Stability of Iterative Decoding of Multi-Edge Type Doubly-Generalized LDPC Codes Over the BEC

Using the EXIT chart approach, a necessary and sufficient condition is developed for the local stability of iterative decoding of multi-edge type (MET) doubly-generalized low-density parity-check (D-GLDPC) code ensembles. In such code ensembles, the use of arbitrary linear block codes as component codes is combined with the further design of local Tanner graph connectivity through the use of multiple edge types. The stability condition for these code ensembles is shown to be succinctly described in terms of the value of the spectral radius of an appropriately defined polynomial matrix.Comment: 6 pages, 3 figures. Presented at Globecom 2011, Houston, T

On a Class of Doubly-Generalized LDPC Codes with Single Parity-Check Variable Nodes

A class of doubly-generalized low-density parity-check (D-GLDPC) codes, where single parity-check (SPC) codes are used as variable nodes (VNs), is investigated. An expression for the growth rate of the weight distribution of any D-GLDPC ensemble with a uniform check node (CN) set is presented at first, together with an analytical technique for its efficient evaluation. These tools are then used for detailed analysis of a case study, namely, a rate-1/2 D-GLDPC ensemble where all the CNs are (7,4) Hamming codes and all the VNs are length-7 SPC codes. It is illustrated how the VN representations can heavily affect the code properties and how different VN representations can be combined within the same graph to enhance some of the code parameters. The analysis is conducted over the binary erasure channel. Interesting features of the new codes include the capability of achieving a good compromise between waterfall and error floor performance while preserving graphical regularity, and values of threshold outperforming LDPC counterparts.Comment: 2009 IEEE Int. Symp. on Information Theory. 5 pages, 3 figure

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 via 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.Comment: The final version to appear in IEEE Trans. Inf. Theory. 18 pages, 10 figure

Bilayer Low-Density Parity-Check Codes for Decode-and-Forward in Relay Channels

This paper describes an efficient implementation of binning for the relay channel using low-density parity-check (LDPC) codes. We devise bilayer LDPC codes to approach the theoretically promised rate of the decode-and-forward relaying strategy by incorporating relay-generated information bits in specially designed bilayer graphical code structures. While conventional LDPC codes are sensitively tuned to operate efficiently at a certain channel parameter, the proposed bilayer LDPC codes are capable of working at two different channel parameters and two different rates: that at the relay and at the destination. To analyze the performance of bilayer LDPC codes, bilayer density evolution is devised as an extension of the standard density evolution algorithm. Based on bilayer density evolution, a design methodology is developed for the bilayer codes in which the degree distribution is iteratively improved using linear programming. Further, in order to approach the theoretical decode-and-forward rate for a wide range of channel parameters, this paper proposes two different forms bilayer codes, the bilayer-expurgated and bilayer-lengthened codes. It is demonstrated that a properly designed bilayer LDPC code can achieve an asymptotic infinite-length threshold within 0.24 dB gap to the Shannon limits of two different channels simultaneously for a wide range of channel parameters. By practical code construction, finite-length bilayer codes are shown to be able to approach within a 0.6 dB gap to the theoretical decode-and-forward rate of the relay channel at a block length of $10^5$ and a bit-error probability (BER) of $10^{-4}$. Finally, it is demonstrated that a generalized version of the proposed bilayer code construction is applicable to relay networks with multiple relays.Comment: Submitted to IEEE Trans. Info. Theor

Design of LDPC Code Ensembles with Fast Convergence Properties

The design of low-density parity-check (LDPC) code ensembles optimized for a finite number of decoder iterations is investigated. Our approach employs EXIT chart analysis and differential evolution to design such ensembles for the binary erasure channel and additive white Gaussian noise channel. The error rates of codes optimized for various numbers of decoder iterations are compared and it is seen that in the cases considered, the best performance for a given number of decoder iterations is achieved by codes which are optimized for this particular number. The design of generalized LDPC (GLDPC) codes is also considered, showing that these structures can offer better performance than LDPC codes for low-iteration-number designs. Finally, it is illustrated that LDPC codes which are optimized for a small number of iterations exhibit significant deviations in terms of degree distribution and weight enumerators with respect to LDPC codes returned by more conventional design tools.Comment: 6 pages, 5 figures, Submitted to the 3rd International Black Sea Conference on Communications and Networking (IEEE BlackSeaCom 2015

EBP-GEXIT charts over the binary-input AWGN channel for generalized and doubly-generalized LDPC codes

This work proposes a tractable evaluation of the maximum a posteriori (MAP) threshold of sparse-graph ensembles, by using an approximation for the extended belief propagation generalized extrinsic information transfer (EBP-GEXIT) function, first proposed by Measson et al. The approximation allows to find a MAP threshold in such numerically involved cases as the binary-input additive white Gaussian noise (AWGN) channel, graph ensembles with general component codes and/or irregularities. The paper contains examples of estimations of the MAP thresholds in the case of irregular low-density parity-check (LDPC), generalized LDPC, and doubly generalized LDPC codes ensembles. Our estimations are confirmed by numerical simulations

On design of doubly-generalized LDPC codes based on multi-type information functions

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Factor Graph Based Detection Schemes for Mobile Terrestrial DVB Systems with Long OFDM Blocks

This PhD dissertation analyzes the performance of second generation digital video broadcasting (DVB) systems in mobile terrestrial environments and proposes an iterative detection algorithm based on factor graphs (FG) to reduce the distortion caused by the time variation of the channel, providing error-free communication in very severe mobile conditions. The research work focuses on mobile scenarios where the intercarrier interference (ICI) is very high: high vehicular speeds when long orthogonal frequency-division multiplexing (OFDM) blocks are used. As a starting point, we provide the theoretical background on the main topics behind the transmission and reception of terrestrial digital television signals in mobile environments, along with a general overview of the main signal processing techniques included in last generation terrestrial DVB systems. The proposed FG-based detector design is then assessed over a simpli ed bit-interleaved coded modulation (BICM)-OFDM communication scheme for a wide variety of mobile environments. Extensive simulation results show the e ectiveness of the proposed belief propagation (BP) algorithm over the channels of interest in this research work. Moreover, assuming that low density parity-check (LDPC) codes are decoded by means of FG-based algorithms, a high-order FG is de ned in order to accomplish joint signal detection and decoding into the same FG framework, o ering a fully parallel structure very suitable when long OFDM blocks are employed. Finally, the proposed algorithms are analyzed over the physical layer of DVB-T2 speci cation. Two reception schemes are proposed which exploit the frequency and time-diversity inherent in time-varying channels with the aim of achieving a reasonable trade-o among performance, complexity and latency.Doktoretza tesi honek bigarren belaunaldiko telebista digitalaren eraginkortasuna aztertzen du eskenatoki mugikorrean, eta faktoreen grafoetan oinarritzen den hartzaile iteratibo bat proposatzen du denboran aldakorra den kanalak sortzen duen distortsioa leundu eta seinalea errorerik gabe hartzea ahalbidetzen duena. Proposatutako detektorea BICM-OFDM komunikazio eskema orokor baten gainean ebaluatu da lurreko broadcasting kanalaren baldintzak kontutan hartuz. Simulazio emaitzek algoritmo honen eraginkortasuna frogatzen dute Doppler frekuentzia handietan. Ikerketa lanaren bigarren zatian, faktoreen grafoetan oinarritutako detektorea eskema turbo zabalago baten baitan txertatu da LDPC dekodi katzaile batekin batera. Hartzaile diseinu honen abantaila nagusia da OFDM simbolo luzeetara ondo egokitzen dela. Azkenik, proposatutako algoritmoa DVB-T2 katearen baitan inplementatu da, bi hartzaile eskema proposatu direlarik seinaleak duen dibertsitate tenporal eta frekuentziala probesteko, beti ere eraginkortasunaren, konplexutasunaren eta latentziaren arteko konpromisoa mantenduz.Este trabajo de tesis analiza el rendimiento de la segunda generación de la televisión digital terreste en escenarios móviles y propone un algoritmo iterativo basado en grafos de factores para la detección de la señal y la reducción de la distorsión causada por la variación temporal del canal, permitiendo así recibir la señal libre de errores. El detector basado en grafos de factores propuesto es evaluado sobre un esquema de comunicaciones general BICM-OFDM en condiciones de transmisión propios de canales de difusión terrestres. Los resultados de simulación presentados muestran la e ciencia del algoritmo de detección propuesto en presencia de frecuencias Doppler muy altas. En una segunda parte del trabajo de investigación, el detector propuesto es incorporado a un esquema turbo junto con un decodi cador LDPC, dando lugar a un receptor iterativo que presenta características especialmente apropiadas para su implementación en sistemas OFDM con longitudes de símbolo elevadas. Por último, se analiza la implementación del algoritmo propuesto sobre la cadena de recepción de DVB-T2. Se presentan dos esquemas de recepción que explotan la diversidad temporal y frecuencial presentes en la señal afectada por canales variantes en el tiempo, consiguiendo un compromiso razonable entre rendimiento, complejidad y latencia