Showing papers on "Sequential decoding published in 1970"
TL;DR: This correspondence deals with simple and efficients methods for coding and decoding methods based on the quasi-cyclic structure, and alternately using syndromes based respectively on C and on C^{-1} , that permit correction to full error-correcting capacity.
Abstract: Many of the best random error-correcting group codes known (cyclic or not) can be reduced to echelon canonical form, in which the parity matrix is mainly or entirely composed of one or several circulants. This correspondence deals with simple and efficients methods for coding and decoding such codes, called quasi-cyclic in recent literature. The main result is that when the parity matrix C , or its complement (C + J) are nonsingular, simplified and fast decoding methods based on the quasi-cyclic structure, and alternately using syndromes based respectively on C and on C^{-1} , permit correction to full error-correcting capacity. This is also extended to the (simplest) case of several parity circulants in a row.
36 citations
TL;DR: Algorithms to decode iterated codes when at least one of the "component codes" is majority decodable are given and all error patterns guaranteed to be correctable by the minimum distance of the iterated code.
Abstract: Algorithms to decode iterated codes when at least one of the "component codes" is majority decodable are given. The decoding algorithms allow the use of the decoders of the component codes and still make it possible to correct all error patterns guaranteed to be correctable by the minimum distance of the iterated code.
33 citations
TL;DR: Several good rate one-half constraint-length 49 systematic codes are obtained quickly with this procedure to enumerate the number of low-weight codewords in a convolutional code.
Abstract: An existing sequential decoding program can be easily modified to enumerate the number of low-weight codewords in a convolutional code, where weight is defined either over a decoding constraint length or "free." We tabulated several good rate one-half constraint-length 49 systematic codes that were obtained quickly with this procedure.
22 citations
TL;DR: Using Rudolph's one-step majority-logic decoding algorithm, it is proved that all single-error-correcting codes can be one- step majority decoded.
Abstract: In this correspondence, a modification of Rudolph's one-step majority-logic decoding algorithm is introduced. Using this modification, it is proved that all single-error-correcting codes can be one-step majority decoded.
16 citations
12 citations
TL;DR: A one-step threshold decoding method previously presented for cyclic block codes is shown to apply generally to linear convolutional codes and generalizes in a natural way to allow decoding of the received sequence in its unquantized analog form.
Abstract: A one-step threshold decoding method previously presented for cyclic block codes is shown to apply generally to linear convolutional codes. It is further shown that this method generalizes in a natural way to allow decoding of the received sequence in its unquantized analog form.
5 citations
TL;DR: It is found that multiple-error-correcting codes inherently have the ability to correct multiple bursts and somewhat stronger theorems are derived here, and a decoding procedure is given.
Abstract: Stone^1 found that multiple-error-correcting codes inherently have the ability to correct multiple bursts. Using his methods, somewhat stronger theorems are derived here, and a decoding procedure is given.
4 citations
TL;DR: It is shown that there is a trade-off between sequential decoder computation and error probability as the bias B is varied and that for many values of B, sequential decoding of systematic convolutional codes gives an exponentially larger error probability than sequential decode of nonsystematic convolutionals when both codes are designed with exponentially equal optimum decoder error probabilities.
Abstract: This paper presents several results involving Fano's sequential decoding algorithm for convolutional codes. An upper bound to the a th moment of decoder computation is obtained for arbitrary decoder bias B and a \leq 1 . An upper bound on error probability with sequential decoding is derived for both systematic and nonsystematic convolutional codes. This error bound involves the exact value of the decoder bias B . It is shown that there is a trade-off between sequential decoder computation and error probability as the bias B is varied. It is also shown that for many values of B , sequential decoding of systematic convolutional codes gives an exponentially larger error probability than sequential decoding of nonsystematic convolutional codes when both codes are designed with exponentially equal optimum decoder error probabilities.
4 citations
TL;DR: A two-step decoding procedure is proposed for improving system performance when error correction is used and should reduce the average decoding time or logic required for realization.
Abstract: Error-correcting codes can be used in digital communication and storage for error control. A two-step decoding procedure is proposed for improving system performance when error correction is used. When applicable it should reduce the average decoding time or logic required for realization. Possible applications to faulty memory arrays and unit-to-unit data transmission are given.
01 Jan 1970
TL;DR: Rate 1/2 binary convolutional codes are analyzed and a lower bound on free distance in terms of the minimum distances of two associated cyclic codes is derived.
Abstract: Rate 1/2 binary convolutional codes are analyzed and a lower bound on free distance in terms of the minimum distances of two associated cyclic codes is derived. Next, the complexity of computing the free distance is discussed and a counterexample to a conjecture on the relationship of row distance to free distance for systematic codes is presented. Finally, an improved Gilbert bound for definite decoding is derived. SECTION
TL;DR: By using suboptimum decoding algorithm and certain criteria to select a generator sequence, error propagation can be avoided and recovery decoding errors can be minimized as mentioned in this paper. But these selection criteria can be applied to a sequential decoding algorithm that is based on a Hamming-distance decoding criterion.
Abstract: By using suboptimum decoding algorithm and certain criteria to select a generator sequence, error propagation can be avoided and recovery decoding errors can be minimized. These selection criteria can be applied to a sequential decoding algorithm that is based on a Hamming-distance decoding criterion.
01 Nov 1970
TL;DR: By using suboptimum decoding algorithm and certain criteria to select a generator sequence, error propagation can be avoided and recovery decoding errors can be minimized.
Abstract: Suboptimum sequential algorithm for recovery decoding errors in convolutional codes, using Hamming distance criterion
01 Sep 1970
TL;DR: The paper gives a survey of recent advances in majority-logic decoding for linear block codes and an improved decoding algorithm for the finite geometry codes that greatly reduces the decoding complexity of the codes.
Abstract: : The paper gives a survey of recent advances in majority-logic decoding for linear block codes. General majority-logic decoding algorithms are reviewed. The decoding schemes for product codes and the finite geometry codes are discussed. An improved decoding algorithm for the finite geometry codes is described. The improved decoding algorithm greatly reduces the decoding complexity of the codes. It should make the finite geometry codes very attractive in practical use on error-control systems. (Author)
01 Sep 1970
TL;DR: Sequential decoding problems considered deal with reliable transmission through noise space channels and encoding of space sources for the purpose of data suppression.
Abstract: Sequential decoding problems considered deal with reliable transmission through noise space channels and encoding of space sources for the purpose of data suppression.
17 Nov 1970
TL;DR: This paper demonstrates that data compression and error control can be united in a single system and held accountable for the required theorems in information theory.
Abstract: Data compression and error control have, over the years, been treated as two separate disciplines. Data compression can substantially reduce the loading of communication channels and error control using coding methodology, can reduce the amount of errors in the messages being transmitted, or allow the system to operate with less power for a comparable uncoded information rate. This paper demonstrates that both functions can be combined into one operation by applying sequential decoding developed for error control to data compression. Because the same general method can be used to solve both problems, data compression and error control can be united in a single system and held accountable for the required theorems in information theory.
TL;DR: In this paper, a new class of double error correcting high rate convolutional codes is proposed and it is shown that these codes exhibit finite error propagation, which is the case for all high rate codes.
Abstract: A new class of double error correcting high rate convolutional codes are given. It is shown that these codes exhibit finite error propagation.
TL;DR: A method for detecting and correcting slippage similar to that used for cyclic codes will be examined and applied to certain Specific convolutional codes, such that there is no change in the code when synchronization is maintained.
Abstract: Loss of Synchronization may have a number of effects on the decoding process of a convolutional code. At best there will be a transient effect on the decoder; at worst error propagation will be initiated; or the information sent Will be made worthless by a loss or gain of digits during transmission. A method for detecting and correcting slippage similar to that used for cyclic codes will be examined and applied to certain Specific convolutional codes. This method is such that there is no change in the code when synchronization is maintained. Only a modest amount of added hardware is needed. The procedures developed are applicable to codes where n -data streams are sent in parallel. For interlaced serial streams, slippage correction of s digits can be corrected if s is a multiple of n ; otherwise slippage can be detected.