Low Complexity Encoding for Network Codes

In this paper we consider the per-node run-time complexity of network multicast codes. We show that the randomized algebraic network code design algorithms described extensively in the literature result in codes that on average require a number of operations that scales quadratically with the blocklength m of the codes. We then propose an alternative type of linear network code whose complexity scales linearly in m and still enjoys the attractive properties of random algebraic network codes. We also show that these codes are optimal in the sense that any rate-optimal linear network code must have at least a linear scaling in run-time complexity

Flexible and Low-Complexity Encoding and Decoding of Systematic Polar Codes

In this work, we present hardware and software implementations of flexible polar systematic encoders and decoders. The proposed implementations operate on polar codes of any length less than a maximum and of any rate. We describe the low-complexity, highly parallel, and flexible systematic-encoding algorithm that we use and prove its correctness. Our hardware implementation results show that the overhead of adding code rate and length flexibility is little, and the impact on operation latency minor compared to code-specific versions. Finally, the flexible software encoder and decoder implementations are also shown to be able to maintain high throughput and low latency.Comment: Submitted to IEEE Transactions on Communications, 201

Complexity Analysis Of Next-Generation VVC Encoding and Decoding

While the next generation video compression standard, Versatile Video Coding (VVC), provides a superior compression efficiency, its computational complexity dramatically increases. This paper thoroughly analyzes this complexity for both encoder and decoder of VVC Test Model 6, by quantifying the complexity break-down for each coding tool and measuring the complexity and memory requirements for VVC encoding/decoding. These extensive analyses are performed for six video sequences of 720p, 1080p, and 2160p, under Low-Delay (LD), Random-Access (RA), and All-Intra (AI) conditions (a total of 320 encoding/decoding). Results indicate that the VVC encoder and decoder are 5x and 1.5x more complex compared to HEVC in LD, and 31x and 1.8x in AI, respectively. Detailed analysis of coding tools reveals that in LD on average, motion estimation tools with 53%, transformation and quantization with 22%, and entropy coding with 7% dominate the encoding complexity. In decoding, loop filters with 30%, motion compensation with 20%, and entropy decoding with 16%, are the most complex modules. Moreover, the required memory bandwidth for VVC encoding/decoding are measured through memory profiling, which are 30x and 3x of HEVC. The reported results and insights are a guide for future research and implementations of energy-efficient VVC encoder/decoder.Comment: IEEE ICIP 202

The Encoding and Decoding Complexities of Entanglement-Assisted Quantum Stabilizer Codes

Quantum error-correcting codes are used to protect quantum information from decoherence. A raw state is mapped, by an encoding circuit, to a codeword so that the most likely quantum errors from a noisy quantum channel can be removed after a decoding process. A good encoding circuit should have some desired features, such as low depth, few gates, and so on. In this paper, we show how to practically implement an encoding circuit of gate complexity $O(n(n-k+c)/\log n)$ for an $[[n,k;c]]$ quantum stabilizer code with the help of $c$ pairs of maximally-entangled states. For the special case of an $[[n,k]]$ stabilizer code with $c=0$, the encoding complexity is $O(n(n-k)/\log n)$, which is previously known to be $O(n^2/\log n)$. For $c>0,$ this suggests that the benefits from shared entanglement come at an additional cost of encoding complexity. Finally we discuss decoding of entanglement-assisted quantum stabilizer codes and extend previously known computational hardness results on decoding quantum stabilizer codes.Comment: accepted by the 2019 IEEE International Symposium on Information Theory (ISIT2019

Real-time complexity constrained encoding

Complex software appliances can be deployed on hardware with limited available computational resources. This computational boundary puts an additional constraint on software applications. This can be an issue for real-time applications with a fixed time constraint such as low delay video encoding. In the context of High Efficiency Video Coding (HEVC), a limited number of publications have focused on controlling the complexity of an HEVC video encoder. In this paper, a technique is proposed to control complexity by deciding between 2Nx2N merge mode and full encoding, at different Coding Unit (CU) depths. The technique is demonstrated in two encoders. The results demonstrate fast convergence to a given complexity threshold, and a limited loss in rate-distortion performance (on average 2.84% Bjontegaard delta rate for 40% complexity reduction)

A Low Complexity Algorithm and Architecture for Systematic Encoding of Hermitian Codes

We present an algorithm for systematic encoding of Hermitian codes. For a Hermitian code defined over GF(q^2), the proposed algorithm achieves a run time complexity of O(q^2) and is suitable for VLSI implementation. The encoder architecture uses as main blocks q varying-rate Reed-Solomon encoders and achieves a space complexity of O(q^2) in terms of finite field multipliers and memory elements.Comment: 5 Pages, Accepted in IEEE International Symposium on Information Theory ISIT 200

Research on low complexity optimization for video encoding

制度:新 ; 報告番号:甲3424号 ; 学位の種類:博士(工学) ; 授与年月日:2011/9/15 ; 早大学位記番号:新574