Walsh Codes, PN Sequences and Their Role in CDMA Technology Term Paper - EEL 201 Kunal Singhal, 2012CS10231 Student, CSE Department, IIT Delhi
1 Walsh Codes, PN Sequences and their role in CDMA Technology Term Paper - EEL 201 Kunal Singhal, 2012CS10231 Student, CSE Department, IIT Delhi 1 1 Abstract—Walsh codes are error correcting orthogonal codes H1 = 1 H2 = and PN sequences are deterministically generated sequences 1 −1 which appear to be random noises. Both of these concepts HN HN are used in error free communication. This paper outlines H2N = HN −HN properties of Walsh codes and PN sequences and discuss the For correctness, we see that, practical implementation in software and hardware. The paper T T T HN HN HN HN explores and model Walsh Codes and Hadamard matrices as a H2N H2N = T T finite orthogonal vector space. It further describe their role in HN −HN HN −HN T T T T communication technologies in particular CDMA. HN HN + HN HN HN HN − HN HN = T T T T Index Terms—Walsh code, Pseudo-Noise sequences, PN se- HN HN − HN HN HN HN + HN HN quence, generator matrix, recursion, hamming weight, hamming 2IN 0 distance, locally decodable, Hadamard matrices, linear codes, = = 2I2N 0 2IN pseudorandom sequences, shift registers, spreading spectrum technique, CDMA, Cryptographic Secure PN codes Walsh codes can be generated from Hadamard matrices of orders which are a power of 2. The rows of the matrix of order 2N constitutes the Walsh codes which encodes N I. INTRODUCTION bit sequences. Now, instead of 1 and -1 consider 1 and 0. ALSH codes are mutually orthogonal error correcting That is consider the matrix and the codes over the field F2 or W codes.
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