where ω = vk and k± = k x̂ ± kΓ ŷ. Slepian also noted that if v < c, then cos(kΓy) = cosh(kΓ′y) where Γ′ = iΓ = √ 1− v2/c2, and the waveform (1) again propagates with speed v. The vector potential (1), together with scalar potential V = 0, satisfy the conditions for the Coulomb, Gibbs, Lorenz and velocity gauges. See, for example, [2]. For completeness, the electric field is E = iωA ≡ E+ + E− wh...

The aim of this paper is to prove theorems for the Slepian-Wolf source coding and the broadcast channel coding (independent messages and no common message) based on the the notion of a stronger version of the hash property for an ensemble of functions. Since an ensemble of sparse matrices has a strong hash property, codes using sparse matrices can realize the achievable rate region. Furthermore...

This paper proposes a practical coding scheme for the Slepian-Wolf problem of separate encoding of correlated sources. Finite-state machine (FSM) encoders, concatenated in parallel, are used at the transmit side and an iterative turbo decoder is applied at the receiver. Simulation results of system performance are presented for binary sources with different amounts of correlation. Obtained resu...

We consider the problem of compressing correlated binary sources when the correlation between sources is defined by a Hidden Markov Model (HMM). Specifically, the HMM describes the correlation pattern, i.e. the modulo-2 addition of the two sources. In this framework, we develop a density evolution analysis of a compression system using irregular LDPC codes as source codes. In order to achieve t...

The basic polarization phenomenon for i.i.d. sources is extended to a framework allowing dependencies within and between multiple sources. In particular, it is shown that taking the polar transform of a random matrix with i.i.d. columns of arbitrary (correlated) distribution allows to extract the randomness and dependencies. This result is then used to develop polar coding schemes (having low c...