Error Probability Of Binary Codes Research Articles

Communication by Energy Modulation: The Additive Exponential Noise Channel

Communication across an additive exponential noise (AEN) channel is studied. The AEN channel is derived from a continuous-time Gaussian channel by assuming decoherence between the signal and noise components. Decoherence renders impossible the use of the complex amplitude and information is transmitted by modulating the signal energy. The AEN channel is shown to perform closely - in terms of channel, information rate, and error probability of binary codes, including the use of bit-interleaved coded modulation - to an equivalent discrete-time Gaussian channel of identical signal-to-noise ratio. Constellations are designed for low signal-to-noise ratios, where the minimum energy per bit is not universally attained by all modulations, and for high signal-to-noise ratios, where an equiprobable nonuniform constellation 0.76 dB away from capacity is described. The multiple-access AEN channel is also considered: its capacity region coincides with that of the Gaussian equivalent; feedback does not, however, enlarge the capacity region.

Gallager bounds on the performance of maximum‐likelihood decoded linear binary block codes in AWGN interference

AbstractPerformance evaluation of maximum‐likelihood (ML) soft‐decision‐decoded binary block codes is usually carried out using bounding techniques. Many tight upper bounds on the error probability of binary codes are based on the so‐called Gallager's first bounding technique (GFBT). In this method, Gallager bisects the error probability to the joint probability of error and noise residing in a region ℜ (here referred to as the Gallager region) plus joint probability of error and noise residing in the complement of ℜ (also referred to as regions of many and few errors, respectively); where ℜ is a volume around the transmitted codeword. In this tutorial review, a comprehensive study of a number of upper bounds on the error probability of ML decoding of binary codes based on GFBT is provided. For some bounds, their applicability to other schemes is also pointed out and argued. We also provide an overview of bounds based on Gallager's second bounding technique (GSBT) and discuss some of their relations and interconnections. Copyright © 2006 AEIT

Gallager first bounding technique for the performance evaluation of maximum-likelihood decoded linear binary block codes

Exact bit or frame error rate expressions for most communication systems are either too complex or unlikely to exist in nice closed forms. A good alternative is to bound the performance measure by tight enough lower and upper bounds. Many tight upper bounds on the error probability of binary codes are based on the so-called Gallager's first bounding technique (GFBT). In this method, Gallager splits the error probability to the joint probability of error and noise residing in a region $\Re$ (here referred to as the Gallager region) plus joint probability of error and noise residing in the complement of $\Re$ (also referred to as regions of many and few errors, respectively); where $\Re$ is a volume around the transmitted codeword. A comprehensive study of a number of upper bounds on the error probability of ML decoding of binary codes based on GFBT is provided. For some bounds, their applicability to other schemes and channels is also pointed out and argued.

A Union Bound on the Error Probability of Binary Codes Over Block-Fading Channels

Block-fading is a popular channel model that approximates the behavior of different wireless communication systems. In this paper, a union bound on the error probability of binary-coded systems over block-fading channels is proposed. The bound is based on uniform interleaving of the coded sequence prior to transmission over the channel. The distribution of error bits over the fading blocks is computed. For a specific distribution pattern, the pairwise error probability is derived. Block-fading channels modeled as Rician and Nakagami distributions are studied. We consider coherent receivers with perfect and imperfect channel side information (SI) as well as noncoherent receivers employing square-law combining. Throughout the paper, imperfect SI is obtained using pilot-aided estimation. A lower bound on the performance of iterative receivers that perform joint decoding and channel estimation is obtained assuming the receiver knows the correct data and uses them as pilots. From this, the tradeoff between channel diversity and channel estimation is investigated and the optimal channel memory is approximated analytically. Furthermore, the optimal energy allocation for pilot signals is found for different channel memory lengths.

A New Upper Bound on the ML DecodingError Probability of Linear Binary Block Codes in AWGN Interference

Performance evaluation of maximum-likelihood (ML) soft-decision-decoded binary block codes is usually carried out using bounding techniques. Many tight upper bounds on the error probability of binary codes are based on the so-called Gallager's first bounding technique (GFBT). The tangential sphere bound (TSB) of Poltyrev which has been believed for many years to offer the tightest bound developed for binary block codes is an example. Within the framework of the TSB and GFBT, we apply a new method referred to as the "added-hyper-plane" (AHP) technique, to the decomposition of the error probability. This results in a bound developed upon the application of two stages of the GFBT with two different Gallager regions culminating in a tightened upper bound beyond the TSB. The proposed bound is simple and only requires the spectrum of the binary code.