Capacity Achieving Code Constructions for Two Classes of (d,k) Constraints

In this paper, we present two low complexity algorithms that achieve capacity for the noiseless (d,k) constrained channel when k=2d+1, or when k-d+1 is not prime. The first algorithm, called symbol sliding, is a generalized version of the bit flipping algorithm introduced by Aviran et al. [1]. In addition to achieving capacity for (d,2d+1) constraints, it comes close to capacity in other cases. The second algorithm is based on interleaving, and is a generalized version of the bit stuffing algorithm introduced by Bender and Wolf [2]. This method uses fewer than k-d biased bit streams to achieve capacity for (d,k) constraints with k-d+1 not prime. In particular, the encoder for (d,d+2^m-1) constraints, 1\le m<\infty, requires only m biased bit streams.Comment: 16 pages, submitted to the IEEE Transactions on Information Theor

Coding for the Optical Channel: the Ghost-Pulse Constraint

We consider a number of constrained coding techniques that can be used to mitigate a nonlinear effect in the optical fiber channel that causes the formation of spurious pulses, called ``ghost pulses.'' Specifically, if $b_1 b_2 ... b_{n}$ is a sequence of bits sent across an optical channel, such that $b_k=b_l=b_m=1$ for some $k,l,m$ (not necessarily all distinct) but $b_{k+l-m} = 0$, then the ghost-pulse effect causes $b_{k+l-m}$ to change to 1, thereby creating an error. We design and analyze several coding schemes using binary and ternary sequences constrained so as to avoid patterns that give rise to ghost pulses. We also discuss the design of encoders and decoders for these coding schemes.Comment: 13 pages, 6 figures; accepted for publication in IEEE Transactions on Information Theor

Algorithmic and explicit determination of the Lovász number for certain circulant graphs

AbstractWe consider the problem of computing the Lovász theta function for circulant graphs Cn,J of degree four with n vertices and chord length J, 2⩽J⩽n. We present an algorithm that takes O(J) operations if J is an odd number, and O(n/J) operations if J is even. On the considered class of graphs our algorithm strongly outperforms the known algorithms for theta function computation. We also provide explicit formulas for the important special cases J=2 and J=3

PERFORMANCE LIMITS FOR ENERGY-CONSTRAINED COMMUNICATION SYSTEMS

Ph.DDOCTOR OF PHILOSOPH