Nonlinear Product Codes for Reliability and Security

Decoding of Z2S Linear Generalized Kerdock Codes

“…These results have led to an increased interest 16 in designing linear codes over finite rings. Several extensions of these codes to the Z 𝑝𝑆 17 (where 𝑝 is a prime and 𝑆 is a positive integer) were also developed [1,[8][9][10][11][12][13][14][15][16][17]. Solé [8] has 18 suggested in 1988 that 𝑝-adic cyclic codes should be investigated [9].…”

“…Generalized Kerdock 21 and Delsarte-Goethals codes over the ring Z 2𝑆 (an extension of Z4 linear Kerdock and 22 Delsarte-Goethals codes to Z 2𝑆 ) were introduced in [12]. Convolutional codes over rings 23 were discussed in [1,13,14], and LDPC codes over rings were investigated in [15][16][17].…”

“…Codes over rings were used in classical coding systems because of their rate properties [13][14][15], while in today's systems, they are considered for applications with great secrecy and reliability [16,17] requirements. On the other hand, modern codes over rings are being used to improve bandwidth efficiency [10] and to better combat phase noise [11,12] in modern wireless systems.…”

SISO Decoding of ℤ4 Linear Kerdock and Preparata Codes

“…Kerdock coded MC-CDMA system with non-linear amplifiers was presented in [18]. More recently, nonlinear codes are often used as components of product codes in order to achieve better reliability and security [19,20]. Codes over rings have also found application in coding for the phase noise channel [21] and network-coded bidirectional relaying systems [22].…”