A study of major coding techniques for digital communication Final report

Coding techniques for digital communication channel

Some new results on majority-logic codes for correction of random errors

The main advantages of random error-correcting majority-logic codes and majority-logic decoding in general are well known and two-fold. Firstly, they offer a partial solution to a classical coding theory problem, that of decoder complexity. Secondly, a majority-logic decoder inherently corrects many more random error patterns than the minimum distance of the code implies is possible. The solution to the decoder complexity is only a partial one because there are circumstances under which a majority-logic decoder is too complex and expensive to implement. [Continues.

An Error-Control System Based on Majority-Logic Decoding

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryJoint Services Electronics Program / DAAB07-72-C-0259Rome Air Development Center / F30602-72-C-003

Coding Theory and its Applications in Communication systems

Error control coding has been used extensively in digital communication systems because of its cost-effectiveness in achieving efficient, reliable digital transmission. Coding now plays an important role in the design of modern communication systems. This paper reviews the development of basic coding theory and state-of-art coding techniques. The applications of coding to communication systems and future trends are also discussed

Versatile Error-Control Coding Systems

$NC research reported in this thesis is in the field of error-correcting codes, which has evolved as a very important branch of information theory. The main use of error-correcting codes is to increase the reliability of digital data transmitted through a noisy environment. There are, sometimes, alternative ways of increasing the reliability of data transmission, but coding methods are now competitive in cost and complexity in many cases because of recent advances in technology. The first two chapters of this thesis introduce the subject of error-correcting codes, review some of the published literature in this field and discuss the advan­tages of various coding techniques. After presenting linear block codes attention is from then on concentrated on cyclic codes, which is the subject of Chapter 3. The first part of Chapter 3 presents the mathemati­cal background necessary for the study of cyclic codes and examines existing methods of encoding and their practical implementation. In the second part of Chapter 3 various ways of decoding cyclic codes are studied and from these considerations, a general decoder for cyclic codes is devised and is presented in Chapter 4. Also, a review of the principal classes of cyclic codes is presented. Chapter 4 describes an experimental system constructed for measuring the performance of cyclic codes initially RC5GI5SCD by random errors and then by bursts of errors. Simulated channels are used both for random and burst errors. A computer simulation of the whole system was made in order to verify the accuracy of the experimental results obtained. Chapter 5 presents the various results obtained with the experimental system and by computer simulation, which allow a comparison of the efficiency of various cyclic codes to be made. Finally, Chapter 6 summarises and dis­cusses the main results of the research and suggests interesting points for future investigation in the area. The main objective of this research is to contribute towards the solution of a fairly wide range of problems arising in the design of efficient coding schemes for practical applications; i.e. a study of coding from an engineering point of view

Easily decoded error correcting codes

This thesis is concerned with the decoding aspect of linear block error-correcting codes. When, as in most practical situations, the decoder cost is limited an optimum code may be inferior in performance to a longer sub-optimum code' of the same rate. This consideration is a central theme of the thesis. The best methods available for decoding short optimum codes and long B.C.H. codes are discussed, in some cases new decoding algorithms for the codes are introduced. Hashim's "Nested" codes are then analysed. The method of nesting codes which was given by Hashim is shown to be optimum - but it is seen that the codes are less easily decoded than was previously thought. "Conjoined" codes are introduced. It is shown how two codes with identical numbers of information bits may be "conjoined" to give a code with length and minimum distance equal to the sum of the respective parameters of the constituent codes but with the same number of information bits. A very simple decoding algorithm is given for the codes whereby each constituent codeword is decoded and then a decision is made as to the correct decoding. A technique is given for adding more codewords to conjoined codes without unduly increasing the decoder complexity. Lastly, "Array" codes are described. They are formed by making parity checks over carefully chosen patterns of information bits arranged in a two-dimensional array. Various methods are given for choosing suitable patterns. Some of the resulting codes are self-orthogonal and certain of these have parameters close to the optimum for such codes. A method is given for adding more codewords to array codes, derived from a process of augmentation known for product codes

Two hybrid ARQ error control schemes for near earth satellite communications

Two hybrid automatic repeat request (ARQ) error control schemes are proposed for NASA near earth satellite communications. Both schemes are adaptive in nature, and employ cascaded codes to achieve both high reliability and throughput efficiency for high data rate file transfer

Two hybrid ARQ error control schemes for near Earth satellite communications

Two hybrid Automatic Repeat Request (ARQ) error control schemes are proposed for NASA near Earth satellite communications. Both schemes are adaptive in nature, and employ cascaded codes to achieve both high reliability and throughput efficiency for high data rate file transfer

Bit flipping decoding for binary product codes

Error control coding has been used to mitigate the impact of noise on the wireless channel. Today, wireless communication systems have in their design Forward Error Correction (FEC) techniques to help reduce the amount of retransmitted data. When designing a coding scheme, three challenges need to be addressed, the error correcting capability of the code, the decoding complexity of the code and the delay introduced by the coding scheme. While it is easy to design coding schemes with a large error correcting capability, it is a challenge finding decoding algorithms for these coding schemes. Generally increasing the length of a block code increases its error correcting capability and its decoding complexity. Product codes have been identified as a means to increase the block length of simpler codes, yet keep their decoding complexity low. Bit flipping decoding has been identified as simple to implement decoding algorithm. Research has generally been focused on improving bit flipping decoding for Low Density Parity Check codes. In this study we develop a new decoding algorithm based on syndrome checking and bit flipping to use for binary product codes, to address the major challenge of coding systems, i.e., developing codes with a large error correcting capability yet have a low decoding complexity. Simulated results show that the proposed decoding algorithm outperforms the conventional decoding algorithm proposed by P. Elias in BER and more significantly in WER performance. The algorithm offers comparable complexity to the conventional algorithm in the Rayleigh fading channel