A New Multi Wavelength - Optical Code Division Multiple Access Code Design Based on Balanced Incomplete Block Design M. Ravi Kumar * , S. S. Pathak † , N. B. Chakrabarti ‡ * G. S. Sanyal School of Telecommunications, Indian Institute of Technology, Kharagpur, India †‡ Department of Electronics & Electrical Communication Engineering, Indian Institute of Technology, Kharagpur, India ravi@gssst.iitkgp.ernet.in * , ssp@ece.iit.kgp.ernet.in † , nirmalbc@yahoo.com ‡ Abstract—A new three-dimensional (Space/ Wavelength/ Time) Multi Wavelength Optical Code Division Multiple Access (MW- OCDMA) code design based on Balanced Incomplete Block Designs (BIBD) is proposed for fiber optic communication. The proposed code has a weight of W = s × w × k, where s is the number of fibers (space) used per user, w is the number of wavelengths used per user and k is the number of ones in a block of BIBD. This code ensures a maximum cross-correlation of ‘1’ between any two users. The cardinality of the code family is higher by a factor of approximately ‘3’ when compared with BIBD codes of one-dimensional OCDMA with equivalent weight, length and cross-correlation. Keywords: Optical Code Division Multiple Access (OCDMA), Multi Wavelength Optical Code Division Multiple Access (MW- OCDMA), Balanced Incomplete Block Design (BIBD) I. I NTRODUCTION Fiber optic communication has been advancing rapidly in recent years. Technology in the form of Wavelength Divi- sion Multiplexing (WDM) efficiently utilizes the available bandwidth in an optical fiber. Dense Wavelength Division Multiplexing (DWDM) is the latest implementation in this fast advancing technology. However, there are issues in DWDM like four wave mixing [1][2] among others which are being pursued to optimize the technology. A. OCDMA OCDMA is the concept of assigning codes to each user in a fiber optic communication network. The user transmits the code whenever a ‘1’ is to be transmitted and does not transmit anything whenever a ‘0’ is to be transmitted. Initially, OCDMA has been viewed as a technology for fiber optic Local Area Networks (LAN) [3][4][5]. With advances in technology, OCDMA is competing with other technologies like WDM and DWDM. Practical experiments [6][7][8] are also being pursued. The major advantage of OCDMA is asynchronous communication, which considerably reduces optical resources required for timing recovery. Synchronous OCDMA [6][9] has also been reported, but the major advantage of OCDMA is lost. OCDMA may be viewed as a viable alternative to DWDM. Many different types of codes [10][11][12] for OCDMA have been proposed. Unlike CDMA which uses bipolar codes, OCDMA uses unipolar codes. Recently phase detection in the optical domain has been reported using a Super Structured Fiber Bragg Grating (SSFBG) [8] which enables the use of bipolar codes. The present design concentrates on unipolar codes. B. MW-OCDMA MW-OCDMA [13] efficiently utilizes the available band- width of optical fiber, in a manner similar to WDM. Codes for MW-OCDMA have to be two-dimensional (2D) to ac- commodate wavelength and time or three-dimensional (3D) to accommodate space, wavelength and time. 2D codes based on primes, Reed-Solomon Codes have been reported such as Temporal/ Spatial Addition Modulo L T (T/S AML) [14], where L T is the temporal length, Multiple Pulse per Row (MPR) [15], Wavelength - Time Spreading Codes [16] to name a few. A 3D design on Space/ Wavelength/ Time [17] based on primes has been reported. The present design is based on a novel algorithm having no cross-correlation among wave- lengths allocated to users having the same BIBD [18] code and Space allocation based on Steiner Triple Systems (STS). The present design can be used with any One-Dimensional (1D) Optical Orthogonal Code having ‘λ c = 1’. STS and Kirkman designs can also be used by choosing only those triples which give ‘λ c = 1’. C. BIBD BIBD is a very old tool of combinatorial theory, having a variety of applications in various fields including 1D OCDMA. The fundamental equations that govern a BIBD are: b × k = v × r and r × (k - 1) = λ × (v - 1) where; b is the number of blocks in a design - equivalent to number of codes in a family (cardinality), k is the number of elements in a block - equivalent to weight W of a code, v is the number of varieties - equivalent to the length (number of time chips) F of the code, r is the number of times each variety is replicated in the design, λ is the number of times each pair of elements occurs in the design - equivalent to cross-correlation (λ c ) of codes in a family. 1-4244-1152-1/07/$25.00 ©2007 IEEE.