A Decoding Algorithm for LDPC Codes Over Erasure Channels with Sporadic Errors

none4An efficient decoding algorithm for low-density parity-check (LDPC) codes on erasure channels with sporadic errors (i.e., binary error-and-erasure channels with error probability much smaller than the erasure probability) is proposed and its performance analyzed. A general single-error multiple-erasure (SEME) decoding algorithm is first described, which may be in principle used with any binary linear block code. The algorithm is optimum whenever the non-erased part of the received word is affected by at most one error, and is capable of performing error detection of multiple errors. An upper bound on the average block error probability under SEME decoding is derived for the linear random code ensemble. The bound is tight and easy to implement. The algorithm is then adapted to LDPC codes, resulting in a simple modification to a previously proposed efficient maximum likelihood LDPC erasure decoder which exploits the parity-check matrix sparseness. Numerical results reveal that LDPC codes under efficient SEME decoding can closely approach the average performance of random codes.noneG. Liva; E. Paolini; B. Matuz; M. ChianiG. Liva; E. Paolini; B. Matuz; M. Chian

Protograph-Based LDPC Code Design for Ternary Message Passing Decoding

A ternary message passing (TMP) decoding algorithm for low-density parity-check codes is developed. All messages exchanged between variable and check nodes have a ternary alphabet, and the variable nodes exploit soft information from the channel. A density evolution analysis is developed for unstructured and protograph-based ensembles. For unstructured ensembles the stability condition is derived. Optimized ensembles for TMP decoding show asymptotic gains of up to 0.6 dB with respect to ensembles optimized for binary message passing decoding. Finite length simulations of codes from TMP-optimized ensembles show gains of up to 0.5 dB under TMP compared to protograph-based codes designed for unquantized belief propagation decoding

On the Application of the Baum-Welch Algorithm for Modeling the Land Mobile Satellite Channel

Accurate channel models are of high importance for the design of upcoming mobile satellite systems. Nowadays most of the models for the LMSC are based on Markov chains and rely on measurement data, rather than on pure theoretical considerations. A key problem lies in the determination of the model parameters out of the observed data. In this work we face the issue of state identification of the underlying Markov model whose model parameters are a priori unknown. This can be seen as a HMM problem. For finding the ML estimates of such model parameters the BW algorithm is adapted to the context of channel modeling. Numerical results on test data sequences reveal the capabilities of the proposed algorithm. Results on real measurement data are finally presented.Comment: IEEE Globecom 201

Irregular Invertible Bloom Look-Up Tables

We consider invertible Bloom lookup tables (IBLTs) which are probabilistic data structures that allow to store keyvalue pairs. An IBLT supports insertion and deletion of key-value pairs, as well as the recovery of all key-value pairs that have been inserted, as long as the number of key-value pairs stored in the IBLT does not exceed a certain number. The recovery operation on an IBLT can be represented as a peeling process on a bipartite graph. We present a density evolution analysis of IBLTs which allows to predict the maximum number of key-value pairs that can be inserted in the table so that recovery is still successful with high probability. This analysis holds for arbitrary irregular degree distributions and generalizes results in the literature. We complement our analysis by numerical simulations of our own IBLT design which allows to recover a larger number of keyvalue pairs as state-of-the-art IBLTs of same size

Analysis of Symbol Message Passing LDPC Decoder for the Poisson PPM Channel

A simple decoding algorithm, dubbed symbol mes- sage passing decoder, is studied for q-ary low-density parity-check codes over the q-ary Poisson pulse-position modulation channel. The messages in the decoder are symbols from the finite field Fq . To improve performance, a second decoder with an extended message set {E ∪ Fq } is also investigated, where E denotes an erasure. Thresholds within 1.3 dB from the Shannon limit are obtained for low field orders

Coherent Communications for Free Space Optical Low-Earth Orbit Downlinks

This work addresses physical layer design aspects of coherent free-space optical downlinks from low-earth orbit satellites to ground. Achievable information rates are derived and assessed that include the availability of diversity, shaping, bitmetric decoding, repetition coding and automatic repeat request with maximum-ratio combining. A channel coding scheme is presented that approaches the theoretic limits within 1 dB. Extrinsic information transfer analysis for the free-space optical fading channel shows that a code design tailored to the additive white Gaussian noise channel is robust for fading channels with various parameters

An Efficient NB-LDPC Decoder Architecture for Space Telecommand Links

In the frame of error correction in space telecommand (TC) links, the Consultative Committee for Space Data Systems (CCSDS) currently recommends short block-length BCH and binary LDPC codes. Other alternatives have been discarded due to their high decoding complexity, such as LDPC and eBCH codes with MRB decoding and NB-LDPC codes. NBLDPC codes perform better than their binary counterparts over AWGN and jamming channels, being excellent candidates for space communications. In this brief, we show the feasibility of NB-LDPC coding for space TC applications by proposing a highly efficient decoding architecture. The proposed decoder is implemented for a (128,64) NB-LDPC code over GF(16) and the design is particularized for a space-certified Virtex-5QV FPGA. The results prove that NB-LDPC coding is an alternative outperforming the standardized binary LDPC at a reasonable cost. Given that the maximum rate for TC recommended by the CCSDS is 2 Mbps, the proposed architecture achieves a throughput of 2.4 Mbps using only 8797 LUTs and 5460 FFs (no dedicated memories are used). In addition, this architecture is suitable for any regular (2,4) NB-LDPC (128,64) code over GF(16) independently of the H matrix, allowing great flexibility for the use with the recently proposed short block-length NBLDPC codes in upcoming telecommand uplink standards

Rate-Adaptive Protograph MacKay-Neal Codes

A class of rate-adaptive protograph MacKay-Neal (MN) codes is introduced and analyzed. The code construction employs an outer distribution matcher (DM) to adapt the rate of the scheme. The DM is coupled with an inner protograph-based low-density parity-check (LDPC) code, whose base matrix is optimized via density evolution analysis to approach the Shannon limit of the binary-input additive white Gaussian noise (biAWGN) channel over a given range of code rates. The density evolution analysis is complemented by finite-length simulations, and by a study of the error floor performance

One and Two Bit Message Passing for SC-LDPC Codes with Higher-Order Modulation

Low complexity decoding algorithms are necessary to meet data rate requirements in excess of 1 Tbps. In this paper, we study one and two bit message passing algorithms for belief propagation decoding of low-density parity-check (LDPC) codes and analyze them by density evolution. The variable nodes (VNs) exploit soft information from the channel output. To decrease the data flow, the messages exchanged between check nodes (CNs) and VNs are represented by one or two bits. The newly proposed quaternary message passing (QMP) algorithm is compared asymptotically and in finite length simulations to binary message passing (BMP) and ternary message passing (TMP) for spectrally efficient communication with higher-order modulation and probabilistic amplitude shaping (PAS). To showcase the potential for high throughput forward error correction, spatially coupled LDPC codes and a target spectral efficiency (SE) of 3 bits/QAM symbol are considered. Gains of about 0.7 dB and 0.1 dB are observed compared to BMP and TMP, respectively. The gap to unquantized belief propagation (BP) decoding is reduced to about 0.75 dB. For smaller code rates, the gain of QMP compared to TMP is more pronounced and amounts to 0.24 dB in the considered example.Comment: Accepted for IEEE/OSA Journal on Lightwave Technolog