Journal Article10.1109/TIT.1979.1056014
Some optimal partial-unit-memory codes (Corresp.)
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TL;DR: A new class of time-invariant binary convolutional codes is defined, called partial-unit-memory codes, which are optimal in the sense of having maximum free distance for given values of R, k, and \mu.
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Abstract: A new class of time-invariant binary convolutional codes is defined, called partial-unit-memory codes. These codes are optimal in the sense of having maximum free distance for given values of R, k (the number of encoder inputs), and \mu (the number of encoder memory cells). New optimal codes are given for rates R=l/4, 1/3, 1/2, \and 2/3 with \mu \leq 4 \and k \leq \mu + \3 , whenever such a code is better than previously known An infinite class of optimal partial-unit-memory codes is also constructed based on equidistant block codes.
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Citations
New short constraint length convolutional code constructions for selected rational rates (Corresp.)
TL;DR: New short constraint length convolutional code constructions are tabulated, determined by iterative search based upon a criterion of optimizing the free distance profile, to maximize the freedistance d_{f} while minimizing the number of adversaries in the distance, or weight, spectrum.
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Constructions of MDS-convolutional codes
TL;DR: This correspondence provides an elementary construction of MDS convolutional codes for each rate k/n and each degree /spl delta/.
Block Markov Superposition Transmission: Construction of Big Convolutional Codes From Short Codes
TL;DR: Numerical results show that the lower bounds can be matched with a moderate decoding delay in the low bit-error-rate (BER) region, implying that the iterative sliding-window decoding algorithm is near optimal.
97
The trellis complexity of convolutional codes
Robert J. McEliece,Wei Lin +1 more
- 15 Nov 1995
TL;DR: A theory of minimal trellises for convolutional codes is developed, which allows a direct performance-complexity comparison of the Viterbi decoding complexity of block and convolutionsal codes.
Bounds on distances and error exponents of unit memory codes
TL;DR: Binary unit memory codes, originally introduced by Lee, are investigated and asymptotic results for the free distance and the error probability are interpreted by Forney's inverse concatenation construction.
61
References
Convolutional codes I: Algebraic structure
TL;DR: Minimal encoders are shown to be immune to catastrophic error propagation and, in fact, to lead in a certain sense to the shortest decoded error sequences possible per error event.
831
Short convolutional codes with maximal free distance for rates 1/2, 1/3, and 1/4 (Corresp.)
TL;DR: In this paper, the authors gave a tabulation of binary convolutional codes with maximum free distance for rates of 1/2, 1/3, and 1/4 for all constraint lengths up to and including nu = 14.
Short binary convolutional codes with maximal free distance for rates 2/3 and 3/4 (Corresp.)
TL;DR: In this paper, a search procedure was developed to find good short binary (N,N - 1) convolutional codes using simple rules to discard from the complete ensemble of codes a large fraction whose free distance d{free} either cannot achieve the maximum value or is equal to d_{free} of some code in the remaining set.
102
Short binary convolutional codes with maximal free distance for rates 2/3 and 3/4
Erik Paaske
- 01 Jan 1974
TL;DR: A search procedure is developed to find good short binary (N,N - 1) convolutional codes and a number of short, optimum (in the sense of maximizing d_{free} ), rate-2/3 and 3/4 codes found by the search procedure are listed.
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Some Partial Unit Memory Convolutional Codes
Khaled Abdel-Ghaffar,Robert J. McEliece,G. Solomon +2 more
- 24 Jun 1991
TL;DR: It was found that these codes can outperform the Voyager code with little or no increase in decoder complexity, suggesting that there may very well be PUM codes that can be used for deep-spacetelemetry that offer both increased performance and decreased implementational complexity over current coding systems.