1-7hit |
Minjia SHI Jie TANG Maorong GE
Let $R$ = $mathbb{F}_{p}+umathbb{F}_{p}+vmathbb{F}_{p}+uvmathbb{F}_{p}$, where u2=u, v2 and uv=vu. A relation between the support weight distribution of a linear code $mathscr{C}$ of type p4k over R and its dual code $mathscr{C}^{ot}$ is established.
Takayuki ITSUI Kenta KASAI Ryoji IKEGAYA Tomoharu SHIBUYA Kohichi SAKANIWA
The average bit erasure probability of a binary linear code ensemble under maximum a-posteriori probability (MAP) decoding over binary erasure channel (BEC) can be calculated with the average support weight distribution of the ensemble via the EXIT function and the shortened information function. In this paper, we formulate the relationship between the average bit erasure probability under MAP decoding over BEC and the average support weight distribution for a binary linear code ensemble. Then, we formulate the average support weight distribution and the average bit erasure probability under MAP decoding over BEC for regular LDPC code ensembles.
Kenji YASUNAGA Toru FUJIWARA Tadao KASAMI
Local weight distribution is the weight distribution of minimal codewords in a linear code. We give the local weight distribution of the (256, 93) third-order binary Reed-Muller code. For the computation, a coset partitioning algorithm is modified by using a binary shift invariance property. This reduces the time complexity by about 1/256 for the code. A necessary and sufficient condition for minimality in Reed-Muller codes is also presented.
Kenta KASAI Yuji SHIMOYAMA Tomoharu SHIBUYA Kohichi SAKANIWA
Multi-Edge type Low-Density Parity-Check codes (MET-LDPC codes) introduced by Richardson and Urbanke are generalized LDPC codes which can be seen as LDPC codes obtained by concatenating several standard (ir)regular LDPC codes. We prove in this paper that MET-LDPC code ensembles possess a certain symmetry with respect to their Average Coset Weight Distributions (ACWD). Using this symmetry, we drive ACWD of MET-LDPC code ensembles from ACWD of their constituent ensembles.
Kazuhiko YAMAGUCHI Toshiaki WATANABE Kingo KOBAYASHI
In this paper, we study unequal error protection (UEP) capabilities of punctured convolutional codes. For constructing the good UEP convolutional codes, the conditional weight distributions of UEP convolutional codes are defined and evaluated. The conditional weight distributions are computed by using the transfer functions of time-varying trellis structures of punctured convolutional codes. The best UEP convolutional codes from the viewpoint of the weight distributions are listed.
Tadao KASAMI Toru FUJIWARA Yoshihisa DESAKI
In this paper cosets of the second order Reed-Muller code of length 2m, denoted RMm,2, in the third order Reed-Muller code of the same length, denoted RMm,3, are studied. The set of cosets, RMm,3/RMm,2 is partitioned into blocks. Two cosets are in the same block, if and only if there is a transformation in the general linear group by which one coset is transformed into the other. Two cosets in the same block have the same weight distribution. For the code length less than or equal to 128, the representative coset leader of each block is presented and the weight distribution of cosets in the block is computed. By using these results, the extended code of a cyclic code of length 128 between RM7,2 and RM7,3 can be decomposed into a set of cosets in RM7,3/RM7,2, and its weight distribution can be derived. Several cyclic codes to length 127 are shown to be equivalent and some new linear unequal error protection codes are found.
Kazuhiko IWASAKI Sandeep K. GUPTA Prawat NAGVAJARA Tadao KASAMI
The aliasing probability was analyzed for MISRs when the error probability for each input was different. A closed form expression was derived by applying the complete weight distributions of linear codes over a Galois field and its dual codes. The aliasing probability for MISRs characterized by non-primitive polynomials was also analyzed. The inner product for binary representation of symbols was used instead of multiplication over a Galois field. The results show the perfect expression for analyzing the aliasing probability of MISRs.