The Complexity of Decoders

The twenty-fifth anniversary of birth of Information Theory, as marked by the publication of Shannon’s seminal 1948 paper [Shannon (1948)], has just recently been celebrated. These have been a most productive and a most stimulating twenty-five years and to a large extent, the goal set out by information theorists has been achieved. That goal is to find and describe the means to obtain reliable communication on noisy channels at tolerably low reduction in data rates. Algebraic and non-algebraic, block and convolutional codes have been discovered along with algebraic and non-algebraic decoding procedures which do permit reliable communication on many types of noisy channels, radio, wire and space.

[1]  Elwyn R. Berlekamp,et al.  Lower Bounds to Error Probability for Coding on Discrete Memoryless Channels. II , 1967, Inf. Control..

[2]  J. Schalkwijk.  A Coding Scheme for Duplex Channels , 1974, IEEE Trans. Commun..

[3]  Ray J. Solomonoff,et al.  A Formal Theory of Inductive Inference. Part II , 1964, Inf. Control..

[4]  Jacob Ziv.  Asymptotic performance and complexity of a coding scheme for memoryless channels , 1967, IEEE Trans. Inf. Theory.

[5]  John E. Savage.  A note on the performance of concatenated codes (Corresp.) , 1970, IEEE Trans. Inf. Theory.

[6]  JOHN E. SAVAGE.  The complexity of decoders-II: Computational work and decoding time , 1971, IEEE Trans. Inf. Theory.

[7]  John E. Savage,et al.  Complexity of decoders-I: Classes of decoding rules , 1969, IEEE Trans. Inf. Theory.

[8]  L. H. Harper,et al.  On the complexity of the marriage problem , 1972 .

[9]  I. Reed,et al.  Polynomial Codes Over Certain Finite Fields , 1960 .

[10]  Jacob Ziv,et al.  Further results on the asymptotic complexity of an iterative coding scheme , 1966, IEEE Trans. Inf. Theory.

[11]  Gregory J. Chaitin,et al.  On the Length of Programs for Computing Finite Binary Sequences , 1966, JACM.

[12]  Robert Mario Fano,et al.  A heuristic discussion of probabilistic decoding , 1963, IEEE Trans. Inf. Theory.

[13]  G. Blustein,et al.  AN INVESTIGATION OF THE FANO SEQUENTIAL DECODING ALGORITHM BY COMPUTER SIMULATION , 1963 .

[14]  Andrei N. Kolmogorov,et al.  Logical basis for information theory and probability theory , 1968, IEEE Trans. Inf. Theory.

[15]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[16]  John E. Savage.  The distribution of the sequential decoding computation time , 1966, IEEE Trans. Inf. Theory.

[17]  Jeffrey D. Ullman,et al.  Formal languages and their relation to automata , 1969, Addison-Wesley series in computer science and information processing.

[18]  John E. Savage,et al.  Progress in Sequential Decoding , 1968 .

[19]  John E. Savage,et al.  Sequential decoding — the computation problem , 1966 .

[20]  R. Gallager.  Information Theory and Reliable Communication , 1968 .

[21]  Jørn Justesen,et al.  Class of constructive asymptotically good algebraic codes , 1972, IEEE Trans. Inf. Theory.

[22]  J. Pieter M. Schalkwijk.  A class of simple and optimal strategies for block coding on the binary symmetric channel with noiseless feedback , 1971, IEEE Trans. Inf. Theory.

[23]  Andrew J. Viterbi,et al.  Error bounds for convolutional codes and an asymptotically optimum decoding algorithm , 1967, IEEE Trans. Inf. Theory.

[24]  Elwyn R. Berlekamp,et al.  A lower bound to the distribution of computation for sequential decoding , 1967, IEEE Trans. Inf. Theory.

[25]  Gregory J. Chaitin,et al.  On the difficulty of computations , 1970, IEEE Trans. Inf. Theory.

[26]  John E. Savage,et al.  Computational Work and Time on Finite Machines , 1972, JACM.