Searching for high-rate convolutional codes via binary syndrome trellises

Florian Hug; Irina Bocharova; Rolf Johannesson; Boris Kudryashov

doi:10.1109/ISIT.2009.5205916

Searching for high-rate convolutional codes via binary syndrome trellises

Florian Hug, Irina Bocharova, Rolf Johannesson, Boris Kudryashov

Department of Electrical and Information Technology

Research output: Chapter in Book/Report/Conference proceeding › Paper in conference proceeding › peer-review

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Abstract

Rate R=(c-1)/c convolutional codes of constraint length nu can be represented by conventional syndrome trellises with a state complexity of s=nu or by binary syndrome trellises with a state complexity of s=nu or s=nu+1, which corresponds to at most 2^s states at each trellis level. It is shown that if the parity-check polynomials fulfill certain conditions, there exist binary syndrome trellises with optimum state complexity s=nu.

The BEAST is modified to handle parity-check matrices and used to generate code tables for optimum free distance rate R=(c-1)/c, c=3,4,5, convolutional codes for conventional syndrome trellises and binary syndrome trellises with optimum state complexity. These results show that the loss in distance properties due to the optimum state complexity restriction for binary trellises is typically negligible.

Original language	English
Title of host publication	[Host publication title missing]
Pages	1358-1362
DOIs	https://doi.org/10.1109/ISIT.2009.5205916
Publication status	Published - 2009
Event	IEEE International Symposium on Information Theory (ISIT), 2009 - Seoul, Korea, Seoul, Korea, Democratic People's Republic of Duration: 2009 Jun 28 → 2009 Jul 3

Conference

Conference	IEEE International Symposium on Information Theory (ISIT), 2009
Country/Territory	Korea, Democratic People's Republic of
City	Seoul
Period	2009/06/28 → 2009/07/03

Subject classification (UKÄ)

Electrical Engineering, Electronic Engineering, Information Engineering

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10.1109/ISIT.2009.5205916

binary_trellis

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title = "Searching for high-rate convolutional codes via binary syndrome trellises",

abstract = "Rate R=(c-1)/c convolutional codes of constraint length nu can be represented by conventional syndrome trellises with a state complexity of s=nu or by binary syndrome trellises with a state complexity of s=nu or s=nu+1, which corresponds to at most 2^s states at each trellis level. It is shown that if the parity-check polynomials fulfill certain conditions, there exist binary syndrome trellises with optimum state complexity s=nu. The BEAST is modified to handle parity-check matrices and used to generate code tables for optimum free distance rate R=(c-1)/c, c=3,4,5, convolutional codes for conventional syndrome trellises and binary syndrome trellises with optimum state complexity. These results show that the loss in distance properties due to the optimum state complexity restriction for binary trellises is typically negligible.",

author = "Florian Hug and Irina Bocharova and Rolf Johannesson and Boris Kudryashov",

year = "2009",

doi = "10.1109/ISIT.2009.5205916",

language = "English",

pages = "1358--1362",

booktitle = "[Host publication title missing]",

note = "IEEE International Symposium on Information Theory (ISIT), 2009 ; Conference date: 28-06-2009 Through 03-07-2009",

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T1 - Searching for high-rate convolutional codes via binary syndrome trellises

AU - Hug, Florian

AU - Bocharova, Irina

AU - Johannesson, Rolf

AU - Kudryashov, Boris

PY - 2009

Y1 - 2009

N2 - Rate R=(c-1)/c convolutional codes of constraint length nu can be represented by conventional syndrome trellises with a state complexity of s=nu or by binary syndrome trellises with a state complexity of s=nu or s=nu+1, which corresponds to at most 2^s states at each trellis level. It is shown that if the parity-check polynomials fulfill certain conditions, there exist binary syndrome trellises with optimum state complexity s=nu. The BEAST is modified to handle parity-check matrices and used to generate code tables for optimum free distance rate R=(c-1)/c, c=3,4,5, convolutional codes for conventional syndrome trellises and binary syndrome trellises with optimum state complexity. These results show that the loss in distance properties due to the optimum state complexity restriction for binary trellises is typically negligible.

AB - Rate R=(c-1)/c convolutional codes of constraint length nu can be represented by conventional syndrome trellises with a state complexity of s=nu or by binary syndrome trellises with a state complexity of s=nu or s=nu+1, which corresponds to at most 2^s states at each trellis level. It is shown that if the parity-check polynomials fulfill certain conditions, there exist binary syndrome trellises with optimum state complexity s=nu. The BEAST is modified to handle parity-check matrices and used to generate code tables for optimum free distance rate R=(c-1)/c, c=3,4,5, convolutional codes for conventional syndrome trellises and binary syndrome trellises with optimum state complexity. These results show that the loss in distance properties due to the optimum state complexity restriction for binary trellises is typically negligible.

U2 - 10.1109/ISIT.2009.5205916

DO - 10.1109/ISIT.2009.5205916

M3 - Paper in conference proceeding

SP - 1358

EP - 1362

BT - [Host publication title missing]

T2 - IEEE International Symposium on Information Theory (ISIT), 2009

Y2 - 28 June 2009 through 3 July 2009

ER -

Searching for high-rate convolutional codes via binary syndrome trellises

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