ITC/USA 2015 Conference Proceedings / The Fifty-First Annual International Telemetering Conference and Technical Exhibition / October 26-29, 2015 / Bally's Hotel & Convention Center, Las Vegas, NV / The performance of telemetry systems may be strongly affected by diverse sources of perturbations. Among them, multipath channels and transmission noise are the most critical. While the effects due to the multipath channels can be attenuated thanks to equalization, the effects of the noise are limited if forward error correction is used. This paper first proves that the combination of blind equalization and forward error correction can strongly improve bit error rates. The other objective of the paper is to show that reasonably powerful codes like Reed-Solomon codes are sufficient to enable quasi-error free transmissions in a large majority of propagation channel scenarios.

<p>We study the problem of list decoding with focus on the case when we have a list size limited to two. Under this restriction we derive general lower bounds on the maximum possible size of a list-of-2-decodable code. We study the set of correctable error patterns in an attempt to obtain a characterization. For a special family of Reed-Solomon codes - which we identify and name 'class-I codes' - we give a weight-based characterization of the correctable error patterns under list-of-2 decoding. As a tool in this analysis we use the theoretical framework of Sudan's algorithm. The characterization is used in an exact calculation of the probability of transmission error in the symmetric channel when list-of-2 decoding is used. The results from the analysis and complementary simulations for QAM-systems show that a list-of-2 decoding gain of nearly 1 dB can be achieved.</p><p>Further we study Sudan's algorithm for list decoding of Reed-Solomon codes for the special case of the class-I codes. For these codes algorithms are suggested for both the first and second step of Sudan's algorithm. Hardware solutions for both steps based on the derived algorithms are presented.</p>

We study the problem of list decoding with focus on the case when we have a list size limited to two. Under this restriction we derive general lower bounds on the maximum possible size of a list-of-2-decodable code. We study the set of correctable error patterns in an attempt to obtain a characterization. For a special family of Reed-Solomon codes - which we identify and name 'class-I codes' - we give a weight-based characterization of the correctable error patterns under list-of-2 decoding. As a tool in this analysis we use the theoretical framework of Sudan's algorithm. The characterization is used in an exact calculation of the probability of transmission error in the symmetric channel when list-of-2 decoding is used. The results from the analysis and complementary simulations for QAM-systems show that a list-of-2 decoding gain of nearly 1 dB can be achieved. Further we study Sudan's algorithm for list decoding of Reed-Solomon codes for the special case of the class-I codes. For these codes algorithms are suggested for both the first and second step of Sudan's algorithm. Hardware solutions for both steps based on the derived algorithms are presented.

In this dissertation, advanced channel decoding techniques based on bit-level soft information are studied. Two main approaches are proposed: bit-level probabilistic iterative decoding and bit-level algebraic soft-decision (list) decoding (ASD). In the first part of the dissertation, we first study iterative decoding for high density parity check (HDPC) codes. An iterative decoding algorithm, which uses the sum product algorithm (SPA) in conjunction with a binary parity check matrix adapted in each decoding iteration according to the bit-level reliabilities is proposed. In contrast to the common belief that iterative decoding is not suitable for HDPC codes, this bit-level reliability based adaptation procedure is critical to the conver-gence behavior of iterative decoding for HDPC codes and it significantly improves the iterative decoding performance of Reed-Solomon (RS) codes, whose parity check matrices are in general not sparse. We also present another iterative decoding scheme for cyclic codes by randomly shifting the bit-level reliability values in each iteration. The random shift based adaptation can also prevent iterative decoding from getting stuck with a significant complexity reduction compared with the reliability based parity check matrix adaptation and still provides reasonable good performance for short-length cyclic codes. In the second part of the dissertation, we investigate ASD for RS codes using bit-level soft information. In particular, we show that by carefully incorporating bit¬level soft information in the multiplicity assignment and the interpolation step, ASD can significantly outperform conventional hard decision decoding (HDD) for RS codes with a very small amount of complexity, even though the kernel of ASD is operating at the symbol-level. More importantly, the performance of the proposed bit-level ASD can be tightly upper bounded for practical high rate RS codes, which is in general not possible for other popular ASD schemes. Bit-level soft-decision decoding (SDD) serves as an efficient way to exploit the potential gain of many classical codes, and also facilitates the corresponding per-formance analysis. The proposed bit-level SDD schemes are potential and feasible alternatives to conventional symbol-level HDD schemes in many communication sys-tems.

Cellular digital packet data (CDPD) is a new service for wide-area data communication with wireless mobile users. CDPD system uses the existing infrastructure of the analog Advanced Mobile Phone Service (AMPS) cellular telephone network to transmit data with a channel hopping technique. The CDPD system employs Gaussian minimum shift keying (GMSK) as a modulation scheme and a Reed-Solomon code for error control to transmit high-quality data in the mobile and wireless environment. Most current CDPD receivers use errors only decoding of the Reed-Solomon code, although an improved errors and erasures decoding technique would also be possible. This thesis undertakes a performance evaluation of the CDPD system with an errors and erasures decoder for the Reed-Solomon coding. A thorough system simulation is conducted for both white Gaussian noise and flat Rayleigh fading channel environments. Results show that improved coding gains of 0.5 ~ 1 dB are possible for the additive white Gaussian noise channel and improved coding gains of 1.9 ~ 2.7 dB are possible for the fading channel. / Master of Science

ITC/USA 2011 Conference Proceedings / The Forty-Seventh Annual International Telemetering Conference and Technical Exhibition / October 24-27, 2011 / Bally's Las Vegas, Las Vegas, Nevada / This paper proposes a telemetering method consisting of delayed frame time diversity (DFTD) as the inner code and Reed-Solomon (RS) code as the outer code. DFTD is used to transmit a real-time frame together with a time-delayed frame which was saved in the memory during a defined period. The RS code is serially concatenated with DFTD. This method was applied to the design of telemetry units that have been used for over ten flight tests. The data results of the flight test for four cases with no applied code, with DFTD only, with the RS code only, and with both DFTD and the RS code are used to compare the number of error frames. The results also show that the proposed method is very useful and applicable to telemetry applications in a communication environment with a deep fade.

Lookup-table (LUT)-based method is a common approach used in all kinds of research topics. In this dissertation, we present several new designs for table-based function evaluation and table-based error correcting coding. In Chapter 3, a new function evaluation method, called two-level approximation, is presented where piecewise degree-one polynomials are used for initial approximation in the first level, followed by the refined approximation for the shared normalized difference functions in the second level. In Chapter 4, we present a new non-uniform segmentation method that searches for the optimal segmentation scheme with the different design goals of minimizing either ROM, total area, or delay. In Chapter 5, a new design methodology for table-based function evaluation is presented. Unlike previous approaches that usually determine the bit widths by assigning allowable errors for individual hardware components, the total error budget of our new design is considered jointly in order to optimized the bit widths of all the hardware components, leading to significant improvements in both area and delay. Finally, in Chapter 6, the similar table-based concept is used in the design of error correcting encoder using the modified polynomial of the Lagrange interpolation formula, resulting in smaller critical path delay and lower power consumption.

Reed-Solomon code is nowadays broadly used in many fields of data transmission. Using of error correction codes is divided into two main operations: information coding before sending information into communication channel and decoding received information at the other side. There are vast of decoding algorithms of Reed-Solomon codes, which have specific features. There is needed knowledge of features of algorithms to choose correct algorithm which satisfies requirements of system. There are evaluated cyclic decoding algorithm, Peterson-Gorenstein-Zierler algorithm, Berlekamp-Massey algorithm, Sugiyama algorithm with erasures and without erasures and Guruswami-Sudan algorithm. There was done implementation of algorithms in software and in hardware. Simulation of implemented algorithms was performed. Algorithms were evaluated and there were proposed methods to improve their work.

In this paper, we develop a scheme to recover a single erasure when using a Cartesian code,in the context of a distributed storage system. Particularly, we develop a scheme withconsiderations to minimize the associated bandwidth and maximize the associateddimension. The problem of recovering a missing node's data exactly in a distributedstorage system is known as theexact repair problem. Previous research has studied theexact repair problem for Reed-Solomon codes. We focus on Cartesian codes, and show wecan enact the recovery using a linear exact repair scheme framework, similar to the oneoutlined by Guruswami and Wooters in 2017. / Master of Science / Distributed storage systems are systems which store a single data file over multiple storage nodes. Each storage node has a certain storage efficiency, the "space" required to store the information on that node. The value of these systems, is their ability to safely store data for extended periods of time. We want to design distributed storage systems such that if one storage node fails, we can recover it from the data in the remaining nodes. Recovering a node from the data stored in the other nodes requires the nodes to communicate data with each other. Ideally, these systems are designed to minimize the bandwidth, the inter-nodal communication required to recover a lost node, as well as maximize the storage efficiency of each node. A great mathematical framework to build these distributed storage systems on is erasure codes. In this paper, we will specifically develop distributed storage systems that use Cartesian codes. We will show that in the right setting, these systems can have a very similar bandwidth to systems build from Reed-Solomon codes, without much loss in storage efficiency.

The main objective of this thesis was to create a model of forward error correction (FEC) system used in ADSL modem, which will be able to check its individual settings using the test methods specified in Recommendation G.996.1. The work is divided into two basic parts – theoretical and practical. The first part describes the basic functional characteristics of ADSL system, with attention being paid to aspects affecting the activity and setting of the error protection system. There are also discussed the theoretical basics of FEC coding techniques used in ADSL. The work also contains a description of the method for testing DSL system resistance against impulsive interference, which is specified in Recommendation G.996.1. The practical part of this thesis contains a description of the proposed model of the FEC system. The model was implemented in the programming environment Matlab Simulink. The proposed model includes the simulation of FEC coding process, DMT modulation and transmission channel with the impulse interference and the background noise. The proposed program is able to calculate parameters for setting FEC system from the specified data transfer rates and the requirement for interleaving. In addition, allows you to set the parameters of transmission line and sources of impulse interference and of the background noise. Under the set of input characteristics of the transmission is calculated bit allocation and the resulting parameters are given to a computational core of the model. In the application can be performed two types of test tasks. The first one is based on the Recommendation G.996.1 and makes it possible to determine probability of errored second. The second test task is for the measurement of resistance of the transmission system against impulsive interference. The results of the simulations are summarized in the conclusion of work.