An algorithm for finding the unequal error protection (UEP) capability of a q-ary image of a low-rate qm-ary cyclic code is presented by combining its concatenated structure with the UEP capability of concatenated codes. The results are independent of a choice of a basis to be used for expanding an element over GF(qm) into GF(q). A table of the UEP capability of binary images of low-rate Reed-S...

A parallel concatenated convolutional coding scheme consists of two constituent systematic convolutional encoders linked by an interleaver. The information bits at the input of the rst encoder are scrambled by the interleaver before entering the second encoder. The codewords of the parallel concatenated code consist of the information bits followed by the parity check bits of both encoders. Par...

We construct error-correcting (nonlinear) binary codes using a construction of Bose and Chowla in additive number theory. Our method extends a construction of Graham and Sloane for constant weight codes. The new codes improve 1028 of the 7168 best known h-error correcting codes of wordlength ≤ 512 with 1 ≤ h ≤ 14. We give asymptotical comparisons to shortened BCH codes.

A serially concatenated code with interleaver consists of the cascade of an outer encoder, an interleaver permuting the outer codeword bits, and an inner encoder whose input words are the permuted outer codewords. In this paper we derive design guidelines for the outer and inner codes that maximize the interleaver gain and the asymptotic slope of the error probability curves.

— To study how to design steganographic algorithm more efficiently, a new coding problem – steganographic codes (abbreviated stego-codes) – is presented in this paper. The stego-codes are defined over the field with q(q ≥ 2) elements. Firstly a method of constructing linear stego-codes is proposed by using the direct sum of vector subspaces. And then the problem of linear stego-codes is convert...

We present families of binary systematic codes that can correct t random errors and detect more than t unidirectional errors. As in recent papers, we start by encoding the k information symbols into a codeword of an [n', k, 2t + 11 error correcting code. The second step of our construction involves adding more bits to this linear error correcting code in order to obtain the detection capability...

A complete classification of the perfect binary oneerror-correcting codes of length 15 as well as their extensions of length 16 was recently carried out in [P. R. J. Östergård and O. Pottonen, “The perfect binary one-error-correcting codes of length 15: Part I—Classification,” submitted for publication]. In the current accompanying work, the classified codes are studied in great detail, and the...

In this paper we demonstrate how data encoded in a five-qubit quantum error correction code can be converted, fault-tolerantly, into a seven-qubit Steane code. This is achieved by progressing through a series of codes, each of which fault-tolerantly corrects at least one error. Throughout the conversion the encoded qubit remains protected. We found, through computational search, that the method...

A powerful class of rate-compatible serially concatenated convolutional codes (SCCCs) has been proposed based on minimizing analytical upper bounds on the error probability in the error floor region. In this paper, this class of codes is further investigated by combining analytical upper bounds with extrinsic information transfer chart analysis to improve performance in the waterfall region. Fo...