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Concept# Code rate

Summary

In telecommunication and information theory, the code rate (or information rate) of a forward error correction code is the proportion of the data-stream that is useful (non-redundant). That is, if the code rate is k/n for every k bits of useful information, the coder generates a total of n bits of data, of which n-k are redundant.
If R is the gross bit rate or data signalling rate (inclusive of redundant error coding), the net bit rate (the useful bit rate exclusive of error correction codes) is \leq R \cdot k/n.
For example: The code rate of a convolutional code will typically be , , , , , etc., corresponding to one redundant bit inserted after every single, second, third, etc., bit. The code rate of the octet oriented Reed Solomon block code denoted RS(204,188) is 188/204, meaning that 204 − 188 = 16 redundant octets (or bytes) are added to each block of 188 octets of useful information.
A few

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Alexios Konstantinos Balatsoukas Stimming, Andrea Bonetti, Andreas Peter Burg, Pascal Giard, Thomas Christoph Müller

Polar codes are a recently proposed class of block codes that provably achieve the capacity of various communication channels. They received a lot of attention as they can do so with low-complexity encoding and decoding algorithms, and they have an explicit construction. Their recent inclusion in a 5G communication standard will only spur more research. However, only a couple of ASICs featuring decoders for polar codes were fabricated, and none of them implements a list-based decoding algorithm. In this paper, we present ASIC measurement results for a fabricated 28 nm CMOS chip that implements two different decoders: the first decoder is tailored toward error-correction performance and flexibility. It supports any code rate as well as three different decoding algorithms: successive cancellation (SC), SC flip and SC list (SCL). The flexible decoder can also decode both non-systematic and systematic polar codes. The second decoder targets speed and energy efficiency. We present measurement results for the first silicon-proven SCL decoder, where its coded throughput is shown to be of 306.8 Mbps with a latency of 3.34 us and an energy per bit of 418.3 pJ/bit at a clock frequency of 721 MHz for a supply of 1.3 V. The energy per bit drops down to 178.1 pJ/bit with a more modest clock frequency of 308 MHz, lower throughput of 130.9 Mbps and a reduced supply voltage of 0.9 V. For the other two operating modes, the energy per bit is shown to be of approximately 95 pJ/bit. The less flexible high-throughput unrolled decoder can achieve a coded throughput of 9.2 Gbps and a latency of 628 ns for a measured energy per bit of 1.15 pJ/bit at 451 MHz.

2017Successive refinement is a technique to encode a source iteratively, improving the distortion at each step. If the code rates of all steps combined can be as efficient as coding only for the final distortion in one go, then the source is said to be successively refinable. We turn our attention to vector sources and we propose to replace the high-distortion first stage by a projection to low-dimensional space. The goal remains the same: code the original, high-dimensional source afterwards by only a small addendum. We look at Gaussian sources subject to an MSE criterion as a first step in this direction. A coding scheme for this problem is developed by turning the projection into an estimator of the source. It is shown that Gaussian vector sources coded via a projection can be successively refinable. We derive a parametric description of distortion pairs that can achieve this state; this region exists for any projection matrix, but its size may vary.

2014We propose a new class of efficient decoding algorithms for Reed-Muller (RM) codes over binary-input memoryless channels. The algorithms are based on projecting the code on its cosets, recursively decoding the projected codes (which are lower-order RM codes), and aggregating the reconstructions (e.g., using majority votes). We further provide extensions of the algorithms using list-decoding. We run our algorithm for AWGN channels and Binary Symmetric Channels at the short code length (

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