Construction of Near-Optimum Burst Erasure Correcting Low-Density Parity-Check Codes

In this paper, a simple, general-purpose and effective tool for the design of low-density parity-check (LDPC) codes for iterative correction of bursts of erasures is presented. The design method consists in starting from the parity-check matrix of an LDPC code and developing an optimized parity-check matrix, with the same performance on the memory-less erasure channel, and suitable also for the iterative correction of single bursts of erasures. The parity-check matrix optimization is performed by an algorithm called pivot searching and swapping (PSS) algorithm, which executes permutations of carefully chosen columns of the parity-check matrix, after a local analysis of particular variable nodes called stopping set pivots. This algorithm can be in principle applied to any LDPC code. If the input parity-check matrix is designed for achieving good performance on the memory-less erasure channel, then the code obtained after the application of the PSS algorithm provides good joint correction of independent erasures and single erasure bursts. Numerical results are provided in order to show the effectiveness of the PSS algorithm when applied to different categories of LDPC codes.Comment: 15 pages, 4 figures. IEEE Trans. on Communications, accepted (submitted in Feb. 2007

Windowed Decoding of Protograph-based LDPC Convolutional Codes over Erasure Channels

We consider a windowed decoding scheme for LDPC convolutional codes that is based on the belief-propagation (BP) algorithm. We discuss the advantages of this decoding scheme and identify certain characteristics of LDPC convolutional code ensembles that exhibit good performance with the windowed decoder. We will consider the performance of these ensembles and codes over erasure channels with and without memory. We show that the structure of LDPC convolutional code ensembles is suitable to obtain performance close to the theoretical limits over the memoryless erasure channel, both for the BP decoder and windowed decoding. However, the same structure imposes limitations on the performance over erasure channels with memory.Comment: 18 pages, 9 figures, accepted for publication in the IEEE Transactions on Information Theor

High-Throughput Random Access via Codes on Graphs

Recently, contention resolution diversity slotted ALOHA (CRDSA) has been introduced as a simple but effective improvement to slotted ALOHA. It relies on MAC burst repetitions and on interference cancellation to increase the normalized throughput of a classic slotted ALOHA access scheme. CRDSA allows achieving a larger throughput than slotted ALOHA, at the price of an increased average transmitted power. A way to trade-off the increment of the average transmitted power and the improvement of the throughput is presented in this paper. Specifically, it is proposed to divide each MAC burst in k sub-bursts, and to encode them via a (n,k) erasure correcting code. The n encoded sub-bursts are transmitted over the MAC channel, according to specific time/frequency-hopping patterns. Whenever n-e>=k sub-bursts (of the same burst) are received without collisions, erasure decoding allows recovering the remaining e sub-bursts (which were lost due to collisions). An interference cancellation process can then take place, removing in e slots the interference caused by the e recovered sub-bursts, possibly allowing the correct decoding of sub-bursts related to other bursts. The process is thus iterated as for the CRDSA case.Comment: Presented at the Future Network and MobileSummit 2010 Conference, Florence (Italy), June 201

Error-correction coding for high-density magnetic recording channels.

Finally, a promising algorithm which combines RS decoding algorithm with LDPC decoding algorithm together is investigated, and a reduced-complexity modification has been proposed, which not only improves the decoding performance largely, but also guarantees a good performance in high signal-to-noise ratio (SNR), in which area an error floor is experienced by LDPC codes.The soft-decision RS decoding algorithms and their performance on magnetic recording channels have been researched, and the algorithm implementation and hardware architecture issues have been discussed. Several novel variations of KV algorithm such as soft Chase algorithm, re-encoded Chase algorithm and forward recursive algorithm have been proposed. And the performance of nested codes using RS and LDPC codes as component codes have been investigated for bursty noise magnetic recording channels.Future high density magnetic recoding channels (MRCs) are subject to more noise contamination and intersymbol interference, which make the error-correction codes (ECCs) become more important. Recent research of replacement of current Reed-Solomon (RS)-coded ECC systems with low-density parity-check (LDPC)-coded ECC systems obtains a lot of research attention due to the large decoding gain for LDPC-coded systems with random noise. In this dissertation, systems aim to maintain the RS-coded system using recent proposed soft-decision RS decoding techniques are investigated and the improved performance is presented

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

Video over DSL with LDGM Codes for Interactive Applications

Digital Subscriber Line (DSL) network access is subject to error bursts, which, for interactive video, can introduce unacceptable latencies if video packets need to be re-sent. If the video packets are protected against errors with Forward Error Correction (FEC), calculation of the application-layer channel codes themselves may also introduce additional latency. This paper proposes Low-Density Generator Matrix (LDGM) codes rather than other popular codes because they are more suitable for interactive video streaming, not only for their computational simplicity but also for their licensing advantage. The paper demonstrates that a reduction of up to 4 dB in video distortion is achievable with LDGM Application Layer (AL) FEC. In addition, an extension to the LDGM scheme is demonstrated, which works by rearranging the columns of the parity check matrix so as to make it even more resilient to burst errors. Telemedicine and video conferencing are typical target applications