Minimum distance is an important parameter of a linear error correcting code. For improved performance of binary Low Density Parity Check (LDPC) codes, we need to have the minimum distance grow fast with n, the codelength. However, the best we can hope for is a linear growth in dmin with n. For binary LDPC codes, the necessary and sufficient conditions on the LDPC ensemble parameters, to ensure...

Recently a new construction of run length limited block error control codes based on control matrices of linear block codes was proposed. In this paper a similar construction for obtaining trellis run length limited error control codes from convolutional codes is described. The main advantage of it, beyond its simplicity is that it does not require any additional redundancy except the one which...

Tree search algorithms have a long history in computer science. In the coding literature, tree search algorithms have traditionally been used for decoding convolutional codes. Convolutional codes are linear codes with a special structure. Classic tree search decoders (most notably the sequential decoder) search one code tree in which the bits are ordered sequentially. We propose a multitree sea...

Product channel codes are proposed to protect progressively compressed and packetized images for noisy channels. Within packets, the product code uses the concatenation of a rate compatible punctured convolutional code and an error detecting parity check code. Across packets, Reed-Solomon codes are used. Beneets include exible choice of delay, adaptability of error protection level (i.e., unequ...

Product channel codes are proposed to protect progressively compressed and packetized images for noisy channels. Within packets, the product code uses the concatenation of a ratecompatible punctured convolutional code and an error detecting parity check code. Across packets, Reed–Solomon codes are used. Benefits include flexible choice of delay, adaptability of error protection level (i.e., une...

Remark 4: The author is unable to deal analytically with the general case of p + l/2 where one does not have the property of symmetry. However, the case that p is close to l/2 may be tractabie an9 interesting. Linear smoothing using measurements containing correlated noise with an application to inertial navigation, " IEEE Trans. Abstract-The covering radius is given for all binary cyclic codes...

Abstract Using algebraic techniques, one of the co-authors has designed a [155,64,20] low density parity check code based on permutation matrices. This code is quasi-cyclic by construction and hence admits a convolutional representation. A set of low density parity check convolutional codes is derived from this quasi-cyclic code and its generalizations. We investigate the performance of these c...

In this paper the low density party check (LDPC) codes used in the IEEE 802.16 standard physical layer are studied, and two novel techniques to enhance the performance of such codes are introduced. In the first technique, a novel parity check matrix for LDPC codes over GF(4) with the non-zero entries chosen to maximize the entropy is proposed, the parity check matrix is based on the binary pari...

A product channel code is proposed to protect progressively compressed and packetized image data that is transmitted across noisy channels. Across packets, the product code is composed of Reed-Solomon codes. Within packets, the product code uses the concatena-tion of a rate compatible punctured convolutional code and an error detecting parity check code. The beneets include exibility in terms o...

It is shown that soft decision maximum likelihood decoding of any (n,k) linear block code over GF(q) can be accomplished using the Viterbi algorithm applied to a trellis with no more than q (n-k) states. For cyclic codes, the trellis is periodic. When this technique is applied to the decoding of product codes, the number of states in the trellis can be much fewer than q n-k. For a binary (n,rz ...