The need to transmit and store massive amounts of data reliably and without error is a vital part of modern communications systems. Error-correcting codes play a fundamental role in minimising data corruption caused by defects such as noise, interference, crosstalk and packet loss. This book provides an accessible introduction to the basic elements of algebraic codes, and discusses their use in a variety of applications. The author describes a range of important coding techniques, including Reed-Solomon codes, BCH codes, trellis codes, and turbocodes. Throughout the book, mathematical theory is illustrated by reference to many practical examples. The book was first published in 2003 and is aimed at graduate students of electrical and computer engineering, and at practising engineers whose work involves communications or signal processing.

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Algebraic Codes for Data Transmission

In this paper, we introduce generalized tail biting encoding as a means to ameliorate the rate deficiency caused by zero-tail convolutional encoding This technique provides an important link between quasi-cyclic block and convolutional codes Optimum and suboptimum decoding algorithms for these codes are described and their performance determined by analytical and simulation techniques

On Tail Biting Convolutional Codes

H. Imai and S. Hirakawa have proposed (1977) a multilevel coding method based on binary block codes that admits a staged decoding procedure. The author extends the coding method to coset codes and shows how to calculate minimum squared distance and path multiplicity in terms of the norms and multiplicities of the different cosets. The multilevel structure allows the redundancy in the coset selection procedure to be allocated efficiently among the different levels. It also allows the use of suboptimal multistage decoding procedures that have performance/complexity advantages over maximum-likelihood decoding. >

Multilevel codes and multistage decoding

A method and system are provided for the synchronous transmission and reception of multiplexed digital signals such as spread spectrum. The system uses biorthogonal modulation (36) of a plurality of orthogonal signals, preferably wideband, together with simultaneous orthogonal multiplexing. The method is found to significantly mitigate the cross-correlation interference that is caused by the interaction between the multiplexed signals. The system transmits a lesser number of multiplexed orthogonal signals than would be required in the corresponding antipodal system, thereby reducing the cross-correlation interference, while maintaining the same information throughput. The bit error rate of the system is reduced. The method combines aspects of unequal error protection (UEP) error correction coding (ECC) (38) with a receiver architecture for biorthogonal signals.

System and method for multiplexing a spread spectrum communication system

A fast algorithm for searching a tree (FAST) is presented for computing the distance spectrum of convolutional codes. The distance profile of a code is used to limit substantially the error patterns that have to be searched. The algorithm can easily be modified to determine the number of nonzero information bits of an incorrect path as well as the length of an error event. For testing systematic codes, a faster version of the algorithm is given. FAST is much faster than the standard bidirectional search. On a microVAX, d/sub infinity /=27 was verified for a rate R=1/2, memory M=25 code in 37 s of CPU time. Extensive tables of rate R=1/2 encoders are given. Several of the listed encoders have distance spectra superior to those of any previously known codes of the same rate and memory. A conjecture than an R=1/2 systematic convolutional code of memory 2M will perform as well as a nonsystematic convolutional code of memory M is given strong support. >

A fast algorithm for computing distance spectrum of convolutional codes

Three optimality criteria for convolutional codes are considered in this correspondence: namely, free distance, minimum distance, and distance profile. Here we report the results of computer searches for rate one-half binary convolutional codes that are "robustly optimal" in the sense of being optimal for one criterion and optimal or near-optimal for the other two criteria. Comparisons with previously known codes are made. The results of a computer simulation are reported to show the importance of the distance profile to computational performance with sequential decoding.

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R. Johannesson

Papers

Robustly optimal rate one-half binary convolutional codes (Corresp.)