Channel Codes

Abstract

Channel coding lies at the heart of digital communication and data storage, and this detailed introduction describes the core theory as well as decoding algorithms, implementation details, and performance analyses. In this book, Professors Ryan and Lin provide clear information on modern channel codes, including turbo and low-density parity-check (LDPC) codes. They also present detailed coverage of BCH codes, Reed-Solomon codes, convolutional codes, finite geometry codes, and product codes, providing a one-stop resource for both classical and modern coding techniques. Assuming no prior knowledge in the field of channel coding, the opening chapters begin with basic theory to introduce newcomers to the subject. Later chapters then extend to advanced topics such as code ensemble performance analyses and algebraic code design. 250 varied and stimulating end-of-chapter problems are also included to test and enhance learning, making this an essential resource for students and practitioners alike.

Optimizing GNSS navigation data message decoding in urban environment

“…At the receiver end, the decoder uses a decoding algorithm in order to recover the transmitted useful bits. The channel decoding algorithms considered in this paper are based on soft inputs generally using Log-Likelihood Ratios (LLRs) based on A Posteriori Probability (APP) [2] [3]. Indeed, most of existing soft input channel decoding algorithms such as Viterbi decoding of trellis based codes, or message passing algorithms based on sub-optimal decoding algorithms like the Belief Propagation for the LDPC codes, or BCJR for turbo-codes, are using LLRs or related approximated expressions as soft inputs.…”

“…For binary random variables as inputs (which is the case in GNSS), the LLR [2] is defined as follows:…”

“…Motivated by the LLR mathematical expression assuming an urban propagation channel and perfect CSI (14), and according to [2], we are looking for a linear expression of the LLR expression considering an urban propagation channel without CSI. The idea is to find a method that can help to find the best linear approximation for an LLR soft input avoiding the complexity burden induced by some statistical knowledge at the receiver end.…”

“…The method proposed in [2] consists in determining the scaling coefficient that maximizes the mutual information between the transmitted symbol and the detector input which is a sufficient statistics:…”

“…When considering binary input memoryless channels as in our case, this expression can be easily expressed as a function of the pdf of the LLR at the input of the receiver [2]:…”