On the Design of Punctured Low Density Parity Check Codes for Variable Rate Systems

The authors face the problem of designing good LDPC codes for applications requiring variable, that is adaptive, rates. More precisely, the object of the paper is twofold. On one hand, we propose a deterministic (not random) procedure to construct good LDPC codes without constraints on the code dimension and rate. The method is based on the analysis and optimization of the local cycles length in the Tanner graph and gives the designer the chance to control complexity of the designed codes. On the other hand, we present a novel puncturing strategy which acts directly on the parity check matrix of the code, starting from the lowest rate needed, in order to allow the design of higher rate codes avoiding additional complexity of the co/decoding hardware. The efficiency of the proposed solution is tested through a number of numerical simulations. In particular, the puncturing strategy is applied for designing codes with rate variable between 0.715 and 0.906. The designed codes are used in conjunction with M-QAM constellations through a pragmatic approach that, however, yields very promising results

Spinal codes

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2012.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from PDF student-submitted version of thesis.Includes bibliographical references (p. 52-55).Spinal codes are a new class of rateless codes that enable wireless networks to cope with time-varying channel conditions in a natural way, without requiring any explicit bit rate selection. The key idea in the code is the sequential application of a pseudo-random hash function to the message bits, to produce a sequence of coded symbols for transmission. This encoding ensures that two input messages that differ in even one bit lead to very different coded sequences after the point at which they differ, providing good resilience to noise and bit errors. To decode spinal codes, we develop an approximate maximum-likelihood decoder, called the bubble decoder, which runs in time polynomial in the message size and achieves the Shannon capacity over both additive white Gaussian noise (AWGN) and binary symmetric channel (BSC) models. The decoder trades off throughput for computation (hardware area or decoding time), allowing the decoder to scale gracefully with available hardware resources. Experimental results obtained from a software implementation of a linear-time decoder show that spinal codes achieve higher throughput than fixed-rate LDPC codes [11], rateless Raptor codes [35], and the layered rateless coding approach [8] of Strider [12], across a wide range of channel conditions and message sizes. An early hardware prototype that can decode at 10 Mbits/s in FPGA demonstrates that spinal codes are a practical construction.by Jonathan Perry.S.M

Iterative algorithms for lossy source coding

Thesis (M. Eng. and S.B.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (p. 65-68).This thesis explores the problems of lossy source coding and information embedding. For lossy source coding, we analyze low density parity check (LDPC) codes and low density generator matrix (LDGM) codes for quantization under a Hamming distortion. We prove that LDPC codes can achieve the rate-distortion function. We also show that the variable node degree of any LDGM code must become unbounded for these codes to come arbitrarily close to the rate-distortion bound. For information embedding, we introduce the double-erasure information embedding channel model. We develop capacity-achieving codes for the double-erasure channel model. Furthermore, we show that our codes can be efficiently encoded and decoded using belief propagation techniques. We also discuss a generalization of the double-erasure model which shows that the double-erasure model is closely related to other models considered in the literature.by Venkat Chandar.M.Eng.and S.B

Integrating spinal codes into wireless systems

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2013.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (p. 85-88).Rateless spinal codes [47] promise performance gains for future wireless systems. These gains can be realized in the form of higher data rates, longer operational ranges, reduced power consumption, and greater reliability. This is due in part to the manner in which rateless codes exploit the instantaneous characteristics of the wireless medium, including unpredictable fluctuations. By contrast, traditional rated codes can accommodate variability only by making overly conservative assumptions. Before spinal codes reach practical deployment, they must be integrated into the networking stacks of real devices, and they must be instantiated in compact, ecient silicon. This thesis addresses fundamental challenges in each of these two areas, covering a body of work reported in previous publications by this author and others [27, 26]. On the networking side, this thesis explores a rateless analogue of link-layer retransmission schemes, capturing the idea of rate adaptation and generalizing the approach of hybrid ARQ/incremental redundancy systems such as LTE [29]. On the silicon side, this thesis presents the development of a VLSI architecture that exploits the inherent parallelism of the spinal decoder.by Peter Anthony Iannucci.S.M

A hybrid packet loss recovery technique in wireless ad hoc networks

TCP utilization in wireless networks poses certain problems due to its inability to distinguish packet losses caused by congestion from those caused by frequent wireless errors, leading to degraded network performance. To avoid these problems and to minimize the effect of intensive channel contention in wireless networks, this work presents a new Hybrid ARQ technique for reliable and efficient packets transfer in static wireless ad hoc network. It is a combination of recent FEC based Raptor coding technique with ARQ based selective retransmission method, which outperforms purely ARQ based method. In contrast to most Hybrid ARQ techniques, which usually employ a byte level FEC, we mostly use packet level FEC in our simulations for the data transfer, on top of less frequent ARQ to recover the residual errors. Existing packet level FEC methods are mostly based on simple parity check codes or Reed Solomon codes with erasure decoding; in this work we use the recent raptor codes. We also introduce the notion of adaptive redundancy which helps to achieve better average network performance and to further improve the redundancy efficiency

Joint source-channel-network coding in wireless mesh networks with temporal reuse

Technological innovation that empowers tiny low-cost transceivers to operate with a high degree of utilisation efficiency in multihop wireless mesh networks is contributed in this dissertation. Transmission scheduling and joint source-channel-network coding are two of the main aspects that are addressed. This work focuses on integrating recent enhancements such as wireless network coding and temporal reuse into a cross-layer optimisation framework, and to design a joint coding scheme that allows for space-optimal transceiver implementations. Link-assigned transmission schedules with timeslot reuse by multiple links in both the space and time domains are investigated for quasi-stationary multihop wireless mesh networks with both rate and power adaptivity. Specifically, predefined cross-layer optimised schedules with proportionally fair end-to-end flow rates and network coding capability are constructed for networks operating under the physical interference model with single-path minimum hop routing. Extending transmission rights in a link-assigned schedule allows for network coding and temporal reuse, which increases timeslot usage efficiency when a scheduled link experiences packet depletion. The schedules that suffer from packet depletion are characterised and a generic temporal reuse-aware achievable rate region is derived. Extensive computational experiments show improved schedule capacity, quality of service, power efficiency and benefit from opportunistic bidirectional network coding accrued with schedules optimised in the proposed temporal reuse-aware convex capacity region. The application of joint source-channel coding, based on fountain codes, in the broadcast timeslot of wireless two-way network coding is also investigated. A computationally efficient subroutine is contributed to the implementation of the fountain compressor, and an error analysis is done. Motivated to develop a true joint source-channel-network code that compresses, adds robustness against channel noise and network codes two packets on a single bipartite graph and iteratively decodes the intended packet on the same Tanner graph, an adaptation of the fountain compressor is presented. The proposed code is shown to outperform a separated joint source-channel and network code in high source entropy and high channel noise regions, in anticipated support of dense networks that employ intelligent signalling. AFRIKAANS : Tegnologiese innovasie wat klein lae-koste kommunikasie toestelle bemagtig om met ’n hoë mate van benuttings doeltreffendheid te werk word bygedra in hierdie proefskrif. Transmissie-skedulering en gesamentlike bron-kanaal-netwerk kodering is twee van die belangrike aspekte wat aangespreek word. Hierdie werk fokus op die integrasie van onlangse verbeteringe soos draadlose netwerk kodering en temporêre herwinning in ’n tussen-laag optimaliserings raamwerk, en om ’n gesamentlike kodering skema te ontwerp wat voorsiening maak vir spasie-optimale toestel implementerings. Skakel-toegekende transmissie skedules met tydgleuf herwinning deur veelvuldige skakels in beide die ruimte en tyd domeine word ondersoek vir kwasi-stilstaande, veelvuldige-sprong draadlose rooster netwerke met beide transmissie-spoed en krag aanpassings. Om spesifiek te wees, word vooraf bepaalde tussen-laag geoptimiseerde skedules met verhoudings-regverdige punt-tot-punt vloei tempo’s en netwerk kodering vermoë saamgestel vir netwerke wat bedryf word onder die fisiese inmengings-model met enkel-pad minimale sprong roetering. Die uitbreiding van transmissie-regte in ’n skakel-toegekende skedule maak voorsiening vir netwerk kodering en temporêre herwinning, wat tydgleuf gebruiks-doeltreffendheid verhoog wanneer ’n geskeduleerde skakel pakkie-uitputting ervaar. Die skedules wat ly aan pakkie-uitputting word gekenmerk en ’n generiese temporêre herwinnings-bewuste haalbare transmissie-spoed gebied word afgelei. Omvattende berekenings-eksperimente toon verbeterde skedulerings kapasiteit, diensgehalte, krag doeltreffendheid asook verbeterde voordeel wat getrek word uit opportunistiese tweerigting netwerk kodering met die skedules wat geoptimiseer word in die temporêre herwinnings-bewuste konvekse transmissie-spoed gebied. Die toepassing van gesamentlike bron-kanaal kodering, gebaseer op fontein kodes, in die uitsaai-tydgleuf van draadlose tweerigting netwerk kodering word ook ondersoek. ’n Berekenings-effektiewe subroetine word bygedra in die implementering van die fontein kompressor, en ’n foutanalise word gedoen. Gemotiveer om ’n ware gesamentlike bron-kanaal-netwerk kode te ontwikkel, wat robuustheid byvoeg teen kanaal geraas en twee pakkies netwerk kodeer op ’n enkele bipartiete grafiek en die beoogde pakkie iteratief dekodeer op dieselfde Tanner grafiek, word ’n aanpassing van die fontein kompressor aangebied. Dit word getoon dat die voorgestelde kode ’n geskeide gesamentlike bron-kanaal en netwerk kode in hoë bron-entropie en ho¨e kanaal-geraas gebiede oortref in verwagte ondersteuning van digte netwerke wat van intelligente sein-metodes gebruik maak.Dissertation (MEng)--University of Pretoria, 2011.Electrical, Electronic and Computer Engineeringunrestricte

Near-capacity fixed-rate and rateless channel code constructions

Fixed-rate and rateless channel code constructions are designed for satisfying conflicting design tradeoffs, leading to codes that benefit from practical implementations, whilst offering a good bit error ratio (BER) and block error ratio (BLER) performance. More explicitly, two novel low-density parity-check code (LDPC) constructions are proposed; the first construction constitutes a family of quasi-cyclic protograph LDPC codes, which has a Vandermonde-like parity-check matrix (PCM). The second construction constitutes a specific class of protograph LDPC codes, which are termed as multilevel structured (MLS) LDPC codes. These codes possess a PCM construction that allows the coexistence of both pseudo-randomness as well as a structure requiring a reduced memory. More importantly, it is also demonstrated that these benefits accrue without any compromise in the attainable BER/BLER performance. We also present the novel concept of separating multiple users by means of user-specific channel codes, which is referred to as channel code division multiple access (CCDMA), and provide an example based on MLS LDPC codes. In particular, we circumvent the difficulty of having potentially high memory requirements, while ensuring that each user’s bits in the CCDMA system are equally protected. With regards to rateless channel coding, we propose a novel family of codes, which we refer to as reconfigurable rateless codes, that are capable of not only varying their code-rate but also to adaptively modify their encoding/decoding strategy according to the near-instantaneous channel conditions. We demonstrate that the proposed reconfigurable rateless codes are capable of shaping their own degree distribution according to the nearinstantaneous requirements imposed by the channel, but without any explicit channel knowledge at the transmitter. Additionally, a generalised transmit preprocessing aided closed-loop downlink multiple-input multiple-output (MIMO) system is presented, in which both the channel coding components as well as the linear transmit precoder exploit the knowledge of the channel state information (CSI). More explicitly, we embed a rateless code in a MIMO transmit preprocessing scheme, in order to attain near-capacity performance across a wide range of channel signal-to-ratios (SNRs), rather than only at a specific SNR. The performance of our scheme is further enhanced with the aid of a technique, referred to as pilot symbol assisted rateless (PSAR) coding, whereby a predetermined fraction of pilot bits is appropriately interspersed with the original information bits at the channel coding stage, instead of multiplexing pilots at the modulation stage, as in classic pilot symbol assisted modulation (PSAM). We subsequently demonstrate that the PSAR code-aided transmit preprocessing scheme succeeds in gleaning more information from the inserted pilots than the classic PSAM technique, because the pilot bits are not only useful for sounding the channel at the receiver but also beneficial for significantly reducing the computational complexity of the rateless channel decoder