IEEE Transactions on Information Theory

Volume 42 Issue 6  Part 1 • Nov. 1996

 This issue contains several parts.Go to:  Part 2 

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Displaying Results 1 - 25 of 32
  • Convolutional codes over groups

    Publication Year: 1996, Page(s):1660 - 1686
    Cited by:  Papers (50)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (2980 KB)

    The basic algebraic structure theory of convolutional codes and their trellises is developed simultaneously for codes over groups, rings, and fields. The first part, which covers fundamental notions such as minimality and observability, is semi-tutorial in that most definitions are already standard (within the modern behavioral theory), as are some of the formally stated results. However, some of ... View full abstract»

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  • Trellis decoding complexity of linear block codes

    Publication Year: 1996, Page(s):1687 - 1697
    Cited by:  Papers (23)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1220 KB)

    In this partially tutorial paper, we examine minimal trellis representations of linear block codes and analyze several measures of trellis complexity: maximum state and edge dimensions, total span length, and total vertices, edges and mergers. We obtain bounds on these complexities as extensions of well-known dimension/length profile (DLP) bounds. Codes meeting these bounds minimize all the comple... View full abstract»

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  • A distance spectrum interpretation of turbo codes

    Publication Year: 1996, Page(s):1698 - 1709
    Cited by:  Papers (294)  |  Patents (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1412 KB)

    The performance of turbo codes is addressed by examining the code's distance spectrum. The "error floor" that occurs at moderate signal-to-noise ratios is shown to be a consequence of the relatively low free distance of the code. It is also shown that the "error floor" can be lowered by increasing the size of the interleaver without changing the free distance of the code. Alternatively, the free d... View full abstract»

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  • Expander codes

    Publication Year: 1996, Page(s):1710 - 1722
    Cited by:  Papers (339)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1560 KB)

    Using expander graphs, we construct a new family of asymptotically good, linear error-correcting codes. These codes have linear time sequential decoding algorithms and logarithmic time parallel decoding algorithms that use a linear number of processors. We present both randomized and explicit constructions of these codes. Experimental results demonstrate the good performance of the randomly chosen... View full abstract»

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  • Linear-time encodable and decodable error-correcting codes

    Publication Year: 1996, Page(s):1723 - 1731
    Cited by:  Papers (101)  |  Patents (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1179 KB)

    We present a new class of asymptotically good, linear error-correcting codes. These codes can be both encoded and decoded in linear time. They can also be encoded by logarithmic-depth circuits of linear size and decoded by logarithmic depth circuits of size O(nlogn). We present both randomized and explicit constructions of these codes. View full abstract»

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  • A linear time erasure-resilient code with nearly optimal recovery

    Publication Year: 1996, Page(s):1732 - 1736
    Cited by:  Papers (58)  |  Patents (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (627 KB)

    We develop an efficient scheme that produces an encoding of a given message such that the message can be decoded from any portion of the encoding that is approximately equal to the length of the message. More precisely, an (n,c,l,r)-erasure-resilient code consists of an encoding algorithm and a decoding algorithm with the following properties. The encoding algorithm produces a set of l-bit packets... View full abstract»

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  • Priority encoding transmission

    Publication Year: 1996, Page(s):1737 - 1744
    Cited by:  Papers (337)  |  Patents (62)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (952 KB)

    We introduce a new method, called priority encoding transmission, for sending messages over lossy packet-based networks. When a message is to be transmitted, the user specifies a priority value for each part of the message. Based on the priorities, the system encodes the message into packets for transmission and sends them to (possibly multiple) receivers. The priority value of each part of the me... View full abstract»

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  • Coding for interactive communication

    Publication Year: 1996, Page(s):1745 - 1756
    Cited by:  Papers (70)  |  Patents (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1524 KB)

    Let the input to a computation problem be split between two processors connected by a communication link; and let an interactive protocol /spl pi/ be known by which, on any input, the processors can solve the problem using no more than T transmissions of bits between them, provided the channel is noiseless in each direction. We study the following question: if in fact the channel is noisy, what is... View full abstract»

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  • A new paradigm for public key identification

    Publication Year: 1996, Page(s):1757 - 1768
    Cited by:  Papers (35)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1504 KB)

    The present paper investigates the possibility of designing zero-knowledge identification schemes based on hard problems from coding theory. Zero-knowledge proofs were introduced by Goldwasser, Micali, and Rackoff (1985). Their practical significance was soon demonstrated in the work of Fiat and Shamir [1986], who turned zero-knowledge proofs of quadratic residuosity into efficient means of establ... View full abstract»

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  • Oblivious transfers and intersecting codes

    Publication Year: 1996, Page(s):1769 - 1780
    Cited by:  Papers (26)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1403 KB)

    Assume A owns t secret k-bit strings. She is willing to disclose one of them to B, at his choosing, provided he does not learn anything about the other strings. Conversely, B does not want A to learn which secret he chose to learn. A protocol for the above task is said to implement one-out-of-t string oblivious transfer, denoted (/sup t//sub 1/)-OT/sup k//sub 2/. This primitive is particularly use... View full abstract»

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  • Linearity testing in characteristic two

    Publication Year: 1996, Page(s):1781 - 1795
    Cited by:  Papers (52)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1632 KB)

    Let Dist(f,g)=Pr/sub u/[f(u)/spl ne/g(u)] denote the relative distance between functions f,g mapping from a group G to a group H, and let Dist(f) denote the minimum, over all linear functions (homomorphisms) g, of Dist(f,g). Given a function f:G/spl rarr/H we let Err(f)=Pr/sub u,/spl upsi//[f(u)+f(/spl upsi/)/spl ne/f(u+/spl upsi/)] denote the rejection probability of the Blum-Luby-Rubinfeld (1993... View full abstract»

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  • Trellis complexity versus the coding gain of lattices. I

    Publication Year: 1996, Page(s):1796 - 1807
    Cited by:  Papers (12)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1258 KB)

    The best possible tradeoff between the coding gain and trellis complexity for lattices is studied. Three trellis complexity functions are defined for lattices as a measure of minimum trellis decoding complexity per dimension required for achieving a coding gain /spl gamma/. The properties of these functions are studied from an analytic perspective. It is also shown that the trellis decoding comple... View full abstract»

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  • Trellis complexity versus the coding gain of lattices. II

    Publication Year: 1996, Page(s):1808 - 1816
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (942 KB)

    For pt.I see ibid., vol. 42, no.6, p.1796-1802, 1996. Every rational lattice has a finite trellis diagram which can be employed for maximum-likelihood decoding over the additive white Gaussian noise channel via the Viterbi algorithm. For an arbitrary rational lattice L with gain /spl gamma/, the average number of states (respectively, branches) in any given trellis diagram of L is bounded below by... View full abstract»

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  • The twisted squaring construction, trellis complexity, and generalized weights of BCH and QR codes

    Publication Year: 1996, Page(s):1817 - 1827
    Cited by:  Papers (12)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1207 KB)

    The structure of the twisted squaring construction, a generalization of the squaring construction, is studied with respect to trellis diagrams and complexity. We show that binary affine-invariant codes, which include the extended primitive BCH codes, and the extended binary quadratic-residue codes, are equivalent to twisted squaring construction codes. In particular, a recursive symmetric reversib... View full abstract»

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  • The trellis structure of maximal fixed-cost codes

    Publication Year: 1996, Page(s):1828 - 1838
    Cited by:  Papers (25)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1224 KB)

    We show that the family of maximal fixed-cost (MFC) codes, with codeword costs defined in a right-cancellative semigroup, are rectangular, and hence admit biproper trellis presentations. Among all possible trellis presentations for a rectangular code, biproper trellises minimize a wide variety of complexity measures, including the Viterbi decoding complexity. Examples of MFC codes include such "no... View full abstract»

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  • An efficient algorithm for constructing minimal trellises for codes over finite abelian groups

    Publication Year: 1996, Page(s):1839 - 1854
    Cited by:  Papers (27)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1665 KB)

    We present an efficient algorithm for computing the minimal trellis for a group code over a finite abelian group, given a generator matrix for the code. We also show how to compute a succinct representation of the minimal trellis for such a code, and present algorithms that use this information to compute efficiently local descriptions of the minimal trellis. This extends the work of Kschischang a... View full abstract»

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  • The trellis complexity of convolutional codes

    Publication Year: 1996, Page(s):1855 - 1864
    Cited by:  Papers (65)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (935 KB)

    Convolutional codes have a natural, regular, trellis structure that facilitates the implementation of Viterbi's algorithm. Linear block codes also have a natural, though not in general a regular, "minimal" trellis structure, which allows them to be decoded with a Viterbi-like algorithm. In both cases, the complexity of an unenhanced Viterbi decoding algorithm can be accurately estimated by the num... View full abstract»

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  • Minimal and canonical rational generator matrices for convolutional codes

    Publication Year: 1996, Page(s):1865 - 1880
    Cited by:  Papers (16)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1611 KB)

    A full-rank K/spl times/n matrix G(D) over the rational functions F(D) generates a rate R=k/n convolutional code C. G(D) is minimal if it can be realized with as few memory elements as any encoder for C, and G(D) is canonical if it has a minimal realization in controller canonical form. We show that G(D) is minimal if and only if for all rational input sequences u(D), the span of u(D)G(D) covers t... View full abstract»

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  • On behaviors and convolutional codes

    Publication Year: 1996, Page(s):1881 - 1891
    Cited by:  Papers (68)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1228 KB)

    It is well known that a convolutional code is essentially a linear system defined over a finite field. In this paper we elaborate on this connection. We define a convolutional code as the dual of a complete linear behavior in the sense of Willems (1979). Using ideas from systems theory, we describe a set of generalized first-order descriptions for convolutional codes. As an application of these id... View full abstract»

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  • Dynamical systems and convolutional codes over finite Abelian groups

    Publication Year: 1996, Page(s):1892 - 1912
    Cited by:  Papers (10)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1954 KB)

    Polynomial algebraic techniques have always played a central role in linear systems theory and also in the theory of convolutional codes. We show how such techniques can be generalized to study systems and codes defined over Abelian groups. The systems are considered from the "behavioral" point of view as developed by Willems in the 1980s, and some of our results can be seen as extensions of Wille... View full abstract»

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  • A linear bound for sliding-block decoder window size. II

    Publication Year: 1996, Page(s):1913 - 1924
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1299 KB)

    For pt.I see ibid., vol.34, p. 389-99, 1988. An input-constrained channel is the set S of finite sequences of symbols generated by the walks on a labeled finite directed graph G (which is said to present S). We introduce a new construction of finite-state encoders for input-constrained channels. The construction is a hybrid of the state-splitting technique of Adler, Coppersmith, and Hassner (1983)... View full abstract»

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  • Complexity and sliding-block decodability

    Publication Year: 1996, Page(s):1925 - 1947
    Cited by:  Papers (11)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (2446 KB)

    A constrained system, or sofic system, S is the set of symbol strings generated by the finite-length paths through a finite labeled, directed graph. Karabed and Marcus (1988), extending the work of Adler, Coppersmith, and Hassner (1983), used the technique of state-splitting to prove the existence of a noncatastrophic, rate p:q finite-state encoder from binary data into S for any input word length... View full abstract»

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  • On the decoding delay of encoders for input-constrained channels

    Publication Year: 1996, Page(s):1948 - 1956
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1115 KB)

    Finite-state encoders that encode n-ary data into a constrained system S are considered. The anticipation, or decoding delay, of such an (S,n)-encoder is the number of symbols that a state-dependent decoder needs to look ahead in order to recover the current input symbol. Upper bounds are obtained on the smallest attainable number of states of any (S, n)-encoder with anticipation t. Those bounds c... View full abstract»

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  • Bounded-delay-encodable, block-decodable codes for constrained systems

    Publication Year: 1996, Page(s):1957 - 1970
    Cited by:  Papers (10)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1613 KB)

    We introduce and investigate the class of bounded-delay-encodable block-decodable (BDB) codes. Several characterizations for this class of codes are given, and some construction methods, especially for one-symbol look-ahead BDB codes, are described. In another direction, we use our results to show the existence of a decision procedure for some basic coding problems. View full abstract»

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  • Suboptimal decoding of linear codes: partition technique

    Publication Year: 1996, Page(s):1971 - 1986
    Cited by:  Papers (19)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1903 KB)

    General symmetric channels are introduced, and near-maximum-likelihood decoding in these channels is studied. First, we define a class of suboptimal decoding algorithms based on an incomplete search through the code trellis. It is proved that the decoding error probability of suboptimal decoding is bounded above for any q-ary code of length n and code rate r by twice the error probability of its m... View full abstract»

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Aims & Scope

IEEE Transactions on Information Theory publishes papers concerned with the transmission, processing, and utilization of information.

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Meet Our Editors

Editor-in-Chief
Alexander Barg

Department of Electrical and Computer Engineering and the Institute for Systems Research, University of Maryland

email: abarg-ittrans@ece.umd.edu