Polar codes with a stepped boundary

We consider explicit polar constructions of blocklength $n\rightarrow\infty$ for the two extreme cases of code rates $R\rightarrow1$ and $R\rightarrow0.$ For code rates $R\rightarrow1,$ we design codes with complexity order of $n\log n$ in code construction, encoding, and decoding. These codes achieve the vanishing output bit error rates on the binary symmetric channels with any transition error probability $p\rightarrow 0$ and perform this task with a substantially smaller redundancy $(1-R)n$ than do other known high-rate codes, such as BCH codes or Reed-Muller (RM). We then extend our design to the low-rate codes that achieve the vanishing output error rates with the same complexity order of $n\log n$ and an asymptotically optimal code rate $R\rightarrow0$ for the case of $p\rightarrow1/2.$Comment: This article has been submitted to ISIT 201

Joint Sum Rate And Error Probability Optimization: Finite Blocklength Analysis

We study the tradeoff between the sum rate and the error probability in downlink of wireless networks. Using the recent results on the achievable rates of finite-length codewords, the problem is cast as a joint optimization of the network sum rate and the per-user error probability. Moreover, we develop an efficient algorithm based on the divide-and-conquer technique to simultaneously maximize the network sum rate and minimize the maximum users' error probability and to evaluate the effect of the codewords length on the system performance. The results show that, in delay-constrained scenarios, optimizing the per-user error probability plays a key role in achieving high throughput.Comment: Accepted for publication in IEEE Wireless Communications Letter