15 research outputs found

    Low-Density Graph Codes for slow fading Relay Channels

    Get PDF
    We study Low-Density Parity-Check (LDPC) codes with iterative decoding on block-fading (BF) Relay Channels. We consider two users that employ coded cooperation, a variant of decode-and-forward with a smaller outage probability than the latter. An outage probability analysis for discrete constellations shows that full diversity can be achieved only when the coding rate does not exceed a maximum value that depends on the level of cooperation. We derive a new code structure by extending the previously published full-diversity root-LDPC code, designed for the BF point-to-point channel, to exhibit a rate-compatibility property which is necessary for coded cooperation. We estimate the asymptotic performance through a new density evolution analysis and the word error rate performance is determined for finite length codes. We show that our code construction exhibits near-outage limit performance for all block lengths and for a range of coding rates up to 0.5, which is the highest possible coding rate for two cooperating users.Comment: Accepted for publication in IEEE Transactions on Information Theor

    ์ƒˆ๋กœ์šด ์†Œ์‹ค ์ฑ„๋„์„ ์œ„ํ•œ ์ž๊ธฐ๋™ํ˜• ๊ตฐ ๋ณตํ˜ธ๊ธฐ ๋ฐ ๋ถ€๋ถ„ ์ ‘์† ๋ณต๊ตฌ ๋ถ€ํ˜ธ ๋ฐ ์ผ๋ฐ˜ํ™”๋œ ๊ทผ ํ”„๋กœํ† ๊ทธ๋ž˜ํ”„ LDPC ๋ถ€ํ˜ธ์˜ ์„ค๊ณ„

    Get PDF
    ํ•™์œ„๋…ผ๋ฌธ (๋ฐ•์‚ฌ)-- ์„œ์šธ๋Œ€ํ•™๊ต ๋Œ€ํ•™์› : ๊ณต๊ณผ๋Œ€ํ•™ ์ „๊ธฐยท์ปดํ“จํ„ฐ๊ณตํ•™๋ถ€, 2019. 2. ๋…ธ์ข…์„ .In this dissertation, three main contributions are given asi) new two-stage automorphism group decoders (AGD) for cyclic codes in the erasure channel, ii) new constructions of binary and ternary locally repairable codes (LRCs) using cyclic codes and existing LRCs, and iii) new constructions of high-rate generalized root protograph (GRP) low-density parity-check (LDPC) codes for a nonergodic block interference and partially regular (PR) LDPC codes for follower noise jamming (FNJ), are considered. First, I propose a new two-stage AGD (TS-AGD) for cyclic codes in the erasure channel. Recently, error correcting codes in the erasure channel have drawn great attention for various applications such as distributed storage systems and wireless sensor networks, but many of their decoding algorithms are not practical because they have higher decoding complexity and longer delay. Thus, the AGD for cyclic codes in the erasure channel was introduced, which has good erasure decoding performance with low decoding complexity. In this research, I propose new TS-AGDs for cyclic codes in the erasure channel by modifying the parity check matrix and introducing the preprocessing stage to the AGD scheme. The proposed TS-AGD is analyzed for the perfect codes, BCH codes, and maximum distance separable (MDS) codes. Through numerical analysis, it is shown that the proposed decoding algorithm has good erasure decoding performance with lower decoding complexity than the conventional AGD. For some cyclic codes, it is shown that the proposed TS-AGD achieves the perfect decoding in the erasure channel, that is, the same decoding performance as the maximum likelihood (ML) decoder. For MDS codes, TS-AGDs with the expanded parity check matrix and the submatrix inversion are also proposed and analyzed. Second, I propose new constructions of binary and ternary LRCs using cyclic codes and existing two LRCs for distributed storage system. For a primitive work, new constructions of binary and ternary LRCs using cyclic codes and their concatenation are proposed. Some of proposed binary LRCs with Hamming weights 4, 5, and 6 are optimal in terms of the upper bounds. In addition, the similar method of the binary case is applied to construct the ternary LRCs with good parameters. Also, new constructions of binary LRCs with large Hamming distance and disjoint repair groups are proposed. The proposed binary linear LRCs constructed by using existing binary LRCs are optimal or near-optimal in terms of the bound with disjoint repair group. Last, I propose new constructions of high-rate GRP LDPC codes for a nonergodic block interference and anti-jamming PR LDPC codes for follower jamming. The proposed high-rate GRP LDPC codes are based on nonergodic two-state binary symmetric channel with block interference and Nakagami-mm block fading. In these channel environments, GRP LDPC codes have good performance approaching to the theoretical limit in the channel with one block interference, where their performance is shown by the channel threshold or the channel outage probability. In the proposed design, I find base matrices using the protograph extrinsic information transfer (PEXIT) algorithm. Also, the proposed new constructions of anti-jamming partially regular LDPC codes is based on follower jamming on the frequency-hopped spread spectrum (FHSS). For a channel environment, I suppose follower jamming with random dwell time and Rayleigh block fading environment with M-ary frequnecy shift keying (MFSK) modulation. For a coding perspective, an anti-jamming LDPC codes against follower jamming are introduced. In order to optimize the jamming environment, the partially regular structure and corresponding density evolution schemes are used. A series of simulations show that the proposed codes outperforms the 802.16e standard in the presence of follower noise jamming.์ด ๋…ผ๋ฌธ์—์„œ๋Š”, i) ์†Œ์‹ค ์ฑ„๋„์—์„œ ์ˆœํ™˜ ๋ถ€ํ˜ธ์˜ ์ƒˆ๋กœ์šด ์ด๋‹จ ์ž๊ธฐ๋™ํ˜• ๊ตฐ ๋ณตํ˜ธ๊ธฐ , ii) ๋ถ„์‚ฐ ์ €์žฅ ์‹œ์Šคํ…œ์„ ์œ„ํ•œ ์ˆœํ™˜ ๋ถ€ํ˜ธ ๋ฐ ๊ธฐ์กด์˜ ๋ถ€๋ถ„ ์ ‘์† ๋ณต๊ตฌ ๋ถ€ํ˜ธ(LRC)๋ฅผ ์ด์šฉํ•œ ์ด์ง„ ํ˜น์€ ์‚ผ์ง„ ๋ถ€๋ถ„ ์ ‘์† ๋ณต๊ตฌ ๋ถ€ํ˜ธ ์„ค๊ณ„๋ฒ•, ๋ฐ iii) ๋ธ”๋ก ๊ฐ„์„ญ ํ™˜๊ฒฝ์„ ์œ„ํ•œ ๊ณ ๋ถ€ํšจ์œจ์˜ ์ผ๋ฐ˜ํ™”๋œ ๊ทผ ํ”„๋กœํ† ๊ทธ๋ž˜ํ”„(generalized root protograph, GRP) LDPC ๋ถ€ํ˜ธ ๋ฐ ์ถ”์  ์žฌ๋ฐ ํ™˜๊ฒฝ์„ ์œ„ํ•œ ํ•ญ์žฌ๋ฐ ๋ถ€๋ถ„ ๊ท ์ผ (anti-jamming paritally regular, AJ-PR) LDPC ๋ถ€ํ˜ธ๊ฐ€ ์—ฐ๊ตฌ๋˜์—ˆ๋‹ค. ์ฒซ๋ฒˆ์งธ๋กœ, ์†Œ์‹ค ์ฑ„๋„์—์„œ ์ˆœํ™˜ ๋ถ€ํ˜ธ์˜ ์ƒˆ๋กœ์šด ์ด๋‹จ ์ž๊ธฐ๋™ํ˜• ๊ตฐ ๋ณตํ˜ธ๊ธฐ๋ฅผ ์ œ์•ˆํ•˜์˜€๋‹ค. ์ตœ๊ทผ ๋ถ„์‚ฐ ์ €์žฅ ์‹œ์Šคํ…œ ํ˜น์€ ๋ฌด์„  ์„ผ์„œ ๋„คํŠธ์›Œํฌ ๋“ฑ์˜ ์‘์šฉ์œผ๋กœ ์ธํ•ด ์†Œ์‹ค ์ฑ„๋„์—์„œ์˜ ์˜ค๋ฅ˜ ์ •์ • ๋ถ€ํ˜ธ ๊ธฐ๋ฒ•์ด ์ฃผ๋ชฉ๋ฐ›๊ณ  ์žˆ๋‹ค. ๊ทธ๋Ÿฌ๋‚˜ ๋งŽ์€ ๋ณตํ˜ธ๊ธฐ ์•Œ๊ณ ๋ฆฌ์ฆ˜์€ ๋†’์€ ๋ณตํ˜ธ ๋ณต์žก๋„ ๋ฐ ๊ธด ์ง€์—ฐ์œผ๋กœ ์ธํ•ด ์‹ค์šฉ์ ์ด์ง€ ๋ชปํ•˜๋‹ค. ๋”ฐ๋ผ์„œ ๋‚ฎ์€ ๋ณตํ˜ธ ๋ณต์žก๋„ ๋ฐ ๋†’์€ ์„ฑ๋Šฅ์„ ๋ณด์ผ ์ˆ˜ ์žˆ๋Š” ์ˆœํ™˜ ๋ถ€ํ˜ธ์—์„œ ์ด๋‹จ ์ž๊ธฐ ๋™ํ˜• ๊ตฐ ๋ณตํ˜ธ๊ธฐ๊ฐ€ ์ œ์•ˆ๋˜์—ˆ๋‹ค. ๋ณธ ์—ฐ๊ตฌ์—์„œ๋Š” ํŒจ๋ฆฌํ‹ฐ ๊ฒ€์‚ฌ ํ–‰๋ ฌ์„ ๋ณ€ํ˜•ํ•˜๊ณ , ์ „์ฒ˜๋ฆฌ ๊ณผ์ •์„ ๋„์ž…ํ•œ ์ƒˆ๋กœ์šด ์ด๋‹จ ์ž๊ธฐ๋™ํ˜• ๊ตฐ ๋ณตํ˜ธ๊ธฐ๋ฅผ ์ œ์•ˆํ•œ๋‹ค. ์ œ์•ˆํ•œ ๋ณตํ˜ธ๊ธฐ๋Š” perfect ๋ถ€ํ˜ธ, BCH ๋ถ€ํ˜ธ ๋ฐ ์ตœ๋Œ€ ๊ฑฐ๋ฆฌ ๋ถ„๋ฆฌ (maximum distance separable, MDS) ๋ถ€ํ˜ธ์— ๋Œ€ํ•ด์„œ ๋ถ„์„๋˜์—ˆ๋‹ค. ์ˆ˜์น˜ ๋ถ„์„์„ ํ†ตํ•ด, ์ œ์•ˆ๋œ ๋ณตํ˜ธ ์•Œ๊ณ ๋ฆฌ์ฆ˜์€ ๊ธฐ์กด์˜ ์ž๊ธฐ ๋™ํ˜• ๊ตฐ ๋ณตํ˜ธ๊ธฐ๋ณด๋‹ค ๋‚ฎ์€ ๋ณต์žก๋„๋ฅผ ๋ณด์ด๋ฉฐ, ๋ช‡๋ช‡์˜ ์ˆœํ™˜ ๋ถ€ํ˜ธ ๋ฐ ์†Œ์‹ค ์ฑ„๋„์—์„œ ์ตœ๋Œ€ ์šฐ๋„ (maximal likelihood, ML)๊ณผ ๊ฐ™์€ ์ˆ˜์ค€์˜ ์„ฑ๋Šฅ์ž„์„ ๋ณด์ธ๋‹ค. MDS ๋ถ€ํ˜ธ์˜ ๊ฒฝ์šฐ, ํ™•์žฅ๋œ ํŒจ๋ฆฌํ‹ฐ๊ฒ€์‚ฌ ํ–‰๋ ฌ ๋ฐ ์ž‘์€ ํฌ๊ธฐ์˜ ํ–‰๋ ฌ์˜ ์—ญ์—ฐ์‚ฐ์„ ํ™œ์šฉํ•˜์˜€์„ ๊ฒฝ์šฐ์˜ ์„ฑ๋Šฅ์„ ๋ถ„์„ํ•œ๋‹ค. ๋‘ ๋ฒˆ์งธ๋กœ, ๋ถ„์‚ฐ ์ €์žฅ ์‹œ์Šคํ…œ์„ ์œ„ํ•œ ์ˆœํ™˜ ๋ถ€ํ˜ธ ๋ฐ ๊ธฐ์กด์˜ ๋ถ€๋ถ„ ์ ‘์† ๋ณต๊ตฌ ๋ถ€ํ˜ธ (LRC)๋ฅผ ์ด์šฉํ•œ ์ด์ง„ ํ˜น์€ ์‚ผ์ง„ ๋ถ€๋ถ„ ์ ‘์† ๋ณต๊ตฌ ๋ถ€ํ˜ธ ์„ค๊ณ„๋ฒ•์„ ์ œ์•ˆํ•˜์˜€๋‹ค. ์ดˆ๊ธฐ ์—ฐ๊ตฌ๋กœ์„œ, ์ˆœํ™˜ ๋ถ€ํ˜ธ ๋ฐ ์—ฐ์ ‘์„ ํ™œ์šฉํ•œ ์ด์ง„ ๋ฐ ์‚ผ์ง„ LRC ์„ค๊ณ„ ๊ธฐ๋ฒ•์ด ์—ฐ๊ตฌ๋˜์—ˆ๋‹ค. ์ตœ์†Œ ํ•ด๋ฐ ๊ฑฐ๋ฆฌ๊ฐ€ 4,5, ํ˜น์€ 6์ธ ์ œ์•ˆ๋œ ์ด์ง„ LRC ์ค‘ ์ผ๋ถ€๋Š” ์ƒํ•œ๊ณผ ๋น„๊ตํ•ด ๋ณด์•˜์„ ๋•Œ ์ตœ์  ์„ค๊ณ„์ž„์„ ์ฆ๋ช…ํ•˜์˜€๋‹ค. ๋˜ํ•œ, ๋น„์Šทํ•œ ๋ฐฉ๋ฒ•์„ ์ ์šฉํ•˜์—ฌ ์ข‹์€ ํŒŒ๋ผ๋ฏธํ„ฐ์˜ ์‚ผ์ง„ LRC๋ฅผ ์„ค๊ณ„ํ•  ์ˆ˜ ์žˆ์—ˆ๋‹ค. ๊ทธ ์™ธ์— ๊ธฐ์กด์˜ LRC๋ฅผ ํ™œ์šฉํ•˜์—ฌ ํฐ ํ•ด๋ฐ ๊ฑฐ๋ฆฌ์˜ ์ƒˆ๋กœ์šด LRC๋ฅผ ์„ค๊ณ„ํ•˜๋Š” ๋ฐฉ๋ฒ•์„ ์ œ์•ˆํ•˜์˜€๋‹ค. ์ œ์•ˆ๋œ LRC๋Š” ๋ถ„๋ฆฌ๋œ ๋ณต๊ตฌ ๊ตฐ ์กฐ๊ฑด์—์„œ ์ตœ์ ์ด๊ฑฐ๋‚˜ ์ตœ์ ์— ๊ฐ€๊นŒ์šด ๊ฐ’์„ ๋ณด์˜€๋‹ค. ๋งˆ์ง€๋ง‰์œผ๋กœ, GRP LDPC ๋ถ€ํ˜ธ๋Š” Nakagami-mm ๋ธ”๋ก ํŽ˜์ด๋”ฉ ๋ฐ ๋ธ”๋ก ๊ฐ„์„ญ์ด ์žˆ๋Š” ๋‘ ์ƒํƒœ์˜ ์ด์ง„ ๋Œ€์นญ ์ฑ„๋„์„ ๊ธฐ๋ฐ˜์œผ๋กœ ํ•œ๋‹ค. ์ด๋Ÿฌํ•œ ์ฑ„๋„ ํ™˜๊ฒฝ์—์„œ GRP LDPC ๋ถ€ํ˜ธ๋Š” ํ•˜๋‚˜์˜ ๋ธ”๋ก ๊ฐ„์„ญ์ด ๋ฐœ์ƒํ–ˆ์„ ๊ฒฝ์šฐ, ์ด๋ก ์  ์„ฑ๋Šฅ์— ๊ฐ€๊นŒ์šด ์ข‹์€ ์„ฑ๋Šฅ์„ ๋ณด์—ฌ์ค€๋‹ค. ์ด๋Ÿฌํ•œ ์ด๋ก  ๊ฐ’์€ ์ฑ„๋„ ๋ฌธํ„ฑ๊ฐ’์ด๋‚˜ ์ฑ„๋„ outage ํ™•๋ฅ ์„ ํ†ตํ•ด ๊ฒ€์ฆํ•  ์ˆ˜ ์žˆ๋‹ค. ์ œ์•ˆ๋œ ์„ค๊ณ„์—์„œ๋Š”, ๋ณ€ํ˜•๋œ PEXIT ์•Œ๊ณ ๋ฆฌ์ฆ˜์„ ํ™œ์šฉํ•˜์—ฌ ๊ธฐ์ดˆ ํ–‰๋ ฌ์„ ์„ค๊ณ„ํ•œ๋‹ค. ๋˜ํ•œ AJ-PR LDPC ๋ถ€ํ˜ธ๋Š” ์ฃผํŒŒ์ˆ˜ ๋„์•ฝ ํ™˜๊ฒฝ์—์„œ ๋ฐœ์ƒํ•˜๋Š” ์ถ”์  ์žฌ๋ฐ์ด ์žˆ๋Š” ํ™˜๊ฒฝ์„ ๊ธฐ๋ฐ˜์œผ๋กœ ํ•œ๋‹ค. ์ฑ„๋„ ํ™˜๊ฒฝ์œผ๋กœ MFSK ๋ณ€๋ณต์กฐ ๋ฐฉ์‹์˜ ๋ ˆ์ผ๋ฆฌ ๋ธ”๋ก ํŽ˜์ด๋”ฉ ๋ฐ ๋ฌด์ž‘์œ„ํ•œ ์ง€์† ์‹œ๊ฐ„์ด ์žˆ๋Š” ์žฌ๋ฐ ํ™˜๊ฒฝ์„ ๊ฐ€์ •ํ•œ๋‹ค. ์ด๋Ÿฌํ•œ ์žฌ๋ฐ ํ™˜๊ฒฝ์œผ๋กœ ์ตœ์ ํ™”ํ•˜๊ธฐ ์œ„ํ•ด, ๋ถ€๋ถ„ ๊ท ์ผ ๊ตฌ์กฐ ๋ฐ ํ•ด๋‹น๋˜๋Š” ๋ฐ€๋„ ์ง„ํ™” (density evolution, DE) ๊ธฐ๋ฒ•์ด ํ™œ์šฉ๋œ๋‹ค. ์—ฌ๋Ÿฌ ์‹œ๋ฎฌ๋ ˆ์ด์…˜ ๊ฒฐ๊ณผ๋Š” ์ถ”์  ์žฌ๋ฐ์ด ์กด์žฌํ•˜๋Š” ํ™˜๊ฒฝ์—์„œ ์ œ์•ˆ๋œ ๋ถ€ํ˜ธ๊ฐ€ 802.16e์— ์‚ฌ์šฉ๋˜์—ˆ๋˜ LDPC ๋ถ€ํ˜ธ๋ณด๋‹ค ์„ฑ๋Šฅ์ด ์šฐ์ˆ˜ํ•จ์„ ๋ณด์—ฌ์ค€๋‹ค.Contents Abstract Contents List of Tables List of Figures 1 INTRODUCTION 1.1 Background 1.2 Overview of Dissertation 1.3 Notations 2 Preliminaries 2.1 IED and AGD for Erasure Channel 2.1.1 Iterative Erasure Decoder 2.1.1 Automorphism Group Decoder 2.2. Binary Locally Repairable Codes for Distributed Storage System 2.2.1 Bounds and Optimalities of Binary LRCs 2.2.2 Existing Optimal Constructions of Binary LRCs 2.3 Channels with Block Interference and Jamming 2.3.1 Channels with Block Interference 2.3.2 Channels with Jamming with MFSK and FHSS Environment. 3 New Two-Stage Automorphism Group Decoders for Cyclic Codes in the Erasure Channel 3.1 Some Definitions 3.2 Modification of Parity Check Matrix and Two-Stage AGD 3.2.1 Modification of the Parity Check Matrix 3.2.2 A New Two-Stage AGD 3.2.3 Analysis of Modification Criteria for the Parity Check Matrix 3.2.4 Analysis of Decoding Complexity of TS-AGD 3.2.5 Numerical Analysis for Some Cyclic Codes 3.3 Construction of Parity Check Matrix and TS-AGD for Cyclic MDS Codes 3.3.1 Modification of Parity Check Matrix for Cyclic MDS Codes . 3.3.2 Proposed TS-AGD for Cyclic MDS Codes 3.3.3 Perfect Decoding by TS-AGD with Expanded Parity Check Matrix for Cyclic MDS Codes 3.3.4 TS-AGD with Submatrix Inversion for Cyclic MDS Codes . . 4 New Constructions of Binary and Ternary LRCs Using Cyclic Codes and Existing LRCs 4.1 Constructions of Binary LRCs Using Cyclic Codes 4.2 Constructions of Linear Ternary LRCs Using Cyclic Codes 4.3 Constructions of Binary LRCs with Disjoint Repair Groups Using Existing LRCs 4.4 New Constructions of Binary Linear LRCs with d โ‰ฅ 8 Using Existing LRCs 5 New Constructions of Generalized RP LDPC Codes for Block Interference and Partially Regular LDPC Codes for Follower Jamming 5.1 Generalized RP LDPC Codes for a Nonergodic BI 5.1.1 Minimum Blockwise Hamming Weight 5.1.2 Construction of GRP LDPC Codes 5.2 Asymptotic and Numerical Analyses of GRP LDPC Codes 5.2.1 Asymptotic Analysis of LDPC Codes 5.2.2 Numerical Analysis of Finite-Length LDPC Codes 5.3 Follower Noise Jamming with Fixed Scan Speed 5.4 Anti-Jamming Partially Regular LDPC Codes for Follower Noise Jamming 5.4.1 Simplified Channel Model and Corresponding Density Evolution 5.4.2 Construction of AJ-PR-LDPC Codes Based on DE 5.5 Numerical Analysis of AJ-PR LDPC Codes 6 Conclusion Abstract (In Korean)Docto

    Analysis and construction of full-diversity joint network-LDPC codes for cooperative communications

    Get PDF
    Cooperative communication is a well known technique to yield transmit diversity and network coding can increase the spectral efficiency. These two techniques can be combined to achieve a double diversity order for a maximum coding rate Rc = 2/3 on the Multiple Access Relay Channel (MARC); Transmit diversity is necessary in harsh environments to reduce the required transmit power for achieving a given error performance at a certain transmission rate. In networks; where two sources share a common relay in their transmission to the destination. However; codes have to be carefully designed to obtain the intrinsic diversity offered by the MARC. This paper presents the principles to design a family of full-diversity LDPC codes with maximum rate. Simulation of the word error rate performance of the new proposed family of LDPC codes for the MARC confirms the full-diversity

    Near-capacity fixed-rate and rateless channel code constructions

    No full text
    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 userโ€™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

    Raptor Codes in the Low SNR Regime

    Full text link
    In this paper, we revisit the design of Raptor codes for binary input additive white Gaussian noise (BIAWGN) channels, where we are interested in very low signal to noise ratios (SNRs). A linear programming degree distribution optimization problem is defined for Raptor codes in the low SNR regime through several approximations. We also provide an exact expression for the polynomial representation of the degree distribution with infinite maximum degree in the low SNR regime, which enables us to calculate the exact value of the fractions of output nodes of small degrees. A more practical degree distribution design is also proposed for Raptor codes in the low SNR regime, where we include the rate efficiency and the decoding complexity in the optimization problem, and an upper bound on the maximum rate efficiency is derived for given design parameters. Simulation results show that the Raptor code with the designed degree distributions can approach rate efficiencies larger than 0.95 in the low SNR regime.Comment: Submitted to the IEEE Transactions on Communications. arXiv admin note: text overlap with arXiv:1510.0772

    Signal optimization for Galileo evolution

    Get PDF
    Global Navigation Satellite System (GNSS) are present in our daily lives. Moreover, new users areemerging with further operation needs involving a constant evolution of the current navigationsystems. In the current framework of Galileo (GNSS European system) and especially within theGalileo E1 Open Service (OS), adding a new acquisition aiding signal could contribute to providehigher resilience at the acquisition phase, as well as to reduce the time to first fix (TTFF).Designing a new GNSS signal is always a trade-off between several performance figures of merit.The most relevant are the position accuracy, the sensitivity and the TTFF. However, if oneconsiders that the signal acquisition phase is the goal to design, the sensitivity and the TTFF havea higher relevance. Considering that, in this thesis it is presented the joint design of a GNSS signaland the message structure to propose a new Galileo 2nd generation signal, which provides ahigher sensitivity in the receiver and reduce the TTFF. Several aspects have been addressed inorder to design a new signal component. Firstly, the spreading modulation definition must considerthe radio frequency compatibility in order to cause acceptable level of interference inside the band.Moreover, the spreading modulation should provide good correlation properties and goodresistance against the multipath in order to enhance the receiver sensitivity and to reduce theTTFF. Secondly, the choice of the new PRN code is also crucial in order to ease the acquisitionphase. A simple model criterion based on a weighted cost function is used to evaluate the PRNcodes performance. This weighted cost function takes into account different figures of merit suchas the autocorrelation, the cross-correlation and the power spectral density. Thirdly, the design ofthe channel coding scheme is always connected with the structure of the message. A joint designbetween the message structure and the channel coding scheme can provide both, reducing theTTFF and an enhancement of the resilience of the decoded data. In this this, a new method to codesign the message structure and the channel coding scheme for the new G2G signal isproposed. This method provides the guideline to design a message structure whose the channelcoding scheme is characterized by the full diversity, the Maximum Distance Separable (MDS) andthe rate compatible properties. The channel coding is essential in order to enhance the datademodulation performance, especially in harsh environments. However, this process can be verysensitive to the correct computation of the decoder input. Significant improvements were obtainedby considering soft inputs channel decoders, through the Log Likelihood Ratio LLRs computation.However, the complete knowledge of the channel state information (CSI) was usually considered,which it is infrequently in real scenarios. In this thesis, we provide new methods to compute LLRlinear approximations, under the jamming and the block fading channels, considering somestatistical CSI. Finally, to transmit a new signal in the same carrier frequency and using the sameHigh Power Amplifier (HPA) generates constraints in the multiplexing design, since a constant orquasi constant envelope is needed in order to decrease the non-linear distortions. Moreover, themultiplexing design should provide high power efficiency to not waste the transmitted satellitepower. Considering the precedent, in this thesis, we evaluate different multiplexing methods,which search to integrate a new binary signal in the Galileo E1 band while enhancing thetransmitted power efficiency. Besides that, even if the work is focused on the Galileo E1, many ofthe concepts and methodologies can be easily extended to any GNSS signa

    On Code Design for Interference Channels

    Get PDF
    abstract: There has been a lot of work on the characterization of capacity and achievable rate regions, and rate region outer-bounds for various multi-user channels of interest. Parallel to the developed information theoretic results, practical codes have also been designed for some multi-user channels such as multiple access channels, broadcast channels and relay channels; however, interference channels have not received much attention and only a limited amount of work has been conducted on them. With this motivation, in this dissertation, design of practical and implementable channel codes is studied focusing on multi-user channels with special emphasis on interference channels; in particular, irregular low-density-parity-check codes are exploited for a variety of cases and trellis based codes for short block length designs are performed. Novel code design approaches are first studied for the two-user Gaussian multiple access channel. Exploiting Gaussian mixture approximation, new methods are proposed wherein the optimized codes are shown to improve upon the available designs and off-the-shelf point-to-point codes applied to the multiple access channel scenario. The code design is then examined for the two-user Gaussian interference channel implementing the Han-Kobayashi encoding and decoding strategy. Compared with the point-to-point codes, the newly designed codes consistently offer better performance. Parallel to this work, code design is explored for the discrete memoryless interference channels wherein the channel inputs and outputs are taken from a finite alphabet and it is demonstrated that the designed codes are superior to the single user codes used with time sharing. Finally, the code design principles are also investigated for the two-user Gaussian interference channel employing trellis-based codes with short block lengths for the case of strong and mixed interference levels.Dissertation/ThesisDoctoral Dissertation Electrical Engineering 201

    Short-length Low-density Parity-check Codes: Construction and Decoding Algorithms

    Get PDF
    Error control coding is an essential part of modern communications systems. LDPC codes have been demonstrated to offer performance near the fundamental limits of channels corrupted by random noise. Optimal maximum likelihood decoding of LDPC codes is too complex to be practically useful even at short block lengths and so a graph-based message passing decoder known as the belief propagation algorithm is used instead. In fact, on graphs without closed paths known as cycles the iterative message passing decoding is known to be optimal and may converge in a single iteration, although identifying the message update schedule which allows single-iteration convergence is not trivial. At finite block lengths graphs without cycles have poor minimum distance properties and perform poorly even under optimal decoding. LDPC codes with large block length have been demonstrated to offer performance close to that predicted for codes of infinite length, as the cycles present in the graph are quite long. In this thesis, LDPC codes of shorter length are considered as they offer advantages in terms of latency and complexity, at the cost of performance degradation from the increased number of short cycles in the graph. For these shorter LDPC codes, the problems considered are: First, improved construction of structured and unstructured LDPC code graphs of short length with a view to reducing the harmful effects of the cycles on error rate performance, based on knowledge of the decoding process. Structured code graphs are particularly interesting as they allow benefits in encoding and decoding complexity and speed. Secondly, the design and construction of LDPC codes for the block fading channel, a particularly challenging scenario from the point of view of error control code design. Both established and novel classes of codes for the channel are considered. Finally the decoding of LDPC codes by the belief propagation algorithm is considered, in particular the scheduling of messages passed in the iterative decoder. A knowledge-aided approach is developed based on message reliabilities and residuals to allow fast convergence and significant improvements in error rate performance
    corecore