In this chapter we introduce our task: communicating a digital message without error (or with as few errors as possible) despite an imperfect communications medium. Figure 1.1 shows a typical communications system. In this text we will assume that our source is producing binary data, but it could equally be an analog source followed by analog-to-digital conversion. Through the early 1940s, engi...

The use of error-correcting codes for tight control of the peak-to-mean envelope power ratio (PMEPR) in orthogonal frequency-division multiplexing (OFDM) transmission is considered in this correspondence. By generalizing a result by Paterson, it is shown that each q-phase (q is even) sequence of length 2 lies in a complementary set of size 2, where k is a nonnegative integer that can be easily ...

In this paper we utilize both the implicit residual source correlation and the explicit redundancy from a forward-error-correction (FEC) scheme for the error protection of packetized variable-length encoded source indices. The implicit source correlation is exploited in a novel symbol-based soft-input a-posteriori probability (APP) decoder, which leads to an optimal decoding process in combinat...

The entanglement-assisted stabilizer formalism provides a useful framework for constructing quantum error-correcting codes (QECC), which can transform arbitrary classical linear codes into entanglement-assisted quantum error correcting codes (EAQECCs) by using pre-shared entanglement between the sender and the receiver. In this paper, we construct five classes of entanglement-assisted quantum M...

Suppose C is a [n, k, d] code over Fq, t < n is a positive integer. For any received vector y = (y1, · · · , yn) ∈ Fq , we refer to any code word c in C satisfying d(c,y) ≤ t as a tconsistent code word. A decoding problem is in fact the problem of finding an effective (or efficient) algorithm which can find t-consistent code words, and we call such an algorithm a decoding algorithm that can cor...

Our purpose here is to show how it is possible to recover the structure of a randomly permuted concatenated code, and how to use this information for decoding. This result prohibits the use of rst order concatenated codes in public-key cryp-tosystems based on error-correcting codes. R esum e Nous montrons ici comment il est possible de reconstituer la structure d'un code concat en e permut e al...

Construction X is known from the theory of classical error control codes. We present a variant of this construction that produces stabilizer quantum error control codes from arbitrary linear codes. Our construction does not require the classical linear code that is used as an ingredient to satisfy the dual containment condition. We prove lower bounds on the minimum distance of quantum codes obt...

In this paper, secure channel coding schemes based on turbo codes are suggested for time reversal ultra wideband (TR-UWB) systems. Turbo code has the capability of error correction near Shannon’s limit. Adding security to turbo code is an attractive idea since it could reduce the overall processing cost of providing secure coded data and enjoys the advantages of high-speed encryption and decryp...