Double Error Correcting Long Code

Abstract

ABSTRACT

Performance Analysis of a Novel Double Error Correcting Code for Image Transmission over UWB Channel

“…This code is very simple and easy to use. Its cyclic nature allows simple implementation of encoder and decoder using shift registers as explained in [12]. Near optimum performance of theoretical code can be achieved with this code using practically simple encoding and decoding procedure.…”

“…If a code can be constructed with the minimum distance of 2t+1 between two code words, then any number of errors per codeword which does not exceed t can be corrected. As per these rules in [12] we devised a binary double error correcting long code (8 2 5) with ¼ code rate, which corrects both the transmitted bits at the receiver achieving 100% data correction. The generator matrix of this code was devised using generator polynomial of GF (2 6 ) as follows [12] [19].…”

“…As per this theorem the code (8 2 5) corrects 2-bit errors at the receiver when two data bits are transmitted thus achieving 100% data correction, as long as the errors occur in less than or equal to two bits. The encoder/decoder circuits and the interesting properties of this code have been presented in our previous work [12]. Along with accuracy, the speed of data delivery can be improved by Hermite based pulse shape modulation techniques introduced in [7][8] [13][14] [15].…”

“…All these and many other codes assumed that the minimum dimension of the code (k) should be three. In [11] [12] we introduced a novel and simple binary long code (8 2 5) for double error correction where code length is '8', code dimension is '2' and minimum (Hamming) distance of the code is '5'. The code performance is directly proportional to the code length.…”

The A3D-TC: An Adaptive Approach for Selecting Third Component Parameters to Generate Robust Turbo Codes

“…Without escalating the power of a transmission the codes are used to boost available bandwidth, and to decrease the amount of power used to broadcast at a certain data rate [20]. On code performance, in knowing how closely practical codes can move toward the theoretical limits, the growth of turbo codes created a new interest [2]. Over a noisy channel, Shannon limit is the theoretical limit of maximum information transfer rate [20] Turbo codes performance is very close to the limits of reliable communication given by Shannon limit [5].…”