Error-trellises for convolutional codes .I. Construction

Ariel, Mira; Snyders, J.

doi:10.1109/26.737397

Cited by 14 publications

(42 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For the purpose, the syndromesubsequence {ζ (2) k } computed from H T 2 (D) is utilized as auxiliary information for decoding. Let σ (1) k−1 be the initial state of any branch in the degenerate trellis module. Since there are 2 ν2 possibilities with respect to the patterns of σ (2) k−1 (cf.…”

Section: A Decoding Methodsmentioning

confidence: 99%

“…The above relation implies that the original error path {e k } associated with H T (D) can be represented using the error trellis based on either H T 1 (D) or H T 2 (D). For example, consider the (3, 1) convolutional code C defined by the check matrix An error trellis of C is constructed by concatenating the errortrellis modules [1] associated with H T (D). The set of four error-trellis modules associated with H T (D) and an example error trellis are depicted in Fig.1 and Fig.2, respectively.…”

Section: Error Trellis Constructed Based On a Submatrix Of A Checmentioning

confidence: 99%

“…in the degenerate trellis module with value ζ (1) k . When viewed from the original trellis module, given the e k , the syndrome former goes from σ k−1 = (σ…”

Section: B Relationship Between Degenerate Error-trellis Modules Andmentioning

confidence: 99%

“…k in a degenerate trellis module corresponds to 2 ν2 /2 m2 branches when viewed from the original trellis module. Also, since the size of H 1 (D) is m 1 × n, the number of branches entering state σ (1) k is 2 n−m1 . Corollary 2: Assume that a degenerate trellis module with value ζ…”

Section: B Relationship Between Degenerate Error-trellis Modules Andmentioning

confidence: 99%

See 3 more Smart Citations

Error-trellis state complexity of LDPC convolutional codes based on circulant matrices

Tajima

Okino

Miyagoshi

2010

2010 International Symposium on Information Theory &Amp; Its Applications

View full text Add to dashboard Cite

We consider the decoding of convolutional codes using an error trellis constructed based on a submatrix of a given check matrix. In the proposed method, the syndromesubsequence computed using the remaining submatrix is utilized as auxiliary information for decoding. Then the ML error path is correctly decoded using the degenerate error trellis. We also show that the decoding complexity of the proposed method is basically identical with that of the conventional one based on the original error trellis. Next, we apply the method to check matrices with monomial entries proposed by Tanner et al. By choosing any row of the check matrix as the submatrix for errortrellis construction, a 1-state error trellis is obtained. Noting the fact that a likelihood-concentration on the all-zero state and the states with many 0's occurs in the error trellis, we present a simplified decoding method based on a 1-state error trellis, from which decoding-complexity reduction is realized.

show abstract

Section: A Decoding Methodsmentioning

confidence: 99%

Section: Error Trellis Constructed Based On a Submatrix Of A Checmentioning

confidence: 99%

“…in the degenerate trellis module with value ζ (1) k . When viewed from the original trellis module, given the e k , the syndrome former goes from σ k−1 = (σ…”

Section: B Relationship Between Degenerate Error-trellis Modules Andmentioning

confidence: 99%

Section: B Relationship Between Degenerate Error-trellis Modules Andmentioning

confidence: 99%

See 2 more Smart Citations

Error-trellis state complexity of LDPC convolutional codes based on circulant matrices

Tajima

Okino

Miyagoshi

2010

2010 International Symposium on Information Theory &Amp; Its Applications

View full text Add to dashboard Cite

show abstract

“…Being motivated by their work, we also examined the same case. The time-k error e k = (e (1) k , · · · , e (n) k ) and syndrome ζ k = (ζ (1) k , · · · , ζ (m) k ) are connected with the relation ζ k = e k H T (D) (T means transpose). From this relation, we noticed [9] that the transformation e (j)…”

Section: Introductionmentioning

confidence: 99%

Simultaneous code/error-trellis reduction for convolutional codes using shifted code/error-subsequences

Tajima

Okino

Miyagoshi

2011

2011 IEEE International Symposium on Information Theory Proceedings

View full text Add to dashboard Cite

Abstract-In this paper, we show that the code-trellis and the error-trellis for a convolutional code can be reduced simultaneously, if reduction is possible. Assume that the error-trellis can be reduced using shifted error-subsequences. In this case, if the identical shifts occur in the subsequences of each code path, then the code-trellis can also be reduced. First, we obtain pairs of transformations which generate the identical shifts both in the subsequences of the code-path and in those of the errorpath. Next, by applying these transformations to the generator matrix and the parity-check matrix, we show that reduction of these matrices is accomplished simultaneously, if it is possible. Moreover, it is shown that the two associated trellises are also reduced simultaneously.

show abstract

Minimal Code(Error)-Trellis Module Construction for Rate-k/n Convolutional Codes: Extension of Yamada-Harashima-Miyakawa's Construction

Tajima¹,

Okino²,

Miyagoshi³

2007

IEICE Transactions on Fundamentals of Electronics, Communicatio

View full text Add to dashboard Cite

Yamada, Harashima, and Miyakawa proposed to use a trellis constructed based on a syndrome former for the purpose of Viterbi decoding of rate-(n − 1)/n convolutional codes. In this paper, we extend their code-trellis construction to general rate-k/n convolutional codes. We show that the extended construction is equivalent to the one proposed by Sidorenko and Zyablov. Moreover, we show that the proposed method can also be applied to an error-trellis construction with minor modification.

show abstract

Error-trellises for convolutional codes .I. Construction

Cited by 14 publications

References 18 publications

Error-trellis state complexity of LDPC convolutional codes based on circulant matrices

Error-trellis state complexity of LDPC convolutional codes based on circulant matrices

Simultaneous code/error-trellis reduction for convolutional codes using shifted code/error-subsequences

Minimal Code(Error)-Trellis Module Construction for Rate-k/n Convolutional Codes: Extension of Yamada-Harashima-Miyakawa's Construction

Contact Info

Product

Resources

About