NDLI: Convolutional-Code-Specific CRC Code Design

Content Provider	IEEE Xplore Digital Library
Author	Chung-Yu Lou Daneshrad, B. Wesel, R.D.
Copyright Year	1972
Abstract	Cyclic redundancy check (CRC) codes check if a codeword is correctly received. This paper presents an algorithm to design CRC codes that are optimized for the code-specific error behavior of a specified feedforward convolutional code. The algorithm utilizes two distinct approaches to computing undetected error probability of a CRC code used with a specific convolutional code. The first approach enumerates the error patterns of the convolutional code and tests if each of them is detectable. The second approach reduces complexity significantly by exploiting the equivalence of the undetected error probability to the frame error rate of an equivalent catastrophic convolutional code. The error events of the equivalent convolutional code are exactly the undetectable errors for the original concatenation of CRC and convolutional codes. This simplifies the computation because error patterns do not need to be individually checked for detectability. As an example, we optimize CRC codes for a commonly used 64-state convolutional code for information length k=1024, demonstrating significant reduction in undetected error probability compared to the existing CRC codes with the same degrees. For a fixed target undetected error probability, the optimized CRC codes typically require 2 fewer bits.
Starting Page	3459
Ending Page	3470
Page Count	12
File Size	903365
File Format	PDF
ISSN	00906778
Volume Number	63
Issue Number	10
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Convolutional codes Cyclic redundancy check codes Error probability Polynomials Tin Decoding Generators undetected error probability catastrophic code convolutional code cyclic redundancy check (CRC) code Catastrophic code
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering

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