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IEEE Transactions on Information Theory

Issue 6  Part 1 • Date Nov. 1996

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Displaying Results 1 - 25 of 32
  • A distance spectrum interpretation of turbo codes

    Publication Year: 1996, Page(s):1698 - 1709
    Cited by:  Papers (243)  |  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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  • Convolutional codes over groups

    Publication Year: 1996, Page(s):1660 - 1686
    Cited by:  Papers (43)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (2708 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 (20)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1104 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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  • 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 (1000 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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  • An efficient algorithm for constructing minimal trellises for codes over finite abelian groups

    Publication Year: 1996, Page(s):1839 - 1854
    Cited by:  Papers (14)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1512 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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  • A table of state complexity bounds for binary linear codes

    Publication Year: 1996, Page(s):2034 - 2042
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (856 KB)

    This article contains a table of bounds on the state complexity of binary linear codes with length smaller than 25. General results on the state complexity of binary linear codes with low dimension or low minimum distance are included 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 (1444 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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  • 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 (1124 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 γ. The properties of these functions are studied from an analytic perspective. It is also shown that the trellis decoding complexity... View full abstract»

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  • The trellis complexity of convolutional codes

    Publication Year: 1996, Page(s):1855 - 1864
    Cited by:  Papers (54)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (848 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 estimate... View full abstract»

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  • Expander codes

    Publication Year: 1996, Page(s):1710 - 1722
    Cited by:  Papers (252)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1432 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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  • A new paradigm for public key identification

    Publication Year: 1996, Page(s):1757 - 1768
    Cited by:  Papers (6)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1372 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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  • Generalized minimum-distance decoding of Euclidean-space codes and lattices

    Publication Year: 1996, Page(s):1992 - 2026
    Cited by:  Papers (41)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (3984 KB)

    It is shown that multistage generalized minimum-distance (GMD) decoding of Euclidean-space codes and lattices can provide an excellent tradeoff between performance and complexity. We introduce a reliability metric for Gaussian channels that is easily computed from an inner product, and prove that a multistage GMD decoder using this metric is a bounded-distance decoder up to the true packing radius... View full abstract»

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  • Suboptimal decoding of linear codes: partition technique

    Publication Year: 1996, Page(s):1971 - 1986
    Cited by:  Papers (15)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1716 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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  • 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 (844 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 γ, the average number of states (respectively, branches) in any given trellis diagram of L is bounded below by a f... View full abstract»

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  • On behaviors and convolutional codes

    Publication Year: 1996, Page(s):1881 - 1891
    Cited by:  Papers (42)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1112 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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  • Oblivious transfers and intersecting codes

    Publication Year: 1996, Page(s):1769 - 1780
    Cited by:  Papers (11)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1268 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 (t 1)-OTk2. This primitiv... 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 (2228 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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  • Proof of a conjecture of McEliece regarding the expansion index of the minimal trellis

    Publication Year: 1996, Page(s):2027 - 2033
    Cited by:  Papers (23)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (848 KB)

    We prove a conjecture of McEliece, establishing that for each fixed order of positions of a linear code C, the minimal trellis minimizes the quantity |E|-|V|+1, where |E| and |V| stand for the number of edges and vertices in the trellis, respectively. As a consequence, it follows that the minimal trellis uniquely minimizes the total number of operations required for Viterbi decoding of a given cod... View full abstract»

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  • On greedy algorithms in coding theory

    Publication Year: 1996, Page(s):2053 - 2057
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (484 KB)

    We study a wide class of problems in coding theory for which we consider two different formulations: in terms of incidence matrices and in terms of hypergraphs. These problems are dealt with using a greedy algorithm due to Stein (1974) and Lovasz (1975). Some examples, including constructing covering codes, codes for conflict resolution, separating systems, source encoding with distortion, etc., a... View full abstract»

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  • Coding for interactive communication

    Publication Year: 1996, Page(s):1745 - 1756
    Cited by:  Papers (35)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1396 KB)

    Let the input to a computation problem be split between two processors connected by a communication link; and let an interactive protocol π 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 the... View full abstract»

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  • Minimal trellis design for linear codes based on the Shannon product

    Publication Year: 1996, Page(s):2048 - 2053
    Cited by:  Papers (12)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (516 KB)

    A novel trellis design technique for both block and convolutional codes based on the Shannon (1956) product of component block codes is introduced. Using the proposed technique, structured trellises for block and convolutional codes have been designed. It is shown that the designed trellises are minimal and allow reduced complexity Viterbi decoding View full abstract»

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  • On the intractability of permuting a block code to minimize trellis complexity

    Publication Year: 1996, Page(s):2042 - 2048
    Cited by:  Papers (19)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (784 KB)

    An important problem in the theory and application of block code trellises is to find a coordinate permutation of a given code to minimize the trellis complexity. We show that the problem of finding a coordinate permutation that minimizes the number of vertices at a given depth in the minimal trellis for a binary linear block code is NP-complete 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 (23)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1096 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 &ld... 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 (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1456 KB)

    A full-rank K×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 the s... View full abstract»

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  • Priority encoding transmission

    Publication Year: 1996, Page(s):1737 - 1744
    Cited by:  Papers (275)  |  Patents (40)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (860 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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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
Frank R. Kschischang

Department of Electrical and Computer Engineering