iterative / maximum likelihood decoding is addressed for the binary erasure channel (BEC). Specifically, we focus on generalized irregular repeat-accumulate (GeIRA) codes, which offer both efficient encoding and design flexibility. We show that properly designed GeIRA codes tightly approach the performance of an ideal maximum distance separable (MDS) code, even for short block sizes. For example, our (2048,1024) code reaches a codeword error rate of 10-5 at channel erasure probability isin= 0.450, where an ideal (2048,1024) MDS code would reach the same error rate at isin = 0.453.

Maximum Likelihood Erasure Decoding of LDPC Codes: Pivoting Algorithms and Code Design

This paper investigates efficient maximum-likelihood (ML) decoding of low-density parity-check (LDPC) codes over erasure channels. A set of algorithms, referred to as pivoting algorithms, is developed. The aim is to limit the average number of pivots (or reference variables) from which all the other erased symbols are recovered iteratively. The suggested algorithms exhibit different trade-offs between complexity of the pivoting phase and average number of pivots. Moreover, a systematic procedure to design LDPC code ensembles for efficient ML decoding is proposed. Numerical results illustrate that the designed LDPC codes achieve a near-optimum performance (very close to the Singleton bound, at least down to a codeword error rate level 10-8) with an affordable decoding complexity. For one of the presented codes and algorithms, a software implementation has been developed which is capable to provide data rates above 1.5 Gbps on a commercial computing platform.

Reliability Options for Data Communications in the Future Deep-Space Missions

Availability of higher capacity for both uplinks and downlinks is expected in the future deep-space missions on Mars, thus enabling a large range of services that could eventually support human remote operations. The provisioning for deep-space links offering data rate up to several megabits per second will be a crucial element to allow new services for the space domain along with the common telecommand and telemetry services with enhanced communication capabilities. On the other hand, also the geometry proper of this scenario with orbiting and landed elements sharing only partial visibility among them and towards Earth provides another challenge. This paper surveys the reliability options that are available in the Consultative Committee for Space Data Systems (CCSDS) Protocol Stack for application in the deep-space missions. In particular, the solutions implemented from the physical up to the application layer are illustrated in terms of channel coding and Automatic Retransmission reQuest (ARQ) schemes. Finally, advanced reliability strategies possibly applicable in next-generation deep-space missions are explored as well.