We consider binary error correcting codes when errors are deletions. A basic challenge concerning deletion codes is determining p (adv) 0 , the zero-rate threshold of adversarial deletions, defined to be the supremumof allp for which there exists a code familywith rate bounded away from0 capable of correcting a fraction p of adversarial deletions. A recent construction of deletion-correcting co...

One of the puzzling problems in mathematical biology is to show the existence of any form of error-correcting code in the DNA structure. Here we propose a model for the biological coding system similar to that of a digital communication system. This model consists of an encoder (a mapper and a BCH code over Z4) and a modulator (genetic code). Here we show that DNA sequences including proteins a...

In this paper the broadband wireless access system, provided by the IEEE 802.16 wireless MAN air interface with its amendment to mobile users (IEEE 802.16e), is being analyzed. We provide performance results for the most important forward error correcting (FEC) schemes intended for IEEE 802.16e – convolutional turbo codes (CTC) and Low Density Parity Check (LDPC) codes.

First, we compute the number of non-minimal codewords of weight 2dmin in the binary Reed-Muller code RM(r,m). Second, we prove that all codewords of weight greater than 2m − 2m−r+1 in binary RM(r,m), are non-minimal.

The performance of a Turbo code with short block length depends critically on the interleaver design. There are two major criteria in the design of an interleaver: the distance spectrum of the code and the correlation between the information input data and the soft output of each decoder corresponding to its parity bits. This paper describes a new interleaver design for Turbo codes with short b...

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...

It is known that t mutually orthogonal latin squares of order n generate a b t 2c-error correcting code with n codewords. In this paper we consider latin squares of order n made up of elements taken from Zn. In this situation we consider when this code is linear. We present neccessary and sufficient conditions on the latin squares and obtain a method of constructing a maximal family of mutually...

Locally decodable codes are a class of error-correcting codes. Errorcorrecting codes help ensure reliable transmission of information over noisy channels. Such codes allow one to add redundancy, or bit strings, to messages, encoding them into longer bit strings, called codewords, in a way that the message can still be recovered even if a certain fraction of the codeword bits are corrupted. In t...

In this paper we look at the serial concatenation of short linear block codes with a rate-1 recursive convolutional encoder, with a goal of designing high-rate codes with low error floor. We observe that under turbo-style decoding the error floor of the concatenated codes with extended Hamming codes is due to detectable errors in many cases. An interleaver design addressing this is proposed in ...

In this article we outline a method for generating linear optics circuits that encode quantum-error-correcting codes. Using this method we produce a single-error-correcting code encoding one wave packet over five which can be implemented using linear optics and feed-forward correction. This code improves on the capacity of the best known code that can be implemented using linear optics and satu...