共查询到20条相似文献,搜索用时 62 毫秒
1.
Patapoutian A. Kumar P.V. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1992,38(4):1375-1382
A simple technique employing linear block codes to construct (d ,k ) error-correcting block codes is considered. This scheme allows asymptotically reliable transmission at rate R over a BSC channel with capacity C BSC provided R ⩽C d,k-(1+C BSC), where C d,k is the maximum entropy of a (d ,k ) source. For the same error-correcting capability, the loss in code rate incurred by a multiple-error correcting (d ,k ) code resulting from this scheme is no greater than that incurred by the parent linear block code. The single-error correcting code is asymptotically optimal. A modification allows the correction of single bit-shaft errors as well. Decoding can be accomplished using off-the-shelf decoders. A systematic (but suboptimal) encoding scheme and detailed case studies are provided 相似文献
2.
Wu J. Costello D.J. Jr. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1992,38(3):933-939
Set partitioning is applied to multidimensional signal spaces over GF(q ), i.e., GFn1(q ) (n 1⩽q ), and it is shown how to construct both multilevel block codes and multilevel trellis codes over GF(q ). Multilevel (n , k , d ) block codes over GF(q ) with block length n , number of information symbols k , and minimum distance d min⩾d are presented. These codes use Reed-Solomon codes as component codes. Longer multilevel block codes are also constructed using q -ary block codes with block length longer than q +1 as component codes. Some quaternary multilevel block codes are presented with the same length and number of information symbols as, but larger distance than, the best previously known quaternary one-level block codes. It is proved that if all the component block codes are linear. the multilevel block code is also linear. Low-rate q -ary convolutional codes, word-error-correcting convolutional codes, and binary-to-q -ary convolutional codes can also be used to construct multilevel trellis codes over GF(q ) or binary-to-q -ary trellis codes 相似文献
3.
Hou X.-D. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1991,37(2):378-379
Whether quasi-perfect codes are normal is addressed. Let C be a code of length n , dimension k , covering radius R , and minimal distance d . It is proved that C is normal if d ⩾2R -1. Hence all quasi-perfect codes are normal. Consequently, any [n ,k ]R binary linear code with minimal distance d ⩾2R -1 is normal 相似文献
4.
Etzion T. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1990,36(4):899-905
Two DC-free codes are presented with distance 2d , b ⩾1 length 2n +2r (d -1) for d ⩽3 and length 2n +2r (d -1)(2d -1) for d >3, where r is the least integer ⩾log2 (2n +1). For the first code l =4, c =2, and the asymptotic rate of this code is 0.7925. For the second code l =6, c =3, and the asymptotic rate of this code is 0.8858. Asymptotically, these rates achieve the channel capacity. For small values of n these codes do not achieve the best rate. As an example of codes of short length with good rate, the author presents a (30, 10, 6, 4) DC-free block code with 221 codewords. A construction is presented for which from a given code C 1 of length n , even weight, and distance 4, the author obtains a (4n , l , c , 4) DC-free block code C 2, where l is 4, 5 or 6, and c is not greater than n +1 (but usually significantly smaller). The codes obtained by this method have good rates for small lengths. The encoding and decoding procedures for all the codes are discussed 相似文献
5.
Kasami T. Takata T. Fujiwara T. Lin S. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1991,37(1):164-167
Two important structural properties of block M (=2' )-ary PSK modulation codes, linear structure and phase symmetry, are investigated. An M -ary modulation code is first represented as a code with symbols from the integer group S M-PSK=(0,1,2,---,M -1) under modulo-M addition. Then the linear structure of block M -PSK modulation codes over S M-PSK with respect to modulo- M vector addition is defined, and conditions are derived under which a block M -PSK modulation code is linear. Once the linear structure is developed, the phase symmetry of block M -PSK modulation codes is studied. In particular, a necessary and sufficient condition for a block M -PSK modulation code that is linear as a binary code to be invariant under 2h/180°M phase rotation, for 1⩽h ⩽l is derived. Finally, a list of short 8-PSK and 16-PSK modulation codes is given, together with their linear structure and the smallest phase rotation for which a code is invariant 相似文献
6.
A design technique to reduce the search time for trellis codes with multilevel phase modulation is presented. Codes are constructed by connecting trellis diagrams for codes with fewer states in parallel. For example, an N -state code can be constructed by connecting two N /2-state codes. The way in which the embedded codes are connected increases the upper limit on minimum free distance otherwise imposed by parallel transitions between states. In some cases, this technique can reduce the number of codes in a code search by a factor of approximately 2ν, the number of coder states. A computer search incorporating this technique for eight-level amplitude modulation (8-AM) codes having 211 and 212 states produced codes with greater minimum free distance than reported previously (i.e. greater than 6 dB coding gain). New eight-level phase-shift-keying (8-PSK) codes, which have a different structure from previously reported codes, are also presented 相似文献
7.
Ytrehus O. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1991,37(2):349-351
A binary, linear block code C with block length n and dimension n is commonly denoted by [n , k ] or, if its minimum distance is d , by [n , k ,d ]. The code's covering radius r (C ) can be defined as the smallest number r such that any binary column vector of length (n -k ) can be written as a sum of r or fewer columns of a parity-check matrix of C . An [n ,k ] code with covering radius r is denoted by [n ,k ]r . R.A. Brualdi et al., (1989) showed that l (m ,r ) is defined to be the smallest n such that an [n ,n -m ]r code exists. l (m ,2) is known for m ⩽6, while it is shown by Brualdi et al. that 17⩽l (7,2)⩽19. This lower bound is improved by A.R. Calderbank et al. (1988), where it is shown that [17,10]2 codes do not exist. The nonexistence of [18,11]2 codes is proved, so that l (7,2)=19. l [7.2)=19 is established by showing that [18,11]2 codes do not exist. It is also shown that [64,53]2 codes do not exist, implying that l (11,2)⩾65 相似文献
8.
On the Hamming distance properties of group codes 总被引:1,自引:0,他引:1
Forney G.D. Jr. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1992,38(6):1797-1801
Under certain mild conditions, the minimum Hamming distance D of an (N , K , D ) group code C over a non-abelian group G is bounded by D ⩽N -2K +2 if K ⩽N /2, and is equal to 1 if K >N /2. Consequently, there exists no (N , K , N -K +1) group code C over an non-abelian group G if 1<K <N . Moreover, any normal code C with a non-abelian output space has minimum Hamming distance equal to D =1. These results follow from the fact that non-abelian groups have nontrivial commutator subgroups. Finally, if C is an (N , K , D ) group code over an abelian group G that is not elementary abelian, then there exists an (N , K , D ) group code over a smaller elementary abelian group G '. Thus, a group code over a general group G cannot have better parameters than a conventional linear code over a field of the same size as G 相似文献
9.
Brualdi R.A. Pless V.S. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1990,36(2):399-401
If C is a code, an orphan is a coset that is not a descendant. Orphans arise naturally in the investigation of the covering radius. Case C has only even-weight vectors and minimum distance of at least four. Cosets that are orphans are characterized, and then the existence is proved of a family of orphans of first-order Reed-Muller codes R (1, m ). For m ⩽5 all orphans of R (1, m ) are identified 相似文献
10.
Honkala I.S. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1991,37(4):1203-1206
The concept of a (k , t )-subnormal covering code is defined. It is discussed how an amalgamated-direct-sumlike construction can be used to combine such codes. The existence of optimal (q , n , M ) 1 codes C is discussed such that by puncturing the first coordinate of C one obtains a code with (q , 1)-subnorm 2 相似文献
11.
Honkala H.S. Hamalainen H.O. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1991,37(2):372-375
The normality of binary codes is studied. The minimum cardinality of a binary code of length n with covering radius R is denoted by K (n ,R ). It is assumed that C is an (n ,M )R code, that is, a binary code of length n with M codewords and covering radius R . It is shown that if C is an (n ,M )1 code, then it is easy to find a normal (n ,M )1 code by changing C in a suitable way, and that all the optimal (n ,M )1 codes (i.e. those for which M =K (n ,1)) are normal and their every coordinate is acceptable. It is shown that if C is an abnormal (n ,M ) code, then n ⩾9, and an abnormal (9118)1 code which is the smallest abnormal code known at present, is constructed. Lower bounds on the minimum cardinality of a binary abnormal code of length n with covering radius 1 are derived, and it is shown that if an (n ,M )1 code is abnormal, then M ⩾96 相似文献
12.
The authors present a general technique for computing P e for all possible shortened versions of cyclic codes generated by any given polynomial. The technique is recursive, i.e. computes P e for a given code block length n from that of the code block length n -1. The proposed computation technique for determining P e does not require knowledge of the code weight distributions. For a generator polynomial of degree r , and |g | nonzero coefficients, the technique yields P e for all code block lengths up to length n in time complexity O (n |g |2r+|g|). Channels with variable bit error probabilities can be analyzed with the same complexity. This enables the performance of the code generator polynomials to be analyzed for burst errors 相似文献
13.
Generalized Hamming weights of linear codes 总被引:4,自引:0,他引:4
Helleseth T. Klove T. Ytrehus O. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1992,38(3):1133-1140
The generalized Hamming weight, d r(C ), of a binary linear code C is the size of the smallest support of any r -dimensional subcode of C . The parameter d r(C ) determines the code's performance on the wire-tap channel of Type II. Bounds on d r(C ), and in some cases exact expressions, are derived. In particular, a generalized Griesmer bound for d r(C ) is presented and examples are given of codes meeting this bound with equality 相似文献
14.
The trellis coding technique is applied to line-coded baseband digital transmission systems. For R =n /n +1(n =1,2,3) coding rates, a new codeword assignment model is proposed to accomplish basic requirements for line coding in which each length n binary data sequence is encoded into a length n +1 ternary (+,0,-) line codeword chosen among the code alphabet with 2n+2 elements. Assuming Viterbi decoding, the system error performance is improved by increasing the free Euclidean distance between coded sequences. A new algorithm is given for the calculation of the free distance between line-coded sequences so obtained. For R =1/2 and R =3/4 rates, the analytical error performance upper bounds are derived. The power spectral densities of the new line codes are also calculated and compared with those of known line codes 相似文献
15.
Chao-Ping X. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1992,38(3):1140-1142
Sufficient and necessary conditions are obtained for which the geometric Goppa codes C (D ,G ) and C ( D ,H ) are equal for two divisors G and H . In particular, it is proven that if G and H are two effective divisors of the same degree smaller than n -1, then C (D ,G ) and C (D ,H ) are equal, if and only if G =H 相似文献
16.
Decoding geometric Goppa codes using an extra place 总被引:1,自引:0,他引:1
Porter S.C. Shen B.-Z. Pellikaan R. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1992,38(6):1663-1676
Decoding geometric Goppa codes can be reduced to solving the key congruence of a received word in an affine ring. If the codelength is smaller than the number of rational points on the curve, then this method can correct up to 1.2 (d *-L)/2-s errors, where d * is the designed minimum distance of the code and s is the Clifford defect. The affine ring with respect to a place P is the set of all rational functions which have no poles except at P , and it is somehow similar to a polynomial ring. For a special kind of geometric Goppa code, namely C Ω(D ,mP ), the decoding algorithm is reduced to solving the key equation in the affine ring, which can be carried out by the subresultant sequence in the affine ring with complexity O (n 3), where n is the length of codewords 相似文献
17.
Weight enumerators of self-dual codes 总被引:4,自引:0,他引:4
Brualdi R.A. Pless V.S. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1991,37(4):1222-1225
Some construction techniques for self-dual codes are investigated, and the authors construct a singly-even self-dual [48,24,10]-code with a weight enumerator that was not known to be attainable. It is shown that there exists a singly-even self-dual code C ' of length n =48 and minimum weight d =10 whose weight enumerator is prescribed in the work of J.H. Conway et al. (see ibid., vol.36, no.5, p.1319-33, 1990). Two self-dual codes of length n are called neighbors, provided their intersection is a code of dimension (n /2)-1. The code C' is a neighbor of the extended quadratic residue code of length 48 相似文献
18.
Westerink P.H. Weber J.H. Boekee D.E. Limpers J.W. 《Communications, IEEE Transactions on》1993,41(3):454-459
Protection of images that are encoded using subband coding from channel error is addressed. In this scheme the low-pass subband is encoded using DPCM (differential pulse-code modulation), and the other subbands are encoded using a scalar quantizer. The quantizers are all Lloyd-Max quantizers, from which the representation levels have fixed length codewords. First, considering only single errors in each codeword, a channel error distortion measure is derived for each quantizer, that is, for each subband. Codewords are assigned to the quantizer representation levels, yielding a low value of the distortion measure. Next, sets S ij consisting of the j th bit from subband i are formed. Each set S ij is assigned a particular BCH code C ij. An algorithm that optimally assigns BCH codes C ij to each set S ij, based on a channel error distortion measure for the entire image, is derived. The protection scheme is adaptive, because each set of bits within each subband can be assigned a different error protection code. Examples show that this approach is preferable to assigning equal error protection codes to each set of bits. It is shown that in the case of a channel error probability of 10 -3, only 5% to 10% extra bits are needed for adequate channel error protection 相似文献
19.
A concatenated coded modulation scheme is presented for error control in data communications. The scheme is achieved by concatenating a Reed-Solomon outer code and a bandwidth efficient block inner code for M -ary phase-shift keying (PSK) modulation. Error performance of the scheme is analyzed for an additive white Gaussian noise (AWGN) channel. It is shown that extremely high reliability can be attained by using a simple M -ary PSK modulation inner-code and a relatively powerful Reed-Solomon outer code. Furthermore, if an inner code of high effective rate is used, the bandwidth expansion required by the scheme due to coding will be greatly reduced. The scheme is particularly effective for high-speed satellite communications for large file transfer where high reliability is required. A simple method is also presented for constructing block codes for M -ary PSK modulation. Soome short M -ary PSK codes with good minimum squared Euclidean distance are constructed. These codes have trellis structure and hence can be decoded with a soft-decision Viterbi decoding algorithm. Furthermore, some of these codes are phase invariant under multiples of 45° rotation 相似文献
20.
Loeliger H.-A. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1991,37(6):1675-1682
Recently, linear codes over Z M (the ring of integers mod M ) have been presented that are matched to M -ary phase modulation. The general problem of matching signal sets to generalized linear algebraic codes is addressed based on these codes. A definition is given for the notion of matching. It is shown that any signal set in N -dimensional Euclidean space that is matched to an abstract group is essentially what D. Slepian (1968) called a group code for the Gaussian channel. If the group is commutative, this further implies that any such signal set is equivalent to coded phase modulation with linear codes over Z M. Some further results on such signal sets are presented, and the signal sets matched to noncommutative groups and the linear codes over such groups are discussed 相似文献