We consider online routing algorithms for routing between the vertices of embedded planar straight line graphs. Our results include (1) two deterministic memoryless routing algorithms, one that works for all Delaunay triangulations and the other that works for all regular triangulations, (2) a randomized memoryless algorithm that works for all triangulations, (3) an O(1) memory algorithm that w...

A variable-toxed length encoding procedure is a mapping from a dictionary of variable length strings of source outputs to the set of codewords of a given length. For memoryless sources, the Tunstall procedure can be applied to construct optimal uniquely parsable dictionaries and the resulting codes are known to work especially well for sources with small entropies. We introduce the idea of plur...

We study the design of a belief propagation decoder for lowdensity parity check (LDPC) codes over binary channels with additive M th-order Markov noise, specifically the queuebased channel (QBC) [1]. The decoder is an extension of the sum product algorithm (SPA) for the case of memoryless channels and is similar to the one developed for the GilbertElliot channel [2, 3, 4]. Simulation results of...

In the memoryless vector quantization scheme, each image block is independently encoded as a corresponding index and then an index table will be generated. In this paper, we apply the side match concept and propose a new scheme, which can further compress the index table without introducing extra encoding distortion. Our scheme exploits the characteristic that the blocks of images are highly co...

The problem of fixed-rate block quantization of an unbounded real memoryless source is studied. It is proved that if the source has a finite sixth moment, then there exists a sequence of quantizers Qn of increasing dimension n and fixed rate R such that the mean squared distortion A(Q,) is bounded as A(Q,) < D(R) + O(dm), where D(R) is the distortion-rate function of the source. Applications of...

The method of types is one of the key technical tools in Shannon Theory, and this tool is valuable also in other fields. In this paper, some key applications will be presented in sufficient detail enabling an interested nonspecialist to gain a working knowledge of the method, and a wide selection of further applications will be surveyed. These range from hypothesis testing and large deviations ...

We consider transmission of discrete memoryless sources (DMSes) across discrete memoryless channels (DMCs) using variable-length lossy source-channel codes with feedback. The reliability function (optimum error exponent) is shown to be equal to max{0, B(1−R(D)/C)}, where R(D) is the rate-distortion function of the source, B is the maximum relative entropy between output distributions of the DMC...

We consider the stationary memoryless channels with input cost. We prove that for transmission rates above the capacity the correct probability of decoding tends to zero exponentially as the block length n of codes tends to infinity. In the case where both of channel input and output sets are finite, we determine the optimal exponent function on the above exponential decay of the correct probab...

T HE discrete memoryless broadcast channel (%P(YJlX), 94 x 3) consists of three finite sets % ., 9, % and a probability transition matrixp(y,zjx). Let p,(ylx) andp,(zIx) be the two marginals of p(y,zlx), and let P, and P2 denote the discrete memoryless channels with probability transition matrices p&y Ix) and pz(zlx), respectively. Recall the following three relations between P, and P2. Definit...

Fast polarization is crucial for the performance guarantees of polar codes. In the memoryless setting, the rate of polarization is known to be exponential in the square root of the block length. A complete characterization of the rate of polarization for models with memory has been missing. We consider polar codes for processes with memory that are characterized by an underlying ergodic finite ...