Codes with multi-level error-correcting capabilities (original) (raw)
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Block-Modulation Codes for Unequal Error Protection
2018
Unequal error protection (UEP) codes find applications in broadcast cbannels, as well as in otber digital communication systems, where messages bave ditTerent degrees of importance, In this correspon dence, binary linear UEP (LUEP) codes combined with a Gray mapped QPSK signal set are used to obtain new efficient QPSK block-modulation codes for unequal error protection. Several examples of QPSK modulation codes that have tbe same minimum squared Euclidean distance as the best QPSK modulation codes, of the same rate and length, are given. In the new constructions of QPSK block-modulation codes, even-length binary LUEP codes are used. Good even-length binary LUEP codes are obtained wben shorter binary linear codes are combined using either the well-known lulu + vi-construction or the so-called construction X, Both constructions have the advantage of resulting in optimal or near-optimal binary LUEP codes of short to moderate lengths, using very simple linear codes, and may be used as ...
Multilevel codes and multistage decoding for unequal error protection
1999 IEEE International Conference on Personal Wireless Communications (Cat. No.99TH8366), 1999
| In this paper, multilevel coded modulation with multistage decoding and unequal error protection is discussed. Three types of unconventional partitionings for 8-PSK and 16(64)-QAM constellations with UEP capabilities are analyzed. Based on the tight upper/approximated bounds on bit error probability, it is shown that more degrees of freedom in the construction of multilevel coding and multistage decoding can be accomplished by introducing asymmetries in PSK and QAM signal constellations. Generalizations to other PSK and QAM type constellations follow the same lines.
EURASIP Journal on Advances in Signal Processing, 2013
Unequal error protection (UEP) codes provide a selective level of protection for different blocks of the information message. The effectiveness of two sub-optimum soft-decision decoding algorithms, namely generalized Chase-2 and weighted erasure decoding, is evaluated in this study for each protection class of UEP block codes. The performances of both algorithms are compared to that of the maximum likelihood algorithm in order to evaluate the performance loss of each protection class provided by less complex algorithms as well as their complexities are evaluated according to the number of arithmetic operations performed at each decoding step. Finally, numerical results and examples are provided which indicate that a trade-off between performance and complexity for each protection class is obtained. The results of this study can be used to select appropriate UEP coding and decoding schemes in applications that demand low energy consumption.
Optimal two-level unequal error control codes for computer systems
… , IEEE Transactions on, 1998
Error control codes are now successfully applied to computer systems and communication systems. When we consider some types of computer words or communication messages, the information in some part of the word is more important than the other. Address and control information in computer words and communication messages and pointer information in database words are good examples. The more important the part of the word is, or the less reliable the part is, the more strongly it should be protected from errors. Based on this, this paper proposes a new class of codes, called unequal error control codes, which have some unequal error control levels in the codeword, that is, have some distinct code functions in the codeword and protect the part of the word from errors according to its importance or reliability level. From a simple and practical viewpoint, this paper adopts the model of the codeword which includes two unequal levels: one having strong error control level in some part of the codeword, called fixed-byte, and the other having relatively weak error control level outside the fixed-byte. This paper deals with three basic unequal error control codes. For all types of codes, the paper clarifies necessary and sufficient conditions and bounds on code length and demonstrates code construction method of the optimal codes and evaluation of these codes from the perspectives of error correction/detection capability and decoder hardware complexity.
On a class of optimal nonbinary linear unequal-error-protection codes for two sets of messages
IEEE Transactions on Information Theory, 1994
Proposition 6: Let m 2 p and j arbitrary. If all weights in c are divisible by 2p, then the degree of the set C,E3(zm) A, does not exceed 2m -2p. Pro03 If the set C1EJ(2m) A, is empty, the proposition is trivial. If A, is nonempty, then j must be divisible by 2p. Hence, the set '&(2m) S, of degree 2" -1 is contained in the set C110(2p) Sa of degree 2p -1. By assumption, the latter set contains the code C, so deg, (C n CzEo(2p) S,) = 0. Hence,
Linear Codes with Non-Uniform Error Correction Capability
Designs, Codes and Cryptography, 1997
This paper introduces a class of linear codes which are non-uniform error correcting, i.e. they have the capability of correcting different errors in different codewords. A technique for specifying error characteristics in terms of algebraic inequalities, rather than the traditional spheres of radius e, is used. A construction is given for deriving these codes from known linear block codes. This is accomplished by a new method called parity sectioned reduction. In this method, the parity check matrix of a uniform error correcting linear code is reduced by dropping some rows and columns and the error range inequalities are modified.
Unequal Error Protection Codes
Wiley Encyclopedia of Telecommunications, 2003
In Literature, Unequal Error Protection codes (UEP) are described and studied based on parity check or generator matrices. In this paper we present a computational algorithm which provides generator polynomials for cyclic and pseudo-cyclic (polynomial) codes which have UEP properties. We devised several C++ programs and then we realized a complete table with all the polynomial codes with UEP properties having length n#30 and distances up to 9.
On linear unequal error protection codes
Information Theory, IEEE Transactions on, 1967
Abstract-The class of codes discussed in this paper has the property that its error-correction capability is described in terms of correcting errors in specific digits of a code word even though other digits in the code may be decoded incorrectly. To each digit of the code words is assigned an ...
A Linear Programming bound for Unequal Error Protection codes
2010 Australian Communications Theory Workshop (AusCTW), 2010
In coding theory, it is important to calculate an upper bound for the size of codes given the length and minimum distance. The Linear Programing (LP) bound is known as a good upper bound for the size of codes. On the other hand, Unequal Error Protection (UEP) codes have been studied in coding theory. In UEP codes, a codeword has special bits which are protected against a greater number of errors than other bits. In this paper, we propose a LP bound for UEP codes. Firstly, we generalize the distance distribution (or weight distribution) of codes. Under the generalization, we lead to the LP bound for UEP codes. Lastly, we compare the proposed bound with a modified Hamming bound.