On the optimum bit orders with respect to the state complexity of trellis diagrams for binary linear codes

Kasami, Tadao; Takata, Takushi; Fujiwara, Toru; Lin, Shu

doi:10.1109/18.179366

Cited by 133 publications

(55 citation statements)

References 4 publications

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“…Unfortunately, there appears to no general agreement as to what this figure of merit should be. Some authors take state complexity [35], [42], some take vertex complexity [18], [19], and some use the number of "addition-equivalent operations" [ 111, [40]. We believe that the results in this paper show that the most appropriate figure of merit is the edge count of the trellis, and we encourage future researchers in this area to take the edge count as the measure of trellis complexity.…”

mentioning

confidence: 99%

On the BCJR trellis for linear block codes

McEliece

1996

IEEE Trans. Inform. Theory

195

138

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Abstruct-In this semi-tutorial paper, we will investigate the computational complexity of an abstract version of the Viterbi algorithm on a trellis, and show that if the trellis has e edges, the complexity of the Viterbi algortithm is @ ( e ) . This result suggests that the "best" trellis representation for a given linear block code is the one with the fewest edges. We will then show that, among all trellises that represent a given code, the original trellis introduced by Bahl, Cocke, Jelinek, and Raviv in 1974, and later rediscovered by Wolf, Massey, and Forney, uniquely minimizes the edge count, as well as several other figures of merit. Following Forney and Kschischang and Sorokine, we will also discuss "trellis-oriented" or "minimal-span" generator matrices, which facilitate the calculation of the size of the BCJR trellis, as well as the actual construction of it.

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mentioning

confidence: 99%

On the BCJR trellis for linear block codes

McEliece

1996

IEEE Trans. Inform. Theory

195

138

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“…For several classes of codes such as RM codes or their subcodes and repetition codes, and their dual codes, there are known code symbol orderings [6], [9] which result in reduced upper bounds on the state complexity of their trellis diagrams compared with Wolf's bound. If there is such a code among C i with 1 i M , then we can adopt the corresponding symbol ordering and evaluate the state complexity of trellis diagram for C by applying upper bounds which are independent of any symbol ordering of each remaining component code.…”

Section: Minimal Trellises and State Complexities Of Decomposablementioning

confidence: 99%

“…A minimal trellis is unique up to graph isomorphism [3]- [5]. It has been shown [3]- [6] that the state complexity of a minimal trellis for a linear block code depends on the order of its code symbol positions. However, symbol ordering does not affect the trellis state complexity of maximumdistance-separable (MDS) codes.…”

Section: Introductionmentioning

confidence: 99%

Constructions of generalized concatenated codes and their trellis-based decoding complexity

Morelos-Zaragoza¹,

Fujiwara²,

Kasami³

et al. 1999

IEEE Trans. Inform. Theory

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Abstract-In this correspondence, constructions of generalized concatenated (GC) codes with good rates and distances are presented. Some of the proposed GC codes have simpler trellis complexity than Euclidean geometry (EG), Reed-Muller (RM), or Bose-Chaudhuri-Hocquenghem (BCH) codes of approximately the same rates and minimum distances, and in addition can be decoded with trellis-based multistage decoding up to their minimum distances. Several codes of the same length, dimension, and minimum distance as the best linear codes known are constructed.

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“…The generalized weight enumerator was defined in [25] and a Macwilliams identity was proved in [34]. The connection between the trellis or state complexity of a code and its GHW's was made in [20,21]. The sequence of GHW's is called the length/dimension profile (LDP) in [13].…”

Section: Introductionmentioning

confidence: 99%